Argyle ISD 2014-2015

Fourth Grade Mathematics Curriculum Guide

Second Quarter (October 20- December 19) This guide provides a timeline and suggested resources for teaching the fourth grade TEKS. It is expected that a minimum of 90 minutes a day be hands-on/minds-on active investigation that utilize the tools and resources available to you.

TEKS Mathematical Process skills will be integrated throughout all units and concepts

Integrated in ALL Concepts

4.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: 4.1A apply mathematics to problems arising in everyday life, society, and the workplace 4.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution 4.1C select tools, including real objects, manipulatives, paper/pencil, and technology as appropriate techniques, including mental math, estimation and number sense, as appropriate to solve problems. 4.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate 4.1E create and use representations to organize, record and communicate mathematical ideas 4.1F analyze mathematical relationships to connect and communicate mathematical ideas 4.1G display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communications

Unit 1 – Numbers & Operations

TEKS/Student Expectations

4.2B- represent the value of the digit in whole numbers through 1,000,000,000 and decimals to the hundredths using expanded notation and numerals 4.2E- represent decimals, including tenths and hundredths, using concrete and visual models and money 4.2F- compare and order decimals using concrete and visual models to hundredths 4.2G- relate decimals to fractions that name tenths and hundredths 4.2H- determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line 4.3A- represent a fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b>0, including when a>b 4.3B decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recordings results with symbolic representations. 4.3C -determine if two given fractions are equivalent using a variety of methods 4.3D -compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, = or < 4.3E- represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties operations 4.3F- evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0. ¼, ½, ¾, and 1. Referring to the same whole 4.3G- represent fractions and decimals to the tenth or hundredths as distances from zero on a number line

TEKS Clarifications

● Students should have flexibility with the different number forms. Traditional expanded

form is 285=200+80+5. Written form or number name is two hundred eighty-five.

However, students should have opportunities to explore the idea that 285 could also be

28 tens plus 5 ones or 1 hundred, 18 tens, and 5 ones.

● Students make connections between fractions with denominators of 10 and 100 and the

place value chart. By reading fraction names, students say 32/100 as thirty-two

hundredths and rewrite this as 0.32 or represent it on a place value model

● Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than

30/100 (or 3/10) and less than 40/100 (or 4/10). It is closer to 30/100 so it would be

placed on the number line near that value

● A fraction with a numerator of one is called a unit fraction. When students investigate

fractions other than unit fractions, such as 2/3, they should be able to join (compose) or

separate (decompose) the fractions of the same whole. Example: 2/3 = 1/3 + 1/3

● Students should justify their breaking apart (decomposing) of fractions using visual

fraction models

● Students use benchmark fractions to estimate and examine the reasonableness of their

answers. Students will recognize that comparisons are valid only when the two fractions

refer to the same whole.

Sample Problems

Matthew has $1.25. Create a visual model that show the same amount.

Example: Draw a model to show that 0.3 < 0.5. (Students would sketch two models of approximately the same size to show the area that represents three-tenths is smaller than the area that represents five-tenths.

 Example with mixed numbers: A cake recipe calls for you to use ¾ cup of milk, ¼ cup of oil, and 2/4 cup of water. How much liquid was needed to make the cake? 

    

  Example: There are two cakes on the counter that are the same size. The first cake has half of it left. The second cake has 5/12 left. Which cake has more left? 

Guiding Questions

1. How are fractions and decimals related?

2. How does knowing about decimals help us with money?

3. How do models and pictures help you understand equivalent numbers and values?

Common Misconceptions

● Keep in mind that Expanded Form and Expanded Notation have two different meanings. Expanded Form is

the traditional breaking apart of a number (325= 300+20+5) while Expanded Notation can show number

broken apart in various ways (325= 32tens +5ones; 1,327 = 1,300+20+7)

● Students may have a hard time visualizing how to combine or separate fractions. Being able to visualize this

decomposition into unit fractions helps students when adding or subtracting fractions. Students need

multiple opportunities to work with mixed numbers and be able to decompose them in more than one

way. Students may use visual models to help develop this understanding.

● A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students will tend to

add or subtract the whole numbers first and then work with the fractions using the same strategies they

have applied to problems that contained only fractions.

Key Academic Vocabulary Decimal Denominator Tenths

Fraction Equivalent Hundredths

Numerator Compare Decimal Point

Vertical Alignment 3rd Grade Before

After

5th Grade

3.3A represent fractions greater than zero and less than or equal to one with denominators or 2,3,4,6 and 8 using concrete objects and pictorial models, including strip diagrams, and number lines 3.3E solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2,3,4,6, or 8. 3.3C explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number 3.3D compose and decompose a fraction with a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b 3.3F represent equivalent fractions with denominators of 2,3,4,6 or 8 using a variety of objects and pictorial models including number lines 3.3G explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model 3.3H compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models.

Suggested Resources

EnVision Lessons: Topic 1 – Decimals Topic 10 & 11- Fractions Mentoring Minds/Motivation Math: Units 5-14

Unit 2 – Algebraic Reasoning

TEKS/Student Expectations

4.5A- represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with letter standing for the unknown quantity 4.5B- represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

TEKS Clarifications

● In a multiplicative comparison, the underlying question is what amount would be added to one quantity in order to result in the other. In a multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in the other 

● Patterns that consist of repeated sequences of shapes or growing sequences of designs can be appropriate for the grade. For example, students could examine a sequence of dot designs in which each design has 4 more dots than the previous one and they could reason about how the dots are organized in the design to determine the total number of dots in the 100th design. 

●  In examining numerical sequences, fourth graders can explore rules of repeatedly adding the same whole number or repeatedly multiplying by the same whole number. Properties of repeating patterns of shapes can be explored with division. 

For example, to determine the 100th shape in a patter that consists of repetitions of the sequence “square, circle, triangle,” the fact that when we divide 100 by 3 the whole number quotient is 33 with remainder 1 tells us that after 33 full repeats, the 99th shape will be a triangle (the last shape in the repeating pattern), so the 100th shape is the first shape in the pattern, which is a square. Notice that the Standards do not require students to infer or guess the underlying rule for a pattern, but rather ask them to generate a pattern from a given rule and identify features of the given pattern 

Sample Problems

Example: Rule: Starting at 1, create a pattern that starts at 1 and multiplies each number by 3. Stop when you have 6 numbers. Students write 1, 3, 9, 27, 81, 243. Students notice that all the numbers are odd and that the sums of the digits of  the 2 digit numbers are each 9. Some students might investigate this beyond 6 numbers. Another feature to investigate is the patterns in the differences of the numbers (3 ­ 1 = 2, 9 ­ 3 = 6, 27 ­ 9 = 18, etc.)

Guiding Questions

1. What are repeating and/or increasing units in a pattern?

2. What strategies can be used to continue a sequence?

3. How does finding patterns help in computations?

4. How is an equation like a balanced scale?

Common Misconceptions

● Patterns and rules are related. A pattern is a sequence that repeats the same process over

and over. A rule dictates what that process will look like. Students investigate different

patterns to find rules, identify features in the patterns, and justify the reason for those

features.

Key Academic Vocabulary Input Patterns

Output Relationshi

p

Tables Value

Vertical Alignment 3rd Grade

Before

After

5th Grade 3.5A represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines and equations 3.5B represent and solve one- and two- step multiplication and division problems within 100 using arrays, strip diagrams and equations. 3.5D determine the unknown whole number in a multiplication or division

5.4B represent and solve multi-step problems involving the four operations with whole numbers using equations with letters standing for the unknown quantity 5.4C generate a numerical pattern when given a rule in the form of y=ax or y= x+a and graph 5.4D recognize the difference between additive and multiplicative numerical patterns given in a table or graph.

equation relating three whole numbers when the unknown is either a missing factor or product 3.5E represent real-world relationships using number pairs in a table and verbal descriptions

Suggested Resources

EnVision Lessons: Topic 9 Lesson 9-4, 9-5, 9-6 Mentoring Minds/Motivation Math: Units- 23-24