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Teacher: CORE Math Grade 4 Year: 2014-15 Course: Math Grade 4 Month: All Months

Lesson 1- Investigation 1

Standards Essential QuestionsAssessments Skills Content Lessons Resources2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

What property of addition allows you to add numbers in any order?

Which parts of an addition problem can be the missing numbers?

Fact Practice-Power Up A 8/31/2014

write a number sentence for a picture and given addends.

identify and use the Commutative Property of Addition and the Identify Property of Addition.

translate and solve "some and some more" problems using a formula.

find a missing addend in a number sentence.

decide if the answer to a word problem is reasonable.

addendadditionCommutative Property of AdditionformulaIdentity Property of Additionnumber sentencesum

Review of Addition

Zero is the identity element for addition.

When you add numbers those numbers are called the addends. The answer is their sum.

A formula describes how certain counts or measure are related to one another. Formulas are used in solving word problems.

Lesson 1 Power Up AUnit cubes*Stopwatch*Two-color counters* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

When you have a missing-addend problem, how do you write a number sentence for the problem?


find a missing addend in an equation with two or more addends.

equation

Missing Addends

A horizontal number sentence is an equation because it contains the symbol (=).

Lesson 2 Power Up AUnit cubes*Two-color counters*Graph paper*Markers *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.8.4.A-Use the concept of equality and concrete objects to demonstrate

What is another name for a sequence?

How do you find the rule for a counting sequence?

How are digits and numbers different?


find a rule for a counting sequence.

find missing numbers in a counting sequence.

state how many digits are in a number.

name the last digit of a number.

counting numbersdigitsequence

SequencesDigits

We order numbers by arranging them by size.Counting order means from least to greatest.

Lesson 3 Power UpUnit cubes*Two-color counters* *optional

understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.C-Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

Why can $1, $10, and $100 bills be used to show place value?

What place is farthest to the right in a whole or counting number?

Fact Practice-Power Up A

use manipulatives or diagrams to show the place value of hundreds, tens, and ones.

use money manipulatives or diagrams to compare two amounts of money.

identify the place value of a digit in a number.

use money amounts to represent place value.

place value

We can use money to show place value because our number system and our money system are both base-ten systems.

Lesson 4 Power Up ALesson Activities 2, 3, 4, and 10Lesson Activity 11*Base ten blocks*Money manipulativesTransparency of Lesson Activity 10* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas.

How are counting numbers and ordinal numbers different?

How is an ordinal number abbreviated?

How are ordinal and counting numbers used with the months of the year?


describe the position or order of an object in a line using ordinal numbers.

use ordinal numbers to describe the months of the year and the days of each month.

use numbers to write the month, day, and year of a specific date.

cardinal numbersordinal numbers

Ordinal NumbersMonths of the Year

To remember the term ordinal number both order and ordinal start with ord.

Lesson 5 Power Up ATwo-color counters* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.

How is subtraction different from addition?

What is a fact family?


subtract two numbers and then use addition to check the answer.

use addition and subtraction fact families to write addition and subtraction facts.

understand how to check subtraction problems.

differenceexpressionfact familysubtraction

Review of Subtraction

An expression can include any symbols except for an equal sign. An equation always has an equal sign.

Lesson 6 Power Up ALesson Activity 1Unit cubes*Two-color counters*Transparency of Lesson Activity 1 *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.

What do you need to remember when you write numbers in word form?


read and write whole numbers through 999 using words.

use words to write a

whole numbers

Writing Numbers Through 99

The names of two-digit numbers

Lesson 7 Power Up ABase ten blocks* *optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you decide which of two numbers is greater?

number shown by a pictorial model.

compare and order numbers up to 3 digits.

greater than twenty that do not end in zero, are written with a hyphen.

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

When we add money amounts with pencil and paper, in what place do we start/

Fact Practice-Power Up B

use money amounts to add two-digit numbers.

use money manipulatives to act out word problems.

Adding Money Lesson 8 Power Up BLesson Activities 2, 3, and 4Lesson Activity 11*Base ten blocks*Money manipulativesPlastic bags*Small envelopes*Transparency of Lesson Activity 6* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

When you use bills to model money problems, what do you do when you have ten or more ones?

What word do we use to mean 'exchanging 10 ones for 1 ten?'


use the addition algorithm to find the sum of two-digit numbers with regrouping.

use money manipulatives to add numbers that involve regrouping.

Adding with Regrouping

Carrying is like going to the bank to exchange smaller bills for larger bills.

Lesson 9 Power Up BMoney manipulatives*Base ten blocksTransparency of Lesson Activity 5* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

Do you have to memorize all the even numbers to know if a number is even? Explain.

Is the sum of two odd numbers even or odd? Explain.

Fact Practice-Power Up K

identify even and odd numbers.

describe and write even numbers.

describe and write odd numbers.

determine all the possible combinations for a given set of digits.

even numbersodd numbers

Even and Odd Numbers

The numbers we say when we start with 2 and then count up by twos are even numbers.

Lesson 10 Power Up KTwo-color counters* *optional

Power-Up Test 1 Cumulative Test Performance Task 1

Assessment

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).

Why do you put arrowheads on the end of a number line?

What are some real-life situations that could involve negative numbers on a number line?

identify lines and line segments.

name points on a number line.

draw number lines with a given scale.

comparison symbolequal togreater thanless thanlineline segmentnegative numbersnumber linepositive numbers

Investigation 1

Lesson Activity 13*RulersTransparency of Lesson Activity 13*Lined paper* *optional

2.9.4.C-Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a two-dimensional coordinate system a point represented by an ordered pair of whole numbers2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

use comparison symbols to compare positive and negative numbers.

tick mark

Number Lines

Lesson 11-Investigation 2 (continued in Oct.)

Standards Essential QuestionsAssessments Skills Content Lessons Resources2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

What formula do we use for a some, some more problem? part-part-whole problem?

How do you show a missing addend when you write the number sentence?


solve an addition word problem in which the total is given and an addend is missing.

write an equation to find a missing addend in an addition word problem.

justify if the answer to a word problem about combining is reasonable.

Addition Word Problems with Missing Addends

A part-part-whole problem differs from "some and some more" problems because part-part-whole problems are concerned with two or more parts of the whole or the whole itself.

Lesson 11 Power Up AUnit cubes*Two-color counters* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.

What are two ways to find the missing number in a subtraction problem?

What is a good way to check a subtraction problem with a missing number?


use the addition algorithm to find the missing number in a subtraction problem.

Missing Numbers in Subtraction

You can "subtract down" to find the bottom number and "add up" to find the top number in a subtraction problem.

Lesson 12 Power Up AUnit cubes*Money manipulatives*Two-color counters*Transparency of Lesson activity 22* *optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

When you use money manipulatives to model an addition problem, how many ones do you need to exchange for 1 ten?

How many tens do you need to exchange for 1 hundred?


use money amounts to represent addition of three-digit numbers with regrouping.

describe how to regroup bills using the fewest number of bills.

Adding Three-Digit Numbers Lesson 13 Power Up KLesson activities 2, 3, and 4Base ten blocks*Money manipulativesGrid paper (or lined paper)**optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.

In what order is subtracting carried out with two-digit numbers?

In what order is subtracting carried out with three-digit numbers?


use money manipulatives to subtract numbers.

use the addition algorithm to find the missing number.

Subtracting Two-Digit and Three-Digit NumbersMissing Two-Digit Addends

Lesson 14 Power Up KLesson Activities 8 and 9*Base ten blocks*Money manipulativesTransparencies of Lesson Activities 5 and 6* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word

When do you have to regroup in subtraction?


use money amounts to represent subtraction of two-digit numbers with

borrowingexchangingregrouping

Lesson 15 Power Up ALesson Activities 2, 3, and 4

problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

What do you trade when you regroup in subtraction?

What happens to the digit you borrow from?

regrouping. Subtracting Two-Digit Numbers with

Regrouping

Just as with addition, sometimes it is necessary to regroup when subtracting.

Base ten blocks*Money manipulatives *optional

Cumulative Test 2

Power-Up Test 2

Test-Day Activity 1

Assessment


How do you write numbers in expanded form?

What do you write in expanded form when there is a zero in the tens place?


use digits to write a number given in expanded form.

use the addition algorithm to find the missing number.

expanded form

Expanded FormMore on Missing Numbers in Subtraction

Numbers can be represented with digits and with words. Another form is to use expanded form. Expanded form is often helpful when doing mental math.

Lesson 16 Power Up KBase ten blocks


How is adding a column of two- and three-digit numbers like adding just two numbers? How is it different?


use the addition algorithm to add two- and three-digit numbers.

Adding Columns of Numbers with Regrouping

When the sum of the digits in the ones column is 20 or more, we move a group of two or more tens to the tens column.

Lesson 17 Power Up BLesson Activity 20*Base ten blocks* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What is a scale?

What are two different scales used for measuring temperature?


read temperature indicated on thermometers.

measure and record the temperature.

solve problems involving Fahrenheit scales and Celsius scales.

CelsiusdegreeFahrenheitscaleTemperature

A scale is a type of number line often used for measuring. Some examples: rulers, gauges, thermometers, and speedometers.

Lesson 18 Power Up KLesson Activity 14Lesson Activity 15*ThermometerItems with scales*Transparency of Lesson Activity 15**optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.C-Calculate elapsed time; use concept of elapsed time to determine start time/end time.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What do the two scales on a clock show?

What letters are used after the time to show that it is morning?

What is elapsed time?


tell time on an analog clock.

use a.m. and p.m. when stating the time of day.

solve elapsed-time problems.

a.m.digital formelapsed timemidnightnoonp.m.

Elapsed-Time Problems

Lesson 19 Power Up KLesson Activity 17Student clocks*Transparencies of Lesson Activities 16 and 17* *optional

The scale on a clock is actually two scales in one. One scale marks hours and is usually numbered. The other scale marks minutes and seconds and is usually not numbered.

2.2.4.A-Develop fluency in the use of basic facts for the four operations. How is an exact amount different from a rounded amount?

How is a number line helpful when rounding a number?


use a number line to round a number to the nearest ten.

round money amounts to the nearest dollar and to the nearest 25 cent.

multiplesround

Rounding

The word about is often but not always used to indicate a rounded amount.

Lesson 20 Power Up BLesson Activity 13*Store receipts*Transparency of Lesson Activity 13* *optional

Cumulative Test 3

Power-Up Test 3

Performance Task 2

Assessment

2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.D-Perform basic conversions within the same system to the unit immediately above or below the given unit.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

Which is longer, a meter or a yard?

How do you find the perimeter of a rectangle?

convert and compare measurements.

use measuring tools to estimate length and the perimeter of objects.

use a formula to determine the perimeter.

centimeterkilometermetermetric systemmillimeterperimeterU.S. Customary Systemyard

Units of Length and Perimeter

The abbreviation for inch is the only abbreviation for the customary units that has a period at the end.

Investigation 2

Lesson Activity 18*Meter stickRulersYardstickDollar billLong piece of stringTransparency of Lesson Activity 18*Masking tape* *optional

Lesson 21-Investigation 3

Standards Essential Questions Assessments Skills Content Lessons Resources2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.

How are squares different from other rectangles?

How are the radius and diameter of a circle related?


draw triangles and rectangles with given side measurements.

use a compass to draw circles with a given

centercirclecircumferencecompassdiameterequilateral triangle

Lesson 21 Power Up KSafety compassesCardboard*, foam board*Index cards*, paper plates*

radius.

determine the diameter of a circle.

radius

Triangles, Rectangles, Squares, and Circles

An equilateral triangle has equal side lengths.

Transparency of Lesson Activity 18* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

What does a fraction name?

What are the names for the numbers in a fractions?


use pictures to name fractions.

use money manipulatives to read, write, compare, and order decimals.

estimate and find the sum of money amounts.

use compatible numbers to estimate a sum.

compatible numbersdecimal pointdenominatorestimatefractionhalfnumeratorquarter

Naming FractionsAdding Dollars and Cents

Compatible numbers are two or more numbers that are relatively easy to work with. When we estimate, we are finding an approximate value.

Lesson 22 use pictures to name fractions.

use money manipulatives to read, write, compare, and order decimals.

estimate and find the sum of money amounts.

use compatible numbers to estimate a sum.

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.2.9.4.B-Identify and draw figures with one or more lines of symmetry.2.10..A-Identify right angles in geometric figures.

How are lines, line segments, and rays alike and different?

How do you know that two lines are parallel?

Are all intersecting lines perpendicular? Explain.


identify, draw, and describe lines, rays, and line segments.

identify and draw pairs of intersecting lines and segments that are perpendicular or oblique.

describe and draw angles as acute, obtuse, right, or straight.

acute angleangleendpoint(s)intersecting linesobtuse angleparallelperpendicularrayright anglevertex

Lines, Segments, Rays, and Angles

Two lines may intersect even if the drawings that represent them do not cross.

Lesson 23 Power Up KBrass fasteners*Construction paper*Index cards, sticky notes* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

How do you know when you have found the easiest form of the equation to solve?

How does writing the fact family for an equation help in solving that equation?


use inverse operations to find missing addends.

use inverse operations to find missing numbers in subtraction problems.

inverse operations

Inverse Operations

The mathematical terms for opposite operations is inverse operations.

Lesson 24 Power Up BBase ten blocks*Two-color counters* *optional

2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations. 2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

Which of the three numbers in a 'some went away' problem can be missing?


write an equation to find a missing number in subtraction word problems.

Subtraction Word Problems

A "some and some more" problem uses an addition formula.

A "some went away" uses a subtraction formula.

Lesson 25 Power Up BBase ten blocks* *optional

Cumulative Test 4

Power-Up Test 4

Test-Day Activity 2

Cumulative Assessment

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you shade two thirds of a rectangle?

Why do you have to be careful to make equal parts when drawing a figure to show a fraction?


draw and shade pictures of fractions representing halves, thirds, and fourths.

Drawing Pictures of Fractions

It is easier to understand fractions if you learn to draw pictures that represent fractions.

Lesson 26 Power Up BSafety compasses*Colored pencils*Grid paper* *optional

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.C-Calculate elapsed time; use concept of elapsed time to determine start time/end time.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.2.4.4.A-Use models, number facts, and properties to make conjectures,

How do you change an addition problem to a multiplication problem?

What are two ways to find the end time when you know the starting time and the elapsed time?


use multiplication to show repeated addition.

count forward or backward on a clock to solve elapsed-time problems.

multiplication

Multiplication as Repeated AdditionMore Elapsed-Time Problems

The multiplication sign means “groups of”.

Lesson 27 Power Up BLesson Activity 17Lesson Activity 16*Classroom clock*Student clocks* *optional

draw conclusions and explain reasons for conclusions.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas. 2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

How are the Identity Property of Addition and the Identity Property of Multiplication alike? How are they different?


use a multiplication table to find the product of two factors.

identify and use the Commutative Property, Property of Zero, and Identity Property of Multiplication.

Commutative Property of MultiplicationfactorIdentity Property of Multiplicationmultiplication tableproductProperty of Zero for Multiplication

Multiplication Table

Each of the two numbers multiplied is called a factor. The answer to a multiplication problem is called the product. Commutative Property of Multiplication changing the order of the factors does not change the product. Property of Zero for Multiplication-the product of zero and any number is zero. The Identity Property of One-the product of 1 and any other factor is the other factor.

Lesson 28 Power Up aColor tiles*Transparency of Lesson Activity 19**optional

2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.

How can you decide if a number is divisible by 2? By 5?


use the multiplication facts (0s, 1s, 2s, 5s).

Multiplication Facts: 0s, 1s, 2s, 5s

The three numbers that make up a multiplication fact form a multiplication and division fact family. The numbers can be arranged to form two multiplication facts and two division facts.

The numbers in a multiplication fact involving zero can be used to form only three facts.


2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.

How do you know when you need to regroup in a subtraction problem?


find the difference between three-digit numbers with regrouping.

subtract dollars and cents with regrouping.

use money manipulatives

Subtracting Three-Digit Numbers with Regrouping

Two-digit subtraction with regrouping is different than two-digit subtraction without regrouping. You need to trade to

Lesson 30 Power Up BLesson Activities 2, 8, and 9Base ten blocks*Money manipulativesTransparency of Lesson Activity6*

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).

to compare, order, and model subtraction. get 10 more if the bottom number

cannot be subtracted from the top number.

*optional

Cumulative Test 5

Power-Up Test 5

Performance Task 3


2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

How is finding the number of objects in an array similar to finding the area of a rectangle?

How are square numbers and square roots related?

write a multiplication problem illustrated by an array.

draw an array to model a multiplication problem.

calculate the area of a rectangle.

use an area model to find the square root of perfect squares.

areaarraysquaresquare centimetersquare inchsquare numbersquare root

Multiplication ProblemsAreaSquares and Square Roots

Rows are horizontal and columns are vertical.

The area of a shape is labeled using square units.

A number is a square number if you can make a square using the number of tiles.

Investigation 3 Lesson Activities 20 and 21Color tiles*RulersCrayons*Grid and plain paper* *optional

Lesson 31-Investigation 4B (continued in Nov.)

Standards Essential Questions Assessments Skills Content Lessons Resources2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade

What does it mean to find the difference of two numbers?

What formula is used to


write an equation for word problems.

solve comparing word problems.

use a number line to subtract whole numbers.

Word Problems About Comparing

“Larger-smaller-difference” word problems can be phrased in different ways. They can use phrases like “how many more,” “how many fewer,” “how much less,” and “how much greater.”


appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.C-Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.2.9.4.C-Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a two-dimensional coordinate system a point represented by an ordered pair of whole numbers

find how much greater or how much less one number is than another number?

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

What strategies can you use to remember the multiplying by 11 facts?


use the multiplication facts (9s, 10s, 11s, 12s).

use patterns o remember the 10s multiples.

Multiplication Facts: 9s, 10s, 11s, 12s

Students can use the “number trick” to learn the multiplying by 9 facts.

Lesson 32 Power Up BLesson Activities19 and 20* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

How are ten thousands different from thousands?

Fact Practice-Power Up C

use words and digits to name numbers through hundreds thousands.

compare and order numbers through hundred thousands.

use expanded form to write numbers through hundred thousands.

Writing numbers through hundred thousands

In this math book, commas will not be used in four-digit numbers.

The base-ten system, as we know it today, originated in India.

Lesson 33 Power Up CLesson Activity 20*Digit cards*Grid paper *optional


How many commas will be used to write 25 million in digits?


use words and digits to name numbers through hundred millions.

read, compare, and order numbers through hundred numbers.

use expanded form to

Writing numbers through hundred millions

A comma in a number is a clue to write or say a group name, such as thousand, million, and so on. Each group of three digits between commas is written or

Lesson 34 Power Up ALesson Activity 11*Newspaper or magazine headlines* *optional

write numbers through hundred millions. read as a three-digit number.

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

What is a mixed number?


use words to write mixed numbers.

represent mixed numbers by drawing pictorial models.

mixed numbers

Naming Mixed Numbers and Money

Mixed numbers can also be expressed as improper fractions. An improper fraction is a fraction with a numerator greater than or equal to the denominator.

Lesson 35 Power Up CLesson Activity 12Lesson Activities 19 and 20*Fraction circles and overhead fraction circles*Safety compasses*Transparency of Lesson Activity12*Rulers*Circle models and index cards* *optional

Cumulative Test 6 Power-Up Test 6 Test-Day Activity 3


2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

What fraction of a dollar is a penny?

What does the term one quarter mean?


name the fraction of a dollar that is shown in a diagram.

compare fractions of a dollar.

find all possible combinations of four coins.

combinations

Fractions of a Dollar

Each of 6 coin pairs is called a combination.

Lesson 36 Power Up CMoney manipulatives* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.C-Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a two-dimensional coordinate system a point represented by an ordered pair of whole numbers2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How many fourths are between 5 and 6?

Fact Practice-Power Up D

use a number line to locate and name mixed numbers.

Reading fractions and mixed numbers from a number line

Number lines can be used to show equivalent fractions.

Lesson 37 Power Up DFraction manipulatives*Transparency of Lesson Activity 13* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.C-Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically.

How many of the 100 facts from 0x0 through 9x9 are memory-group facts?


identify and memorize the memory group of multiplication facts.

Multiplication Facts (Memory Group)

3x4=12, 3x6=18, 3x7=21, 3x8=24, 4x6=24, 4x7=28, 4x8=32, 6x7=42, 6x8=48, and 7x8=56 are called memory group facts.

Lesson 38 Power Up DPower Up FLesson Activity 20*Base ten blocks*Grid paperTransparency of Lesson Activity 19* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What marks divide half-inch segments into two parts?

Fact Practice-Power Up E

identify fourths using a ruler or inch scale.

estimate the length and width of concrete objects.

Reading an inch scale to the nearest fourth

Measurements are often described using the words accurate and precise. Accuracy refers to how close a measurement is to the actual or accepted value. Precision refers to how close the results are when the same thing is measured several times.

Lesson 39 Power Up ELesson Activity 18*RulersStrips of tag board (6 inches long by 1 inch wide)Transparency of Lesson Activity 18*Yardsticks, meter sticks* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.D-Perform basic conversions within the same system to the unit immediately above or below the given unit.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What are some units of capacity in the U.S. Customary System?


convert between units of liquid measure in the U.S. Customary System and in the metric system.

compare units of liquid measure in the U.S. Customary and metric systems.

estimate and measure containers of liquid.

capacityfluid ounceliter

Capacity

Teaspoons and tablespoons are U.S. customary units of measure for smaller amounts.

Lesson 40 Power Up DBalance scale with weights*RulersCup, pint, quart, 1/2 gallon, and gallon containersDropper used for liquid medicine, funnel*Liter of 2-liter container, water *optional

Cumulative Test 7 Power-Up Test 7 Performance Task 4


2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole

What are the first places to the right and the left of the decimal point in a number?

use money manipulatives to model amounts of money.

name decimal numbers through hundredths using pictorial models.

base-ten systemdecimal placehundredthtenth

Tenths and hundredths

Investigation 4A

Lesson Activities 2, 3, 4, 8, and 9Lesson Activity 10*Money manipulativesTransparency of

number.

When people speak of money denominations, they mean the faces values of coins and bills.

Lesson Activity 22**optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

If 25 out of 100 squares are shaded, what decimal number and fraction represent the shaded part?

use unit squares to relate fraction to decimal numbers.

read decimal numbers aloud.

use a stopwatch to generate decimal numbers.

Relating fractions and decimals

Adding zeros to the end of a decimal number does not affect the value of the number because it does not change the place values of the non-zero digits.

Investigation 4B

Lesson Activity 23Lesson Activity 22*Money manipulatives*Rulers*StopwatchesLocking plastic bags*Plain paper* *optional

Lesson 41-Investigation 5 (continued in Dec.)

Standards Essential Questions Assessments Skills Content Lessons Resources

2.1.4. D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4. F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

If you know the product and one factor, how can you find the missing factor?


use the subtraction algorithm to find the difference between three-digit numbers with regrouping.

solve comparing word problems.

find the missing factor of a multiplication problem.

Subtracting Across zeroMissing Factors

When you are subtracting and the top number has a zero as one of its digits you will need to regroup more than once or regroup two or more places at one time.

Lesson 41 Power Up EMoney manipulatives*Base ten blocks* *optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.

Does the product of a one-digit number and a multiple of 10 always have one zero? Explain.


find the product of a number and multiples of ten, and multiples of one hundred.

round numbers to the nearest ten and hundred using a number line.

estimate solutions to multiplication word problems using rounding.

Rounding Numbers to Estimate

It is not always convenient to draw a number line to round a number. It is helpful to circle or underline the digit you need to look at when deciding whether to round a number up or down.

Lesson 42 Power Up ELesson Activity 20*Grid paperIndex cards*String, tape*Transparency of Lesson Activity 13* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

How do you write 5¢ with a dollar sign and a decimal point?


add and subtract money amounts written with a dollar sign.

compare decimal numbers.

Adding and Subtracting Decimal Numbers, Part 1

One method of subtracting money amounts involves “adding up” from the second amount to the first.

Lesson 43 Power Up ELesson Activity 24Lesson Activity 22*Rulers*Transparency of Lesson Activity 22* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What are two methods you can use to multiply?

Fact Practice-Power Up F 11/19/2014

use the multiplication algorithm to multiply a two-digit number by a one-digit number.

use multiplication to find area.

Multiplying Two-digit Numbers, Part 1

The Distributive Property says that we can multiply a number by a sum by multiplying the number by each addend and then adding the two products.

Lesson 44

Power Up FBase ten blocks* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.2.9.4.B-Identify and draw figures with one or more lines of symmetry.2.9.4.C-Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a two-dimensional coordinate system a point represented by an ordered pair of whole numbers

What property of addition makes both sides of the equation equal?

How are the Associative Property of Addition and the Associative Property of Multiplication

Fact Practice-Power Up E 11/22/2014

use the Associative Property to solve problems involving parentheses.

name line segments using two points on a line.

use symbols to identify line segments.

identify parallel and perpendicular segments in two- and three-dimensional figures.

Associative Property of AdditionAssociative Property of Multiplicationorder of operationsparentheses

Parentheses and the Associative PropertyNaming Lines and Segments

Parentheses are used to tell which group of numbers needs to be evaluated first when working with a complicated expression.

Lesson 45

Power Up EBase ten blocks, color tiles* *optional

alike? Cumulative Test

8 11/23/2014

Power-Up Test 8 11/23/2014

Test-Day Activity 4 11/23/2014


2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.C-Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

How do the factors and product of a multiplication problem change to make a division problem?


use multiplication to divide.

use the division algorithm to find a missing factor.

identify division facts using a multiplication table.

division

Relating Multiplication and division, Part 1

Multiplication and division are inverse operations. One operation undoes the other.

Lesson 46

Power Up FLesson Activity 19*Color tiles*Two-color counters*Grid paper*Transparency of Lesson Activity 19* *optional

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.C-Recognize, describe, extend, create, replicate, and make generalizations for a variety of patterns, sequences, and relationships verbally and numerically.

What are three symbols that are used to show division?


write fact families for multiplication and division.

show division three different ways.

use the multiplication algorithm to solve multiplication word problems.

Relating Multiplication and Division, Part 2

When both addends in an addition problem are the same, only one addition fact and one subtraction fact can be formed with the set of numbers. When both factors in a multiplication and division fact family are the same; only one multiplication fact and one division fact can be formed.

Lesson 47

Power Up FTwo-color counters*Transparency of Lesson Activity 1* *optional

2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.

How is multiplying amounts of money similar to multiplying whole


use the multiplication algorithm to multiply a two-digit number by a one-digit number.

estimate solutions to

Multiply Two-digit Numbers, Part 2

In an addition problem the sum for a column had to be regrouped when it has more than one digit. When the product in a place has more than one

Lesson 48

Power Up FLesson Activities 2 and 3*Base ten blocks*Money manipulatives

2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.

numbers? How is it different?

multiplication problems using rounding.

use money manipulatives to demonstrate multiplication.

digit, it must also be regrouped. *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

What operations are used to solve equal groups problems?

Fact Practice-Power Up G 12/2/2014

write an equation to solve word problems about equal groups.

use compatible numbers to estimate solutions to multiplication problems.

Word Problems About Equal Groups, Part 1

Equal groups word problems can be solved by using a multiplication formula.Array: number of columns x number of rows = totalArea: length x width = area

Lesson 49

Power Up GTwo-color counters* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

What are the names of the first two places after the decimal point in a number?

Fact Practice-Power Up G 12/3/2014 add, subtract, and

compare decimal numbers through hundredths.

relate fractions to decimals that name tenths and hundredths.

Adding and Subtracting Decimal Numbers, Part 2

The value of the places to the left of the ones place increases(x10) but the value to the right of the ones place decreases (÷ 10).

Lesson 50

Power Up GLesson Activity 25Lesson Activities 20 and 22*Money manipulatives*Grid paper* *optional

Cumulative Test 9 12/7/2014



2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.D-Apply place value concepts and base-ten numeration to order and

What percent of a dollar is a dime?

When have you seen or heard

name percent of a dollar.

identify percent of a whole.

compare and relate

PercentThere are two ways to change a decimal to a percent:-write the decimal as a fraction with a denominator of 100. The numerator is the percent.-move the decimal point two places to the right. This is the same as multiplying

Investigation 5

Lesson Activity 26Lesson Activity 22Transparency of Lesson Activity 22* *optional

compare larger whole numbers. percent being used?

decimals to fractions and percent that name tenths and hundredths.

the decimal by 100.


Standards Essential QuestionsAssessmentsSkills Content Lessons Resources


How can you check a division answer?

Fact Practice-Power Up H 12/8/2014

use the addition algorithm to solve problems with three or more digit addends.

use multiplication to check a one-digit division answer.

Adding Numbers with More Than Three DigitsChecking One-Digit Division

In a division problem, the number being divided is called the dividend, the number doing the dividing is called the divisor, and the result is called the quotient.

Lesson 51

Power Up HColor tiles*Two-color counters* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

How do you subtract numbers with more than three digits?


use the subtraction algorithm to solve problems with three or more digits.

write an equation to solve word problem about equal groups where the total is known.

Subtracting Numbers with More Than Three DigitsWord Problems About Equal Groups, Part 2

Subtracting numbers with more than three digits is not very different from subtracting numbers with two digits.

Lesson 52

Power Up HTwo-color counters* *optional

2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

When you are making an estimate for a division problem and do not want to have a remainder, what kind of number do you look for?

Fact Practice-Power Up I 12/10/2014

solve division problems with a remainder.

solve division problems using manipulatives.

use rounding to estimate solutions to division problems.

remainder

One-Digit Division with a Remainder

The remainder in a division problem can be represented as one of the following:-remainder as a whole number-remainder as a decimal-remainder as a fraction-remainder rounded up

Lesson 53

Power Up IColor tiles*Two-color counters* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.

Which months have exactly 30 days?


identify the relationship between days, months, years, decades, and centuries.

solve elapsed-time problems involving dates.

use a number line

centurychronological ordercommon yeardecadeleap year

The CalendarRounding Numbers to the Nearest Thousand

The Gregorian calendar is the calendar used by most of the

Lesson 54

Power Up ICalendars, poster or bulletin board*Transparency of Lesson Activity 13* *optional

to round numbers to the nearest thousand.

world. We have a leap year every seven years.

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas.

Why is 2 the only even prime number?


identify multiples and factors of a given number.

draw arrays and area models to represent the factors of a given number.

distinguish between prime and composite numbers.

composite numbersdivisibleprime numbers

Prime and Composite Numbers

Counting numbers that have exactly two different factors are prime numbers.

A number with more than two facts is a composite number. The number 1 is neither prime nor composite.

Lesson 55

Power Up ILesson Activities 20 and 21*Color tilesTwo-color countersGrid paperTransparency of Lesson Activity 19* *optional





2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

Why do you need to draw congruent figures when you shade drawings to compare fractions?


compare and order fractions with different denominators using pictorial models and manipulatives.

congruent

Using Models and Pictures to Compare Fractions

A unit fraction is a fraction with a numerator of 1. When comparing two unlike fractions, the fraction with the smaller denominator is greater in value.

Lesson 56

Power Up ILesson Activities 37, 38, and 39Fraction circles*Fraction manipulativesFraction bars* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.C-Calculate elapsed time; use concept of elapsed time to determine start time/end time.2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.

What does the word per mean?

What strategy can be used to solve rate problems?

Fact Practice-Power Up J 12/17/2014

solve a word problem involving rate.

find a pattern or make a table to solve multiplication problems.

write an equation to solve rate problems.

rate

Rate Word Problems

A unit rate tells how much of one measure there is per 1 unit of the other measure. One common type of unit rate is a unit price.

Lesson 57

Power Up JRulers*Two-color counters* *optional

2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data. 2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

What happens when the product for a place value is a two-digit number?


multiply a three-digit number, decimals, and money by a one-digit number.

write an equation to solve multiplication problems.

create a table to find a pattern.

Multiplying Three-Digit Numbers

You can multiply a three-digit number by a one-digit number by writing the three-digit number in expanded form, multiplying the one-digit number by each addend, and then adding the three results.

Lesson 58

Power Up JBase ten bocks* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

How can you tell whether an estimate will be greater than or less than the actual value?


determine if an estimated answer is more than, equal to, or less than the actual answer.

use rounding to estimate solutions to problems involving money amounts.

estimate answers to problems using rounding.

evaluate the reasonableness of a solution.

Estimating Arithmetic Answers

You can estimate arithmetic answers by rounding the numbers before doing the arithmetic. Estimating does not give you the exact answer but it can give you an answer that is close to the exact answer. Estimating is a way to decide if an exact answer is reasonable.

Lesson 59

Power Up JRulersSafety compasses*Grid paper. index cards* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.

Why is the same formula used for both kinds of rate problems-those with a missing total and those with a known total?


find either the rate or the time in a rate problem.

write and solve equations for a rate word problems.

Rate Problems with a Given Total

Rate problems involving time consist of three quantities: a rate, an amount of time, and a total. If you know two of the quantities, you can find the third.

Lesson 60

Power Up JTwo-color counters* *optional



Performance Task 6 12/23/2014

2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.6.4.A-Gather data from surveys and observations within the classroom or homes.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.6.4.E-Determine the reasonableness of a statement based on a comparison to data displayed in a graph.2.7.4.D-List or graph the possible results of an experiment.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

What are 4 kinds of graphs that can be used to display data?

display and interpret data using a pictograph, bar graph, line graph, and circle graph.

describe the relationship between sets of data.

bar graphcircle graphgraphkeylegendline graphpictograph

Displaying Data Using Graphs

Line graphs are often used to show information or data that change over time.A circle graph shows how a whole is divided into parts.

Investigation 6

Lesson Activities 27 and 28Newspapers and magazines*Transparencies of Lesson Activities 27 and 28* *optional

Lesson 61- Investigation 7

Standards Essential QuestionsAssessments Skills Content Lessons Resources

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

If you remove one fraction of a whole, how do you find the remaining fraction?


find the fraction of a whole when the size of the other portion is given.

solve two-step problems with a missing factor.

verify the solution to a problem.

Remaining FractionTwo-Step Equations

If more than one step is needed to solve an equation students will practice simplifying the equation by performing arithmetic that does not involve the variable.

Lesson 61 Power Up IFraction manipulatives* *optional

2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data. 2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.4.4.B-Recognize and use precise language to describe connections between mathematical ideas.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

What is an exponent?

What is a formula for the area of a square?


multiply three or more factors.

read exponents.

write a power as a whole number and exponent.

evaluate an exponential expression for a given value.

represent the area of a square as an exponential expression.

baseexponent

Multiplying Three or More FactorsExponents

Exponents greater than three are read "to the nth power." There are two steps to simplify expressions:-simplify the numbers with exponents.-perform the operation of addition.

Lesson 62 Power Up IDot cubes* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.2.10..A-Identify right angles in geometric figures.

What is a polygon?

What is a regular polygon?


classify polygons by the number of their sides.

draw different kinds of polygons.

identify a figure's vertices, angles, and edges.

decagonhexagonoctagonpentagonpolygonquadrilateralregular polygontriangle

Polygons

A polygon may be convex or concave. In a convex polygon, all the angles are smaller than a straight angle. In a concave polygon, one angle is larger than a straight angle. A concave polygon appears to have a dent.

Lesson 63 Power Up JSafety compasses*Spinners*Circular objects*Grid paper* *optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

What does divisible mean?

Why do we write the first digit of the quotient in the tens place?


write an equation to solve "equal groups" word problems with two-digit answers.

determine whether a number is divisible by 3.

Division with Two-Digit Answers, Part 1

If there is no remainder when a number is divided by another, we say that the first number is divisible by the second number.

Lesson 64 Power Up JBase ten blocks* *optional


What are the names of the parts of a division problem?

How are the three parts of a division problem related?


identify the divisor, dividend, and quotient in a division problem.

divide a three-digit number by a one-digit number.

determine whether a number is divisible by 9.

use rounding to estimate solutions to division problems.

dividenddivisionquotient

Division with Two-Digit Answers, Part 2

Lesson 65 Power Up JTwo-color counters*Place-value work mats* *optional





2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.

When are two figures similar?

When are two figures congruent?


identify and draw congruent figures.

identify similar figures.

demonstrate transformations to determine if two figures are congruent.

similar

Similar and Congruent Figures

Figures that are the same shape are similar. Figures that are the same shape and the same size are congruent.

Lesson 66 Power Up JLesson Activity 29Geoboards and geobands*Dot paper* *optional

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.8.4.A-Use the concept of equality and concrete objects to demonstrate understanding of commutative, associative, and identity properties.

What is a multiple of 10? Name some examples.


multiply by multiples of 10.

multiply dollars and cents by a two-digit number.

Multiplying by Multiples of 10

Regrouping factors using the Associative Property of Multiplication by regrouping the factors in a problem allows you to create a form of the problem that can be solved with mental math.

Lesson 67 Power Up ILesson Activity 20*Base ten blocks* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.

What are the four steps in the pencil-and-paper method for dividing?

How many times are the steps repeated?


solve division problems with two-digit answers and a remainder.

find reasonable estimates of a quotient.

Division with Two-Digit Answers and a Remainder

Students should become familiar with the steps to division: divide, multiply, subtract, bring down.

Lesson 68 Power Up ILesson Activity 20*Two-color counters*Grid paper*Place-value work mats* *optional

How is a division answer with a remainder checked?


How many millimeters is 1 centimeter?

How many centimeters is 46 millimeters?


relate millimeters to centimeters using a pictorial model.

convert centimeters to millimeters using fractions and decimals.

use the appropriate metric unit to measure the length of objects.

Millimeters

Milli-means thousandthCenti-means hundredthDeci-means tenthDeca-means tenHecto-means hundredKilo-means thousand

Lesson 69 Power Up IRulersTransparent ruler* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you draw a diagram to represent a problem about 1/4 of a group of 40?


use a fraction to find a portion of a group.

draw a picture to represent fractions of a group.

Word Problems About a Fraction of a Group

The phrase one half often indicates division by 2.

We can use fractions to name part of a whole, part of a group or number, and part of a distance.

Lesson 70 Power Up ILesson Activity 21*Rulers*Two-color counters* *optional





2.6.4.A-Gather data from surveys and observations within the classroom or homes.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.C-Describe and calculate the mean and use this quantity to describe the data.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.6.4.E-Determine the reasonableness of a statement based on a comparison to data displayed in a graph.

What is a survey?

interpret data from a survey.

represent information on a tally sheet.

analyze data from a survey and validate conclusions.

conduct a survey to collect

biasdatapopulationsamplesurveytally mark

Collecting Data with Surveys

A poll is sometimes

Investigation 7

Lesson Activity 27*Thermometers*optional

data and display the results in a graph.

used to refer to a survey.

Lesson 71-Investigation 8 (continued from Jan.)

Standards Essential Questions AssessmentsSkills Content LessonsResources


What are the four steps used to divide?

How often do you repeat the four steps as you divide?


solve problems to find a quotient ending in zero.

use compatible numbers to estimate solutions to division problems.

Division Answers Ending with Zero

The only digits in a dividend that do not always have a digit above them are the digits at the beginning of the dividend.

It is not possible to divide a number by 0.

Lesson 71

Power Up HLesson Activities 20 and 21*RulersTwo-color counters*Grid paper (centimeter and inch)*Place-value work mats* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.

What do you need to know to choose the information required to solve a problem?


analyze a problem and choose the information needed to solve a problem.

Finding Information to Solve Problems

A permutation is an arrangement of objects in a particular order.

Sometimes problems contain too much information. It is important to look for the necessary information needed to solve the problem.

Lesson 72

Power Up H

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.

What is a geometric transformation? Name 3 of them.


describe transformation of a figure.

use translations, reflections, and rotations to change the position of a figure in quadrant I of the coordinate plane.

name the transformations that could be used to prove that two figures are congruent.

use classroom objects to act out transformations.

geometryorientationreflectionrotationtransformationtranslation

Geometric Transformations

The word geometry comes from the ancient Greeks. Geo comes from the Greek "geo" meaning earth and the second part "metry" comes from the Greek word "metron" meaning a measure.

To determine whether two triangles are congruent, you can try to find a combination of slides, flips, and turns that moves one triangle so that it matches exactly with the other.

Lesson 73

Power Up HMirror*RulersConstruction paper*Index cards*Scissors* *optional

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.

What fraction of the letters in the alphabet are vowels? Consonants?


find fractions of a set. Fraction of a Set

There can be more than one fraction name for a part of a set.

Lesson 74


2.2.4.A-Develop fluency in the use of basic facts for the four operations. 2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

What unit is used to measure turns or rotations?

How many degrees are in a full turn?


describe the amount and the direction of a turn.

demonstrate a rotation for a specific number of degrees.

determine congruence using turns.

clockwisecounterclockwisedegreefull turnhalf turnquarter turn

Measuring Turns

Lesson 75

Power Up HLesson Activity 29*Protractors*Chalk*Scissors *optional




2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.

When do you stop repeating the four steps of the division process?

When dollars and cents are divided, where is the decimal point placed in the answer?


solve division problems with three-digit answers and money.

use compatible numbers to estimate a quotient.

Division with Three-Digit Answers

To divide dollars and cents by a whole number, divide the digits just like you divide whole numbers. The decimal point in the answer is placed directly above the decimal point inside the division box.

Lesson 76

Power Up GTwo-color counters*Place-value work mats* *optional


How can a weight in ounces be converted to a weight in pounds?


distinguish between mass and weight.

estimate the weight of an object using customary units.

estimate an object's mass using metric units.

massouncepoundtonweight

Mass and Weight

The mass of an object shows how much matter an object has. Weight is the measure of the force of gravity on that object.

Lesson 77

Power Up GLesson Activity 30Balance scale with weights#2 pencilsBathroom scale and food scale*Record sheets* *optional


Can any three segments form a triangle? Why or why not?


classify triangles by their angles and side measurements.

describe triangles as acute, obtuse, right, equilateral, isosceles, or scalene.

determine congruence of

acute triangleequiangularisoscelesobtuse triangleright trianglescalene

Classifying Triangles

Lesson 78

Power Up GLesson Activity 31RulersGrid paper and index cards*Scissors *optional

triangles using transformations. If two triangles are congruent, they have congruence.

A scalene triangle may be acute, right, or obtuse. An isosceles triangle may be acute, right, or obtuse. An equilateral triangle cannot be right or obtuse.

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.9.4.B-Identify and draw figures with one or more lines of symmetry.

Which capital letters in the alphabet are symmetrical?


locate a line of symmetry for a figure.

distinguish between rotational symmetry and reflective symmetry.

identify figures with rotational symmetry.

line of symmetryreflective symmetryrotational symmetrysymmetry

Symmetry

About half of the uppercase letters in the alphabet have lines of symmetry.

A rectangle has two lines of symmetry.

An isosceles triangle has one line of symmetry.

Lesson 79

Power Up GLesson Activity 32MirrorsConstruction paper*Scissors**optional


How many times are the four steps in the division process repeated?


solve division problems with zeros in three-digit answers.

draw a diagram to represent the four steps of division.

Division with Zeros in Three-Digit Answers

When a remainder is zero and there are only zeros to bring down in the dividend, the rest of the quotient will also be zeros.

Lesson 80

Power Up GTwo color counters*Place-value work mats* *optional





2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model

What are some ways that a relationship between two sets of data can be represented?

extend a table of values that shows the relationship between two quantities.

describe the relationship between two sets of data in a table.

write an equation to generalize the rule for a set of data.

coordinate(s)

Analyzing and Graphing Relationships

Graphs can be used to display relationships between two quantities, such as pay and time worked.

Investigation 8

mathematical situations.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.2.9.4.C-Identify on a 2- dimensional coordinate system the location of points with whole number coordinates; plot in a two-dimensional coordinate system a point represented by an ordered pair of whole numbers

graph a set of ordered pairs on a coordinate grid.

name the coordinates of a point on a coordinate grid.

The first number in each coordinate pair is taken from the horizontal scale. The second number in each pair is taken from the vertical scale. The coordinates are written in parentheses.


Standards Essential Questions AssessmentsSkills Content LessonsResources

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.10..A-Identify right angles in geometric figures.

How does the measure of a right angle compare to the measure of a straight angle?


estimate the measure of an angle in degrees.

create and use an angle measurement tool to estimate angle measures.

straight angle

Angle Measures

Two angles whose measures add to 90° are complementary. Two angles whose measures add to 180° are supplementary.

Lesson 81

Power Up IBrad*Classroom clock*Protractors*Tag board*3-by-5-inch rectangles of unlined paperTransparency of Lesson Activity 16* *optional


What is a tessellation?


identify and create tessellations.

describe the transformation that can be used to tessellate a shape.

use reflections to determine that a tessellation has symmetry.

tessellation

Tessellation

The only three regular polygons that tessellate are the equilateral triangle, the square, and the regular hexagon.

Lesson 82

Power Up ILesson Activities 35 and 36MirrorsOverhead pattern blocks*Crayons or markers*Glue, grid paper, and paper*Scissors *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

How is arithmetic related o the concept of sales tax?


find the total cost of a purchase including sales tax.

find the sales tax on a purchase.

calculate the amount of change that should be given back after a purchase has been made.

find all possible combinations of a set.

sales tax

Sales Tax

Sales-tax rate is usually given as a percent. To find the amount of sales tax on an item, you can multiply the price by the percent, expressed in decimal or fraction form.

Lesson 83

Power Up IMoney manipulatives* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for

What place value does a decimal number with three digits to the right of the decimal point represent?


write a fraction with a denominator of 1000 as a decimal number and use words to name both the fraction and the decimal number.

write a decimal number with three decimal places as a fraction

thousandth

Decimal Numbers to Thousandths

When two or more fractions have the same denominators, the fraction with the greatest numerator is the greatest fraction.

Lesson 84

Power Up I

the four operations. or mixed number.

use words to name both the decimal number and the fraction or mixed number.

2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

How can mental math be used to name the product of two numbers when one number is 10, 100, or 1000?


find patterns for multiplying a whole number by 10, 100, and 1000.

find patterns for multiplying money amounts by 10, 100, and 1000.

Multiplying by 10, by 100, and by 1000

A quick way to multiply a decimal number by 10, 100, or 1000 involves shifting the decimal point to the right. To multiply by 10, shift the decimal point one place to the right. To multiply by 100, shift the decimal point two places to the right. To multiply by 1000, shift the decimal point three places to the right.

Lesson 85

Power Up G




2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

What other factors can be used to multiply 400 x 700?


use patterns to multiply by multiples of 10 and 100.

Multiplying Multiples of 10 and 100.

Once the multiplication facts are memorized, you can multiply rounded numbers in your head. You can multiply the first digits of the factors and count zeros.

Lesson 86

Power Up GBase ten blocks* *optional


How do you know the number of partial products a multiplication will produce?

Fact Practice-Power Up G 2/22/2015 multiplying two two-digit numbers

without regrouping.

Multiplying Two Two-Digit Numbers, Part 1

The Commutative Property of Multiplication states that the order of two factors can be changed without changing the product of those factors. One way to apply this property is to switch the factors, multiply again, and see if you have the same answer.

Lesson 87

Power Up GLesson Activity 20*Base ten blocks*Grid paper (or lined paper)* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and

What do you do with the

Fact Practice-Power Up G

solve "equal groups" problems with remainders.

Remainders in Word Problems About Equal Groups

Lesson 88

Power Up GLesson Activity 20*

division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.

remainder in a division story problem?

2/23/2015 interpret the remainder for a division word problem.

When a division problem has a remainder, most calculators give the answer in decimal form.

Rulers, two-color counters* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you change a mixed number into an improper fraction?


rename improper fractions as mixed numbers.

write improper fractions using pictorial models.

improper fraction

Mixed Numbers and Improper Fractions

Fractions that are greater than or equal to 1 are called improper fractions.

Lesson 89

Power Up GLesson Activities 37 and 38Base ten blocks*Fraction manipulativesOverhead fraction circles*Rulers*Fraction bars*Grid paper*Transparency of Lesson Activity 16* *optional


How is regrouping in addition similar to regrouping in multiplication?


multiply two two-digit numbers with regrouping.

round numbers to estimate a product.

Multiplying Two Two-Digit Numbers, Part 2

The number of partial products in a multiplication problem is related to the number of digits in the number you are multiplying by. There will be two partial products if the number you are multiplying by is a two-digit number.

Lesson 90

Power Up ILesson Activity 20* *optional





2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.B-Multiply single- and double-digit numbers

What fractions are equal to 1/2?

What are three ways to represent the number for 1 of 4 equal parts?

use fraction manipulatives to model, compare, and order equivalent fractions.

use fraction manipulatives to reduce fractions.

use fraction manipulatives to add and subtract fractions.

use fraction manipulatives to

lowest termsreduce

Investigating Fractions with Manipulatives

Fraction manipulatives can be used to reduce fractions, find equivalent fractions, and reducing fractions to lowest terms.

Investigation 9

Lesson Activities 37, 38, 39, and 40Fraction manipulativesOverhead fraction circles*Activity mats, envelopes or locking plastic bags*Permanent marker*Scissors

and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

model mixed numbers.

use fraction manipulatives to explore how fractions, decimals, and percent are related.

Transparencies of Lesson Activities 37, 38, and 39**optional


Standards Essential Questions AssessmentsSkills Content Lessons Resources


How is decimal place value different from whole-number place value? How is it the same?


represent decimal place value using money.

compare decimal numbers through hundreds.

add and subtract decimal numbers through thousandths.

mill

Decimal Place Value

The values placed to the right of the decimal point are less than one.

Lesson 91

Power Up IMoney manipulatives*Rulers*Grid paper* *optional


What are the names of five different quadrilaterals?

Which quadrilaterals have at least one pair of parallel sides?


classify and draw quadrilaterals by their characteristics.

find examples of different quadrilaterals.

identify lines of symmetry for quadrilaterals.

parallelogramrectanglerhombussquaretrapezoid

Classifying Quadrilaterals

The prefix "quad" represents four.

Trapezoids are not parallelograms and parallelograms are not trapezoids, but both trapezoids and parallelograms are quadrilaterals.

Lesson 92

Power Up ILesson Activity 41MirrorsStraws or other straight objects**optional

2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.2.4.D-Estimate sums and differences, products, and quotients, and conclude the reasonableness of those estimates.

What should you do if you find that an estimate is very different from an exact answer?


use rounding to estimate the solution to multiplication and division problems.

determine the reasonableness of an answer.

Estimating Multiplication and Division Answers

Estimation can help prevent mistakes. If you estimate the answer before you multiply, you can tell whether the answer is reasonable.

Lesson 93

Power Up IFraction manipulatives*Money manipulatives* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide

What are the names of several strategies you can use to help solve word problems?


translate and solve two-step word problems by drawing a picture or listing the information given.

locate and name points on

Two-Step Word Problems

When you translate a problem you identify the goal and list the steps.

Lesson 94

Power Up HTwo-color counters

by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.

a number line.

describe the relationship between ordered pairs in a table.

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.5.4.B-Use appropriate mathematical vocabulary, graphs, and symbols when explaining how to solve a problem.

How do you find 3/4 of a number?


solve multi-step word problems to find a fraction of a group.

draw a diagram to find a fraction of a group.

Two-Step Problems About a Fraction of a Group

In two step problems involving fractions of a group you first divide to find the number in one part, then multiply to find the number in more than one part.

Finding a fraction of a number is the same as multiplying the number by the fraction.

Lesson 95





2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.6.4.C-Describe and calculate the mean and use this quantity to describe the data.

If there are several stacks of coins and there are a different number of coins in each stack. How would you find the average number of coins in each stack?


find the average of a set of data.

average

Average

Finding the average is a two-step process. An average is a way to describe a set of data using one number.

Lesson 96

Power Up HColor tiles* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.6.4.C-Describe and calculate the mean and use this quantity to describe the data.

How do you find the mean, median, mode, and range of a set of data that contains six numbers?


describe the characteristics of data in a set.

determine the mean, median, mode, and range of a set of data.

meanmedianmodeoutlierrange

Mean, Median, Range, and Mode

The terms mean and average represent the same measure. To find either measure, you divided the sum of the addends by the number of addends.

Lesson 97

Power Up HIndex cards* *optional


How is a polygon different from a solid?


classify geometric solids by their sides, bases, and vertices.

find real-world examples of geometric solids.

apexbaseconecubecylinderedgefacegeometric solidpyramidrectangular prismspheretriangular prismGeometric Solids

Two-dimensional figures such as triangles, rectangles, and circles are flat shapes that cover an area but do not take up space. They have length and width but not depth. Geometric solids are geometric shapes that take up space. They have three dimensions.

Lesson 98

Power Up HLesson Activity 42Dot cube*Relational GeoSolids*Rectangular box*Unopened, cylindrical containers* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.

How is a cube similar to a rectangular prism? How is it different?


construct, compare, and contrast three-dimensional models of rectangular and triangular prisms.

identify faces, edges, and vertices.

identify acute, obtuse, and right angles.

identify intersecting, perpendicular, and parallel faces.

net

Constructing Prisms

A net is a two-dimensional representation of a three-dimensional geometric figure.

Lesson 99

Power Up JLesson Activities 43, 44, and 45Fraction manipulativesRelational GeoSolids*Rulers*Empty boxes*Scissors, tape or glue *optional

2.4.4.A-Use models, number facts, and properties to make conjectures, draw conclusions and explain reasons for conclusions.2.9.4.A-Identify, describe, and define 1-, 2-, and 3- dimensional shapes and their related parts; compare 2-dimensional shapes; compare 3- dimensional shapes.

What are three examples of plane figures and three examples of geometric solids? How are the figures and solids alike? Different?


construct three-dimensional models of pyramids using nets.

describe the characteristics of pyramids; compare and contrast pyramids and prisms.

Constructing Pyramids

A polyhedron is a solid made up of polygons joined at their edges.

A plane is an endless 2-dimensional, flat surface.

Lesson 100

Power Up JLesson Activity 46Fraction manipulatives, rulers*Glue or tape, scissorsGrid paper* *optional




2.6.4.A-Gather data from surveys and observations within the classroom or homes.

What does probability

use a fraction to describe the chance that

certainchance Investigation

Lesson Activity 47

2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.6.4.E-Determine the reasonableness of a statement based on a comparison to data displayed in a graph.2.7.4.A-Determine the chance of an event occurring by performing simulations with concrete devices (e.g., dice, spinner).2.7.4.B-Determine whether different outcomes of the same event are equally likely or not equally likely.2.7.4.C-Express probabilities as fractions.2.7.4.D-List or graph the possible results of an experiment.2.7.4.E-Describe possible reasons for the difference between predicted and actual outcomes.

mean?

How is probability like chance? How are they different?

an event will occur or not occur.

find the probability of an outcome in an experiment.

record the results of a probability experiment in a frequency table.

record the results of an experiment using percent.

draw a graph to display outcome of a probability experiment.

probabilitysector

Probability

Chance is usually expressed as a percent and probability is usually written as a fraction or decimal number.

10 Dot cubes


Standards Essential QuestionsAssessmentsSkills Content LessonsResources

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.C-Calculate elapsed time; use concept of elapsed time to determine start time/end time.2.6.4.B-Organize and display data using tables, pictures, tallies, bar graphs, line graphs, or pictographs.2.6.4.D-Analyze data shown in tables, charts, diagrams, and graphs; compare the data from two categories displayed in a graph and compare representations of a set of data in different graphs.2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

What is a schedule?

How is data in a schedule organized?


read and use schedules to solve elapsed-time problems.

use tables to solve problems.

use clocks to solve elapsed-time problems.

scheduletable

Tables and Schedules

The United States and Canada use a 12-hour time system. Many other countries use a 24-hour time system.

Lesson 101

Power Up JFraction manipulatives*Rulers*Student clocks*ThermometersGrid paper*Paper strips* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).

How do you draw a number line from 0 to 2 in tenths?


locate and name tenths and hundredths on a number line.

round decimal numbers to the nearest tenth.

relate decimals to fractions that name tenths.

measure objects to the nearest centimeter using a meter stick.

Tenths and Hundredths on a Number Line

Not all number lines are exactly the same. Some may not have a label for tick marks. No matter how close together two numbers are on a number line, you can always find another number between them. This is known as density property.

Lesson 102

Power Up ABase ten blocks, color tiles, fraction manipulatives*Grid paper (or lined paper), meter sticks *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of

Explain how to write a fraction


write fractions equivalent to one and one half.

represent and compare

Fractions Equal to 1 and Fractions Equal to 1/2

2/2, 3/3,4/4 and 5/5 are examples of equivalent fractions. Equivalent

Lesson 103

Power Up AFraction manipulatives*Relational

concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.D-Perform basic conversions within the same system to the unit immediately above or below the given unit.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

that is equal to 1/2 and then name three fractions that are equal to 1/2.

fractions equal to one half using pictorial models.

compare fractions to the nearest half.

fractions are different names for the same number.

GeoSolids*Fraction bars* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

How can division be used to change an improper fraction to a whole or mixed number?


convert improper fractions to whole or mixed numbers.

Changing Improper Fractions to Whole or Mixed Numbers

An improper fraction can be converted to a mixed number by dividing the numerator by the denominator.

In order to be an improper fraction, the numerator needs to be larger than the denominator or the numerator and denominator can be the same number.

Lesson 104

Power Up AFraction manipulativesOverhead fraction circles* *optional

2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.1.4.D-Apply place value concepts and base-ten numeration to order and compare larger whole numbers.2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

What are the 4 steps in division?


divide three-digit numbers by ten.

Dividing by 10

You can divide a number by 10 quickly by shifting the decimal point one place to the left. If the number is a whole number, you can imagine the decimal point at the end of the number.

Lesson 105

Power Up ALesson Activity 20*Color tiles*Rulers*Deck of playing cards*Grid paper* *optional




2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.5.4.A-Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense, and explain how the problem was solved in grade appropriate contexts.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

What does it mean to evaluate an expression?


evaluate expressions when given the value of the unknown variable.

evaluate

Evaluating Expressions

A letter of the alphabet is often used to represent a missing number, any letter of the alphabet can be used.

Evaluating an expression involves substituting a given number for a letter, and then using operations such as addition, subtraction, multiplication and/or division to simplify the

Lesson 106

Power Up ARulers*Two-color counters*Grid paper*Index cards* *optional

2.8.4.E-Describe data represented in equations, inequalities, tables, or graphs and/or create a story that matches that data.

expression.

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.

How do you add two mixed numbers whose fraction parts have the same denominator?

Fact Practice-Power Up B 3/30/2015

add fractions with common denominators.

subtract fractions with common denominators.

Adding and Subtracting Fractions with Common Denominators

When adding fractions, it helps to think of the denominators as objects such as apples.

When you add mixed numbers, the fraction part of the sum is sometimes greater than 1. The answer can either be adjusted when the addition is finished or can be regrouped as if they are whole numbers.

Lesson 107

Power Up BFraction circles*Overhead fraction circles*Fraction bars* *optional

2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

How does the formula P=2(l+w) and the Distributive Property help you to find the perimeter of a rectangle?


use formulas to find perimeter.

use the Distributive Property to solve multiplication problems.

Distributive Property

FormulasDistributive Property

You can find the area of a rectangle by multiplying its length by its width.Area=length x width

Lesson 108

Power Up BBase ten blocks*Fraction manipulatives* *optional


What property states that you can multiply any number by 1 and the answer is that number?


use pictures to show that two fractions are equivalent.

find fractions that are equivalent to a given fraction.

equivalent fraction

Equivalent Fractions

Finding equivalent fractions is helpful when you want to compare fractions. Equivalent is another word for equal.

Lesson 109

Power Up BFraction circles*Overhead fraction circles*Relational GeoSolids*Fraction bars* *optional


How do you decide where the first digit of a quotient will be?


divide by multiples of 10. Dividing by Multiples of 10

To help find the quotient when dividing by a two-digit number you may think of dividing by the first digit only.

It is important to compare the remainder to the divisor. If the remainder is greater than or equal to the divisor, it is a signal that the number placed in the quotient should

Lesson 110

Power Up BFraction circles*Grid paper (or lined paper)* *optional

be increased. Cumulative Test

21 4/5/2015




2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

How do you find the volume of a rectangular solid that is 5 units long, 3 units wide, and 10 units high?

How many cubic feet are in 1 cubic yard?

count cubes to find the volume of rectangular solids

find the volume of rectangular solids.

estimate the volume of real-world objects.

cubic unitsvolume

Volume

Investigation 11

Lesson Activities 45 and 48Base ten blocks, meter sticks, yardsticks, rulers*Liquid measuring cupsEmpty containersLarge cubes*Rectangular boxesTape or glue *optional


Standards Essential Questions AssessmentsSkills Content Lessons Resources

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.3.4.A-Use concrete objects to demonstrate an understanding of measurement quantities (e.g., length, weight, temperature).2.3.4.B-Select and use appropriate tools and units for measuring quantities (e.g., length, time, weight, temperature).2.3.4.F-Estimate and verify measurements of length, perimeter, area, weight, capacity, temperature, and time.

How is an estimate different than an exact answer?

Fact Practice-Power Up C 4/7/2015

estimate the perimeter and area of a shape using a grid.

estimate volume using cubes and cubic units.

estimate the volume of real-world objects.

approximation

Estimating Perimeter, Area, and Volume

Volume can be estimated using cubes and cubic units.

To estimate the area of shapes you can use a grid.

Lesson 111

Power Up CLesson Activities 20, 21, and 45Base ten blocksFraction manipulatives*Geoboards and geobands*Meter stick, rulers, yardstick*Box *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit

How would you reduce the fraction 5/10?


write the reduced form of a fraction.

Reducing Fractions

You reduce a fraction by dividing it by a fraction that is equivalent to one.

When you reduce a fraction you find an equivalent fraction written with smaller numbers.

Lesson 112

Power Up GFraction circles*Fraction bars* *optional

fractions (e.g., more, less, same, least, most, greater than, less than). 2.1.4.F-Understand the concepts of addition and subtraction and their inverse relationships; understand the concepts of multiplication and division; use the four basic operations to solve problems, including word problems and equations.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

How do you know where to put the decimal point in a multiplication problem involving money?


multiply a three-digit number by a two-digit number.

multiply dollars and cents by a two-digit number.

Multiplying a Three-Digit Number by a Two-Digit Number

The number of decimal places in the answer will be the total of the numbers of decimal places in the two factors.

Lesson 113

Power Up IBase ten blocks*Fraction manipulatives*Scissors* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you know when a fraction cannot be reduced?


write an answer that contains a fraction in the simplest form possible.

add and subtract fractions and mixed numbers with common denominators.

Simplifying Fraction Answers

We often write answers to math problems in the simplest form possible. A simple fraction, which is also called a common fraction, is a fraction in which the numerator and denominator are integers. A proper fraction is a fraction in which the numerator is less than the denominator.

Lesson 114

Power Up HFraction bars* *optional


How is multiplication used to find equivalent fractions?


find a fraction with a specified denominator that is equivalent to a given fraction.

Renaming Fractions

A statement that two fractions are equal is a proportion.

Lesson 115

Power Up HFraction bars* *optional




2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.C-Use drawings, diagrams, or models to show the concept of a fraction as a part of a set and as division of a whole number by a whole number.2.2.4.A-Develop fluency in the use of basic facts for the four

What number is a common denominator for 2/3 and 1/4?


rename fractions whose denominators are not equal by using a common denominator of the fractions.

common denominatorleast common denominator (LCD)

Common Denominators

One way to find a common denominator is to multiply the denominators.

The least common denominator is sometimes called LCD.

Lesson 116

Power Up HFraction bars*Scissors* *optional

operations. 2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.1.4.E-Apply factors and multiples to represent larger numbers in various ways.

How would you round 349,850 to the nearest thousand?


round whole numbers to the nearest ten thousand, the nearest hundred thousand, and through the nearest million.

Rounding Whole Numbers Through Hundred Millions

A method for rounding a whole number to any place is to underline the digit in the place you are rounding to. Then look at the digit to the right of the underlined digit-if it is less than 5, change all the digits to the right of the underlined digits to 0-if it is 5 or greater, increase the underlined digit by 1 and change all the digits to the right of the underlined digit to 0.

Lesson 117

Power Up JBase ten blocks*Relational GeoSolids*Square pyramid* *optional


What are the four steps in division?


divide by two-digit numbers.

Dividing by Two-Digit Numbers

Mental math can be used to help place the first digit in each quotient.

Lesson 118

Power Up IRulers*Grid paper (or lined paper)* *optional

2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.2.4.B-Multiply single- and double-digit numbers and divide by single digit numbers, add and subtract fractions with like denominators, and add and subtract decimals.

How do you find a common denominator?


add and subtract fractions with different denominators and reduce fractions when possible.

Adding and Subtracting Fractions with Different Denominators

Fractions with different denominators can be added and subtracted.

In order to add or subtract fractions that have different denominators, you must first rename the fractions so that they have common denominators.

Lesson 119

Power Up JBase ten blocks*Color tiles*Rulers*Fraction bars* *optional

2.1.4.A-Apply number patterns and relationships to count and compare values of whole numbers and simple fractions, and decimals.2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.2.2.4.A-Develop fluency in the use of basic facts for the four operations.2.11..A-Make comparisons of whole numbers and of unit fractions (e.g., more, less, same, least, most, greater than, less than).

How do you subtract fractions with mixed numbers and different denominators?


add and subtract mixed numbers with different denominators and reduce fractions when possible.

Adding and Subtracting Mixed Numbers with Different Denominators

Mixed numbers can be subtracted by subtracting the fraction parts and the whole-number parts separately.

Lesson 120

Power Up JRelational GeoSolids* *optional





2.8.4.B-Select and use strategies, including concrete objects, to solve number sentences (equations and inequalities) involving whole numbers or unit fractions and explain the method of solution.2.8.4.D-Use words, tables, and graphs to represent and analyze functions. Use concrete objects and combinations of symbols and numbers to create expressions, equations, and inequalities that model mathematical situations.

What is an equation?

What do you have to do to keep a scale balanced?

write an equation and discuss how to get the unknown on one side of the equal sign while keeping the equation balanced.

Solving Balanced Equations

An equation states that two quantities are equal. One model for an equation is a balanced scale.

Investigation 12

Lesson Activity 49Balance scale with weights* *optional

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.

Where have you seen Roman numerals used?

write Roman numerals through 39.

Roman Numerals Through 39

Roman numerals were used by the ancient Romans to write numbers. Today Roman numerals are used to number things like book chapters, movie sequels, Super Bowl games, clocks and buildings.

Appendix A

2.1.4.B-Represent equivalent forms of the same whole number, the same fraction, or the same decimal through the use of concrete objects, drawings, word names, and symbols.

What are some rules for evaluating Roman numerals?

write Roman numerals through thousands.

Writing larger Roman numerals is done the same as writing smaller Roman numerals. The same rules apply.

Appendix B

web viewhow are counting numbers and ordinal numbers different?how is an ordinal number ... word...

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