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Groton Public SchoolsCurriculum Map

INTRODUCTIONCourse Title: Math

Curriculum Area and Grade: Math – Grade 4

Course Purpose:The purpose of this course is to provide a means to implement meaningful methods to understand mathematical concepts, approach problem solving and learn computation at the fourth grade level. The course incorporates best practices of both traditional and reform mathematics curricula and strikes a balance between promoting children’s natural solution methods and introducing new and effective mathematical practices. In order to promote and implement natural and new methods, as well as to encourage students to become reflective and resourceful problem solvers, the course will assist teachers in developing lessons that create a progressive and logical mathematical environment.

The Learner at this Level:The Fourth Grade Child: Learns better on her own than younger and older schoolmates as she gains mastery of basic skills. Is often anxious and complains about aches and pains. Has a growing sense of peer importance and solidarity. Likes to negotiate. Struggles with abstractions. Needs clear expectations, encouragement and positive language.

Major Learning Goals and Understandings:Algebraic Reasoning: The Fourth Grade Child: Recognizes a variety of patterns and trends. Uses growing patterns to explore functions. Discovers the relationship of equivalence on both sides of the equation. Explores the usefulness of algebraic reasoning to create generalizations. Likes rules and logic. Demonstrates the rule of a function, relationship or pattern. Expresses relationships using open sentences with one operation. Prepares for traditional algebraic expressions by utilizing horizontal equations. Applies inverse operations and explains the solution. Uses letters as variables not only as unknowns. Explores ratio and proportion. Creates simple formulas about area and perimeter of a rectangle. Describe changes in geometric designs or patterns.

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Numerical and Proportional Reasoning: The Fourth Grade Child: Demonstrates four-digit place value by using models and pictures. Chooses compatible numbers based on place value or number pairs. Constructs strategies for flexible methods of computing, depending on the situation or the numbers. Uses regrouping for accurate computation. Identifies equivalent fractions using models and pictures. Uses the number line to represent both decimals and fractions in a geometric and visual manner. Discovers fractions and decimals are rational numbers. Efficiently uses multiplication and division facts. Models multiplication and division using objects, base-10 materials, or parts of a rectangle. Estimates in situations involving money. Creates story problems for all four operations.Geometry and Measurement: The Fourth Grade Child: Employs appropriate units to measure the area of rectangular shapes. Recognizes the relationship between the area and perimeter of rectangles. Finds the area of more complex figures by dividing the figures into basic shapes. Uses models and drawings of shapes to construct and test hypothesis and to make generalizations about geometry. Develops formulas for measuring area and perimeter of geometric shapes. Identifies locations on a coordinate grid with ordered pairs. Measures attributes accurately with standard measures and tools. Determines when a precise measurement is appropriate. Iterates a unit of measure physically and/or mentally. Plans and schedule events using calendars and clocks.Working with Data: The Fourth Grade Child: Formulates questions for surveys and collects the information to make comparisons about groups. Collects data, including the use of measuring devices, printed or electronic resources, and surveys or samplings to answer questions. Sorts, re-sorts and organizes the same set of data or objects in multiple ways and records results on graphic organizers. Determines whether data are presented graphically in an adequate format for examining relationships. Discusses data, communicates conclusions, and makes predictions and inferences. Generates new questions from displayed data. Refines information from data by calculating mean, median, mode and range.

Units/Concepts for the Year1. Fact Fluency Review 2. Multiplication & Division Problem Solving

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3 Quadrilaterals 4. Place Value & Multi-Digit Addition & Subtraction5. Angles and Polygons 6. Multi-Digit Multiplication7. Metric Measurement System 8. Multi-Digit Division9. Patterns, Functions, & Graphs 10. Fractions11. Three Dimensional Figures 12. Decimal Numbers13. U.S. Customary System

Part 1 – Unit 1Grade: Subject: Course: Length of Unit:

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4 Math Fact Fluency Review About 10 days

Essential Questions and Big IdeasEQ – How do patterns help you become fluent with your multiplication and division facts? BI – The fluency of facts depend on the recognition of patterns.EQ - How are multiplication and division related? BI - Multiplication and division have an inverse relationship.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.1 Understand and describe patterns and functional relationships. 1.2 Represent and analyze quantitative relationships in a variety of ways. 1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems.Numerical and Proportional Reasoning 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Grade Level Expectations Students will be able to: CMT Correlations1.1.1 Extend and compare numerical and geometric sequences and classify patterns as growing or repeating, e.g. 2, 4, 8, _, _, grows and the following sequence repeats.

1.1.2 Develop and test generalizations based on observable patterns and relationships and describe the rules for number patterns using equations, e.g., in this sequence 1, 6, 16, 36 …, to get the next number the current number can be doubled and four added to the product.

1.2.3 Describe mathematical relationships and situations, involving ratios and computations of whole numbers, in all four

Identify patterns in basic multiplication and division facts.

Model multiplication and division word problems. Apply properties of multiplication. Connect the concept of repeated addition to

multiplication. Connect the concept of repeated subtraction to

division. Use properties, patterns, models, and other strategies

to recall addition, subtraction, multiplication, and division facts.

Solve, write, and explain multiplication and division word problems.

Write about and explain the relationship between multiplication and division.

Use order of operations to simplify expressions.

2A. Relate fractions and decimals to pictorial representations and vice versa.

2B. Relate fractions of regions and sets to pictures and vice versa.

2C. Label and/or shade fractional parts of regions and/or sets.

3A. Relate equivalent fractions to pictorial representations.

5 A. Relate multiplication and division facts to rectangular arrays and pictures.

5B. Identify the appropriate operation or number sentence to solve a story problem.

5C. Write story problems from addition or subtraction number sentences.

6A. Add and subtract facts to 18.

6B. Multiply and divide by 2, 5 and 10.

7A. Add and subtract one- and two-digit whole

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operations with using symbols, number sentences, and equations.

1.3.5 Solve problems and demonstrate an understanding of equivalence in mathematical situations that reflect the commutative and associative properties of addition and multiplication of whole numbers and the distributive property.

2.1.5 Relate multiplication and division to number patterns and models of groups and rectangular arrays.

2.2.16 Create story problems to match a given number sentence. (equation)

2.2.17 Recall the multiplication and division facts 1 through 10.

2.2.18 Write multiplication and division story problems involving basic facts and two- and three-digit by one-digit numbers to match a given number sentence and vice versa; solve the problems using strategies that include models and arrays and justify the solutions.

numbers without regrouping.

7B. Add one- and two-digit whole numbers with regrouping.

8A. Add and subtract fractions with like denominators.

9A. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping).

9B. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping) with extraneous information.

10A. Identify the best expression to find an estimate.

11 A. Identify a reasonable estimate to a problem.

17A. Identify and recognize two-dimensional geometric shapes and figures, including number of angles and sides of polygons.

19A. Identify correct information from tables, bar graphs, pictographs and charts.

22A. Extend or complete patterns, or identify rules using numbers and attributes.

22B. Extend or complete patterns and state rules using numbers and attributes.

23A. Solve simple one-step algebraic equations involving addition, subtraction and fact families.

24A. Identify objects that are the same or different by one attribute.

24B. Sort objects into two groups by a common attribute.

25A. Solve extended numerical and statistical problems.

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Part 3 – Common Unit AssessmentsPre Assessment:Math Expressions Assessment GuideUnit 1 Test Form B (multiple choice)

Post Assessment:Math Expressions Assessment GuideUnit 1 Test Form A (short response)

Weekly Math Review Quiz

Part 4 – Common/Assured Learning ExperiencesPromethean Board Activity: Student Work

FASTTMATH: 3 times per week

Study Island: Reinforcement of CMT basic skills

Common Vocabulary: sum, addend, difference, Associative Property, multiplier, product, array, equation, Commutative Property of Multiplication, pictograph, equal shares, Identity Property of Multiplication, Inverse Operation, factor, order of operations, expression, number sentence, inequality, square number, Distributive Property, simplify

Daily Math Review (Computational review)

Math Journaling (End of Unit)

Part 5-Teacher Notes

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Teacher Resources

Differentiated Instruction

LESSON PLANS

FLIP CHARTS

Electronic Resources:http://prometheanplanet.comhttp://thinkcentral.com

Part 1 – Unit 2 Grade: Subject: 8 Course: Length of Unit:

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http://thinkcentral.com/

http://prometheanplanet.com/

4 Math Multiplication & Division Problem Solving

About 11days

Essential Question and Big IdeasEQ – What are some ways to represent mathematical situations and solve problems? BI – Pictures, models, equations, and tables are ways to represent word problems.EQ – Why is data gathered and organized? BI – Data is gathered and organized to answer questions about the population from which the data comes.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.2 Represent and analyze quantitative relationships in a variety of ways. Numerical and Proportional Reasoning 2.1 Understand that a variety of numerical representation can be used to describe quantitative relationships. 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Working With Data: Probability and Statistics 4.1 Collect, organize and display data using appropriate statistical and graphical methods. 4.2 Analyze data sets to form hypotheses and make predictions. 4.3 Understand and apply basic concepts of probability.Grade Level Expectations Students will be able to: CMT Correlations1.2.3 Describe mathematical relationships and situations, involving ratios and computation of whole numbers in all four operations with using symbols, number sentences, and equations.

2.1.6 Identify prime and composite numbers through the use of models including rectangular arrays, place value models and pictures.

2.2.24 Write and solve multistep contextual problems, including problems with extraneous information and explain orally and in writing how the answers were determined.

Write an equation to solve comparison problems. Use tables to solve combination problems. Write multiplication and division equations for

comparison problems about a pictograph and a bar graph.

Ask and answer questions relating to pictographs and bar graphs.

Make a bar graph to represent data in a table. Solve problems that involve more than one step and

explain their strategy. Use factoring to determine if a number is prime.

1D. Use place value concepts to identify and compare the magnitude and value of digits in two- and three-digit numbers.





7A. Add and subtract one- and two-digit whole numbers without regrouping.


9A. Solve simple story problems involving addition (with/without regrouping) or subtraction

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4.2.3 Discuss, make predictions and write about patterns and trends in categorical and numerical data that have been represented in a variety of ways.

4.3.6 Determine and describe possible combinations where order does not matter, e.g., when there is a choice of vanilla (V), chocolate (C), or strawberry (S) ice cream for a two scoop and two different scoops are desired, the possible combinations are CV, CS, or VS.

(without regrouping).



21A. Identify correct solutions to problems involving elementary notions of probability.




24A. Solve logic, counting and classification problems involving the organization of data.

24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams and transitive reasoning questions.





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Common Vocabulary:table, data, row, column, cell, function, rule, combinations, equation, compare, comparison bars, pictograph, vertical bar graph, horizontal bar graph, axes, scale, factor, prime number, composite number, multiple



Part 5-Teacher NotesTeacher Resources:


LESSON PLANS

FLIP CHARTS


Part 1 – Unit 3Grade: Subject: Course: Length of Unit:

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4 Math Quadrilaterals About 7 days

Essential Questions and Big IdeasEQ – How are shapes identified? BI – Shapes are alike or different based on their attributes.EQ – What is perimeter and how is it measured? BI – Perimeter is the measurement of the distance around a polygon measured in linear units.EQ – What is area and how is it measured? BI – Area is a measure of covering expressed in square units.

Part 2 – Standards and State FrameworksGeometry and Measurement 3.1 Use properties and characteristics of two- and three- dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems. 3.2 Use spatial reasoning, location, and geometric relationships to solve problems.Grade Level Expectations Students will be able to: CMT Correlations3.1.2 Compare and classify polygons based on relationships such as parallel or perpendicular lines, symmetry and congruence

3.1.3 Make and test conjectures about polygons using geometric relationships such as symmetry and congruence.

3.2.5 Analyze geometric reflections (flips), rotations (turns), and translations (slides) of plane figures and describe the relationship to the original figure.

Analyze and explain geometric figures by using symmetry, congruence, and similarity.

Calculate perimeter and area of rectangles. Identify and draw lines of symmetry. Draw and describe lines, line segments, and rays.

17A. Identify two-dimensional geometric shapes, including number of angles and sides of polygons.

17B. Identify, describe and draw two-dimensional geometric shapes and figures.


Part 3 – Common Unit Assessments

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Pre Assessment:Math Expressions Assessment GuideUnit 3 Test Form B (multiple choice)






Common Vocabulary:plane, congruent, similar, line of symmetry, line, line segment, ray, angle, vertex, oblique, perpendicular, right angle, parallel, quadrilateral, trapezoid, isosceles trapezoid, parallelogram, rhombus, rectangle, square, unit, perimeter, length, width, area, square unit. reflection



Part 5-Teacher NotesTeacher Resources

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LESSON PLANS

FLIP CHARTS


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Part 1 – Unit 4Grade:

4Subject:

MathCourse:

Place Value and Multi-Digit Addition

and Subtraction

Length of Unit: About 35 days

Essential Questions and Big IdeasEQ - Why do we use estimation? BI – Estimation can be used to determine a reasonable answer to a problem.EQ - What gives a number its value? BI - The position of a digit in a number determines its value.EQ - How can you use the knowledge of the number system to add and subtract? BI – Numbers can be taken apart or combined to add and subtract.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.2 Represent and analyze quantitative relationships in a variety of ways. 1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.Numerical and Proportional Reasoning 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Geometry and Measurement 3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.Grade Level Expectations Students will be able to: CMT Correlations1.2.3 Describe mathematical relationships and situations involving ratios and computation of whole numbers, in all four operations with using symbols, number sentences, and equations.


Add and subtract whole numbers up to 100,000, including money amounts.

Write and solve a variety of problems involving addition and subtraction. Explain the strategy used and the solution.

Compare, order, and round numbers up to 100,000.

Write numbers up to 100,000 in a variety of ways, including regrouping and expanded notation

Identify the value of a digit. Use =, “not equal”, <, and > signs to make true

statements.

1A. Solve problems involving 10 more/less or 100 more/less than a given number.

1B. Identify alternative forms of expressing whole numbers less than 1,000 using expanded notation.

1C. Identify alternative forms of expressing whole numbers less than 1,000 using regrouping.

1D. Use place value concepts to identify and compare the magnitude and value of digits in two- and three-digit numbers.

4A. Order whole numbers less than 10,000.

4B. Describe magnitude of two- and three-digit

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2.1.1 Locate, label, compare, and order numbers up to 100,000 using place value models, number lines and number patterns (including multiples of 1,000 and 10,000).

2.1.2 Extend number patterns to determine 1,000 and 10,000 more and less than a given number in practical situations.

2.1.3 Round whole numbers up to 100,000 using number patterns, number lines, diagrams and place value models.

2.1.4 Write and describe equivalent representations of four- and five-digit whole numbers up to 100,000 and beyond, in expanded and regrouped forms. Use the forms to support computational strategies.

2.2.14 Develop and use a variety of computation strategies including place value concepts, number lines and the commutative and associative properties to add and subtract three- and four-digit numbers and money amounts up to $1,000.00.

2.2.15 Solve contextual problems involving addition and subtraction of whole numbers using a variety of methods, including writing appropriate number sentences (equations) and explaining the strategies used.

2.2.16 Create story problems to match a given number sentence (equation).

Identify a reasonable estimate to a problem. Round numbers. Determine whether an exact answer or an

estimate is appropriate.

whole numbers, fractions, mixed numbers and decimals (tenths).

4C. Round two- and three-digit whole numbers in context.

5A. Identify members of multiplication and division fact families from arrays (factors of 2, 3, 4, 5 and 10).







9A. Solve simple story problems involving addition (with/without regrouping) or subtraction (without regrouping).




14A. Solve problems involving time, elapsed time (minutes and hours) and calendars.

14 B. Solve problems involving conversions of measures of time.

22A. Extend or complete patterns, or identify

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2.2.19 Determine and explain in writing when an estimate is appropriate and whether a particular estimation strategy is reasonable or will result in an overestimate or underestimate involving computation with three- and four-digit numbers and money amounts up to $1,000.

2.2.24 Write and solve multistep contextual problems, including problems with extraneous information and explain orally and in writing how the answers were determined.

3.3.6 Use calendars and clocks to solve problems and schedule events involving elapsed time.

rules using numbers and attributes.






Part 4 – Common/Assured Learning Experiences

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Promethean Board Activity: Student Work



Common Vocabulary:equation, sum, difference, Commutative Property of Addition, inverse operation, addend, inequality, fewer, total, factor, product, place value, standard form, expanded form, greater than, less than, digit, least, range, equality, expression, estimate





LESSON PLANS

FLIP CHARTS


Part 1 – Unit 5

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Grade: 4

Subject: Math

Course: Angles and Polygons


Essential Question and Big IdeasEQ – What is perimeter and how is it measured? BI – Perimeter is the measurement of the distance around a polygon measured in linear units.EQ – What is area and how is it measured? BI – Area is a measure of coverage expressed in square units.EQ – How are triangles classified? BI – Triangles are classified by their attributes.EQ - What are some ways to locate and relocate shapes? BI – Shapes can be moved in a plane or space. These changes can be described as translations, reflections, and rotations.

Part 2 – Standards and State FrameworksGeometry and Measurement 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate idea and solve problems. 3.2 Use spatial reasoning, location and geometric relationships to solve problems. 3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.Grade Level Expectations Students will be able to: CMT Correlations3.1.1 Describe and represent polygons, solids, and other familiar two- and three-dimensional objects.

3.1.2 Compare and classify polygons based on relationships such as parallel or perpendicular lines, symmetry and congruence.


3.3.6 Use calendars and clocks to solve problems and schedule events involving elapsed time.

Classify triangles by the lengths of their sides and the measure of their angles.

Identify and draw two-dimensional figures with rotational symmetry.

Rotate, translate, and reflect plane figures. Draw or construct a variety of polygons and explain. Use a protractor to measure angles. Find the perimeter and area of polygons.



15A. Estimate lengths and areas by comparing.

16A. Measure lengths to the nearest inch, half-inch or centimeter.

16B. Draw lengths to the nearest inch, half-inch or centimeter.

16 C. Identify appropriate customary or metric units of measure for a given situation.


17B. Identify, describe and draw two-dimensional

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3.3.8 Use customary and metric tools and units and non-standard units to estimate, measure and solve problems involving length and perimeter to the nearest quarter-inch or half-centimeter, area, capacity, weight, temperature and volume.

geometric shapes and figures.










Common Vocabulary:right angle, acute angle, obtuse angle, protractor, rotation, rotational symmetry, congruent, equilateral, isosceles, scalene, diagonal, triangle, quadrilateral, perimeter, area, polygon, octagon, pentagon, hexagon, square



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LESSON PLANS

FLIP CHARTS


Part 1 – Unit 6

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Grade: 4

Subject: Math

Course: Multi-Digit

Multiplication


Essential Questions and Big IdeaEQ – Why do we use estimation? BI – Estimation can be used to determine a reasonable answer to a problem.EQ – How can you use the knowledge of the number system to multiply? BI – Numbers can be taken apart or combined to multiply.EQ – What are some ways to represent mathematical situations and solve problems? BI – Pictures, models, equations, and tables are ways to represent word problems.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.2 Represent and analyze quantitative relationships in a variety of ways. 1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.Numerical and Proportional Reasoning 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Grade Level Expectation Students will be able to: CMT Correlations

1.2.3 Describe mathematical relationships and situations, involving ratios and computation of whole numbers, in all four operations with using symbols, number sentences and equations.


2.2.18 Write multiplication and division story problems involving basic facts and two- and three-digit

Create models to match a given multiplication number sentence.

Solve multiplication problems using mental math and explain their thinking.

Multiply by a one-digit number. Estimate products. Multiply by a two-digit number. Identify when a problem has too much information or

too little information. Solve problems with extraneous information. Explain at least one multiplication method.









9A. Solve simple story problems involving

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by one-digit numbers to match a given number sentence and vice versa; solve the problems using strategies that include models and arrays and justify the solutions.

2.2.19 Determine and explain in writing when an estimate is appropriate and whether a particular estimation strategy will result in an overestimate or underestimate involving computation with three- and four-digit numbers and money amounts up to $1,000.

2.2.24 Write and solve multi-step contextual problems, including problems with extraneous information and explain how the answers were determined, orally and in writing.

3.1.1 Describe and represent polygons, solids, and other familiar two- and three-dimensional objects.

3.1.2 Compare and classify polygons based on relationships such as parallel or perpendicular lines, symmetry and congruence.


3.3.6 Use calendars and clocks to solve problems and schedule events

addition (with/without regrouping) or subtraction (without regrouping).














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involving elapsed time.







Common Vocabulary: array, area, factor, product, square units, estimate, rounding,




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Teacher Resources


LESSON PLANS

FLIP CHARTS


Part 1 – Unit 7

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Grade: 4

Subject: Math

Course: Metric Measurement

System


Essential Questions and Big IdeasEQ - How is the metric system organized? BI - The metric system is based on the base-ten structure of the place value system.EQ – How is an appropriate unit of measurement chosen? BI – Meaningful measurement and estimations of measurements depend on a personal familiarity with the unit to be measured.

Part 2 – Standards and State FrameworksGeometry and Measurement 3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure. Working With Data: Probability and Statistics 4.2 Analyze data sets to from hypotheses and make predictions.Grade Level Expectations Students will be able to: CMT Correlations3.3.8 Use customary and metric tools and units and non-standard units to estimate, measure and solve problems involving length and perimeter to the nearest quarter-inch or half-centimeter, area, capacity, weight, temperature and volume.

3.3.9 Use estimation strategies to predict reasonable answers to measurement problems and explain the reasoning used orally and in writing.

4.2.3 Discuss, make predictions, and write about patterns and trends in categorical and numerical data that have been represented in a variety of ways.

Convert measurement into metric units. Choose and explain the appropriate units of metric

measures and explain. Solve problems involving metric measures. Measure to the nearest half-centimeter. Estimate lengths and areas by comparing.










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Common Vocabulary millimeter, centimeter, decimeter, meter, kilometer, metric system, square unit, liter, kiloliter, milliliter, volume , capacity, cubic unit, mass, gram, kilogram, milligram, Celsius, Fahrenheit




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Teacher Resources


LESSON PLANS

FLIP CHARTS


Part 1 – Unit 8

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Grade: 4

Subject: Math

Course: Multi-Digit Division

Length of Unit: About 20 Days

Essential Questions and Big IdeaEQ – What is division? BI – Division shows the number of equal groups in a given quantity.EQ – How is a remainder used? BI – The use of a remainder is determined by its context.EQ – How can data be analyzed? BI – Data sets can be analyzed in various ways to provide a sense of the shape of the data, including range, median, and mode.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.2 Represent and analyze quantitative relationships in a variety of ways. 1.3 Use operations, properties, and algebraic symbols to determine equivalence and solve problems.Numerical and Proportional Reasoning 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Working With Data: Probability and Statistics 4.2 Analyze data sets to form hypotheses and make predictions.Grade Level Expectations Students will be able to: CMT Correlations1.2.3 Describe mathematical relationships and situations, involving ratios and computation of whole numbers, in all four operations using symbols, number sentences and equations. If= Then = ___

1.3.4 Represent possible values by using symbols, e.g. variables, to represent quantities in expressions and number sentences. Use number sentences (equations) to model and solve word problems.

1.3.5 Solve problems and demonstrate an understanding of equivalence in mathematical

Explain at least one division method. Give (orally or in writing) a story problem for a given

division problem. Divide whole numbers up to 3 digits by one digit

divisors with and without remainders. Use rounding and estimating to determine if quotients

are reasonable. Explain what a remainder means in the context of a

real world problem. Find the mean, median, mode, and range of a set of

data. Solve problems involving elapsed time and explain

strategies. Convert units of time including seconds, minutes,

hours, days, weeks, months, years, decades, and centuries.

Solve multistep problems.









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situations that reflect the commutative and associative properties of addition and multiplication or whole numbers and the distributive property.

2.2.18 Write multiplication and division story problems involving basic facts and two and three digit by one digit numbers to match a given number sentence and vice versa; solve the problems using strategies that include models and arrays and justify solutions.

2.2.19 Determine and explain in writing when an estimate is appropriate and whether a particular estimation strategy is reasonable or will result in an overestimate or underestimate involving computation with three and four digit numbers and money amounts up to $1,000.

3.3.6 Use calendars and clocks to solve problems and schedule events involving elapsed time..

3.3.7 Write and solve problems involving the conversion of simple measures of time, e.g. minutes to hours, hours to days, and days to weeks and months.

4.2.3 Discuss, make predictions, and write about patterns and trends in categorical and numerical data that have been represented in a

Evaluate and solve one and two step equations. 9A. Solve one-step story problems involving whole numbers and money amounts. Use two- and three-digit numbers in addition and subtraction problems. Use one- and two-digit numbers in multiplication problems.

9B. Solve one-step story problems involving addition or subtraction with extraneous information. Use two-and three-digit numbers in addition and subtraction problems.











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variety of ways.

4.2.4 Determine the range, median, mode, and mean of a set of data and describe characteristics of the data set as typical or average based on those determinations.

Part 3 – Common Unit Assessments

Pre Assessment:Math Expressions Assessment GuideUnit 8 Test Form B (multiple choice)






Common Vocabulary:dividend, divisor, quotient, remainder, equation, mean, median, mode, range, divisible, analog, digital, simplify, term, evaluate, expression, inequality




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Teacher Resources


LESSON PLANS

FLIP CHARTS


Part 1 – Unit 9

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Grade: 4

Subject: Math

Course: Patterns, Functions,

and Graphs


Essential Questions and Big IdeasEQ - How can you describe a pattern or function? BI- Patterns and functions can be described using rules.EQ - What is a coordinate plane used for? BI - A coordinate plane can be used to plot and locate points and distances.

Part 2 – Standards and State FrameworksAlgebraic Reasoning: Patterns and Functions 1.1 Understand and describe patterns and functional relationships.Geometry and Measurement 3.2 Use spatial reasoning, location, and geometric relationships to solve problems.Working With Data: Probability and Statistics 4.1 Collect, organize, and display data using appropriate statistical and graphical methods. 4.2 Analyze data sets to form hypotheses and make predictions.Grade Level Expectations Students will be able to: CMT Correlations1.1.1 Extend and compare numerical and geometric sequences and classify patterns as growing or repeating.

1.1.2 Develop and test generalizations based on observable patterns and relationships and describe the rules for number patterns using equations.

3.2.4 Draw and interpret simple maps with ordered pairs of numbers and/or letters in quadrant one of an x,y coordinate system and find the possible paths between two points.

3.2.5 Analyze geometric reflections (flips), rotations (turns), and

Classify patterns as growing or repeating and explain reasoning.

Extend patterns. Determine a rule for a function table and explain

orally or in writing reasoning. Write an equation to describe a pattern (function

table). Read and plot points on a coordinate grid. Make a line graph. Interpret and make predictions using a line graph and

explain thinking.

17A. Identify and recognize two-dimensional geometric shapes and figures, including number of angles and sides of polygons.


19B. Create bar graphs and pictographs from data in tables and charts.





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translations (slides) or plane figures and describe the relationship to the original figure.

4.1.2 Collect, organize, and represent the data that answers the questions including the use of simple circle graphs, and broken line graphs.

4.2.3 Discuss, make predictions, and write about patterns and trends in categorical and numerical data that have been represented in a variety of ways.

24A. Identify objects that are the same or different by one attribute.

24B. Sort objects into two groups by a common attribute.






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Common Vocabulary:pattern, sequence, repeating pattern, growing pattern, inverse operation, function, rule, coordinate plane, ordered pair, origin, translation, reflection, x-axis, y-axis, line graph





LESSON PLANS

FLIP CHARTS


Part 1 – Unit 10

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Grade: 4

Subject: Math

Course: Fractions


Essential Questions and Big IdeasEQ - What is a fraction? BI - In a fraction, the denominator is the total number of equal parts. BI - In a fraction, the numerator is the number of equal parts.EQ - What are equivalent fractions? BI - Equivalent fractions represent the same quantity.EQ - How do we use fractions in real life? BI - Fractions can be added, subtracted, and multiplied to solve real-world problems.EQ - How can we draw conclusions from data? BI - Probability is a way to draw conclusions from data.

Part 2 – Standards and State FrameworksNumerical and Proportional Reasoning 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Working With Data: Probability and Statistics 4.1 Collect, organize and display data using appropriate statistical and graphical methods. 4.2 Analyze data sets to form hypotheses and make predictions. 4.3 Understand and apply basic concepts of probability.Grade Level Expectations Students will be able to: CMT Correlations2.1.7 Construct and use number lines, pictures and models, including rulers, to determine and identify equivalent ratios and fractions.

2.1.8 Locate, label and estimate (round) fractions with like and unlike denominators of 2, 3, 4, 5, 6, 8 and 10 by constructing and using models, pictures and number lines.

2.1.9 Construct and use models, pictures, and number lines, including rulers, to compare and

Recognize real-world uses of fractions. Construct models and draw pictures to represent

fractions. Locate fractions on a number line, including rulers. Compare and order fractions. Write fractions in equivalent forms. Add and subtract fractions with like and unlike

denominators. Convert improper fractions to mixed numbers and

vice versa. Write fractions in simplest form. Solve simple problems involving fractions and justify

the solutions. Write contextual problems involving addition and

subtraction of fractions and explain.

2A. Relate fractions and decimals to pictorial representations and vice versa.

2B. Relate fractions of regions and sets to pictures and vice versa.

2C. Label and/or shade fractional parts of regions and/or sets.

3A. Relate equivalent fractions to pictorial representations.

4A. Order whole numbers less than 10,000.

4B. Describe magnitude of two- and three-digit whole numbers, fractions, mixed numbers and decimals (tenths).4C. Round two- and three-digit whole numbers in

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order fractional parts of a whole and mixed numbers with like and unlike denominators of 2, 3, 4, 5, 6, 8 and 10.

2.1.10 Construct and use models, pictures, and number lines, including rulers, to identify wholes and parts of a whole (including part of a group or groups) as simple fractions and mixed numbers.

2.1.12 Express a ratio or division problem as a fraction and describe the relationship between the divisor and the remainder written as a fraction.

2.2.20 Use models and pictures to add and subtract fractions with like and unlike denominators of 2, 3, 4, 5, 6, 8 and 10 and match number sentences or equations to the problems.

2.2.21 Identify or write number sentences to solve simple problems involving fractions with like denominators, decimals (tenths) and mixed numbers.

2.2.22 Write contextual problems involving the addition and subtraction of fractions with like denominators, decimals (tenths) and mixed numbers; solve the problems and justify the solutions.

2.2.24 Write and solve multi-step

Find a fractional part of a group, such as 2/3 of 12. Express probabilities as fractions. Identify the characteristics of a circle. Interpret the meaning of fractional parts of a circle

graph. Make line plots and draw conclusions about the data.

context.

4D. Identify points representing two- and three-digit whole numbers, fractions (halves, thirds, fourths) and decimals (tenths) on a number line and vice versa.

7B. Multiply and divide two-digit whole numbers by one digit.


9A. Solve one-step story problems involving whole numbers and money amounts. Use two- and three-digit numbers in addition and subtraction problems. Use one- and two-digit numbers in multiplication problems.



11A. Identify a reasonable estimate to a problem, including estimating change from $1, $5 and $10.


19B. Create bar graphs and pictographs from data in tables and charts.

21A. Identify correct solutions to problems involving elementary notions of probability.

22A. Identify the missing terms in a pattern, or identify rules for a given pattern using whole numbers and attributes.

22B. Extend or complete patterns and state rules for given patterns using whole numbers and

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contextual problems, including problems with extraneous information and explain orally and in writing how the answers were determined.

4.1.1 Pose questions and develop a plan to collect data using observations, surveys and experiments to answer the questions.

4.1.2 Collect, organize, and represent the data that answer the questions using simple circle graphs and broken line graphs.

4.2.3 Discuss, make predictions and write about patterns and trends in categorical and numerical data that have been represented in a variety of ways.

4.2.4 Determine the range, median, mode and mean of a set of data and describe characteristics of the data set as typical or average based on those determinations.

4.3.5 Conduct probability experiments and express the probability based on possible outcomes, e.g., 8 out of 10 tiles chosen were red.

4.3.6 Determine and describe possible combinations, where order does not matter.

attributes.





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Common Vocabulary:fraction, numerator, denominator, unit fraction, improper fraction, mixed number, equivalent fraction, simplify, simplest form, common denominator, least common denominator, probability, likely, equally likely, impossible, outcome center, radius, diameter, circumference, pi, circle graph, frequency table, line plot, plot cluster, gap, outlier




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Teacher Resources


LESSON PLANS

FLIP CHARTS


Part 1 – Unit 11

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Grade: 4

Subject: Math

Course: Three-Dimensional

Figures


Essential Questions and Big IdeasEQ - How can we describe, compare and contrast different objects we find in our world? BI - Objects in our world can be described, compared and contrasted based on their characteristics.

Part 2 – StandardsGeometry and Measurement 3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.

Grade Level Expectations Students will be able to: CMT Correlations3.1.1 Describe and represent polygons, solids, and other familiar two- and three- dimensional objects.

Identify and build three-dimensional figures. Name a prism according to its polygonal base. Compare and contrast three-dimensional figures. Sort and classify three-dimensional solids based on

their characteristics. Describe three-dimensional solids using attributes

such as flat and curved surfaces, and number of faces, vertices, and edges.

Use the properties of prisms to identify nets for solids.








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Common Vocabulary:circle, solid, radius, base, triangular prism, rectangular prism, pentagonal prism, hexagonal prism, octagonal prism, trapezoidal prism cylinder, cube, face, edge, vertex (vertices), sphere, plane figure, solid figure, two-dimensional, three-dimensional, pyramid, cone, net





LESSON PLANS

FLIP CHARTS


Part 1 – Unit 12

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Grade: 4

Subject: Math

Course: Decimal Numbers

Length of Unit: About 5 Days

Essential Questions and Big IdeasEQ - How are decimals and fractions related? BI - Decimals and fractions are two different ways to express the same quantity.EQ - How are decimals related to the place value system? BI - Decimals share the same properties of the whole number place value system.

Part 2 – Standards and State FrameworksNumerical and Proportional Reasoning 2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships. 2.2 Use numbers and their properties to compute flexibly and fluently and to reasonably estimate measures and quantities.Grade Level Expectations Students will be able to: CMT Correlations2.1.11 Use models to represent tenths and hundredths and record the representations using equivalent ratio, fraction, and decimal notation.

2.2.21 Identify or write number sentences to solve simple problems involving fractions with like denominators, decimals (tenths), and mixed numbers.

2.2.23 Estimate a reasonable answer to simple problems involving fractions, mixed numbers, and decimals (tenths).

Represent fractions as decimals. Compare and order decimals (tenths). Round decimals to the nearest whole number or

nearest tenths. Locate decimals (tenths) on a number line. Add and subtract decimals (tenths). Create and interpret models of decimals.


4D. Identify points representing two- and three-digit whole numbers, fractions (halves, thirds, fourths) and decimals (tenths) on a number line and vice versa.

9A. Solve one-step story problems involving whole numbers and money amounts. Use two- and three-digit numbers in addition and subtraction problems. Use one- and two-digit numbers in multiplication problems.



11A. Identify a reasonable estimate to a problem, including estimating change from $1, $5 and $10.


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Common Vocabulary:mixed number, tenths, hundredths, decimal number



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LESSON PLANS

FLIP CHARTS


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Part 1 – Unit 13Grade:

4Subject:

MathCourse:

The U.S. Customary System

Length of Unit: 5 days

Essential Questions and Big IdeasEQ - Why do we use different units and tools to measure? BI - Different sizes and tools of different types allow us to measure with different levels of precision.EQ - How do benchmarks help us? BI - Knowledge of the size of benchmarks assists in measuring.EQ - What are ways you can measure the same object? BI - The same object can be described by using different measurements.

Part 2 – StandardsGeometry and Measurement 3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.Grade Level Expectations Students will be able to: CMT Correlations3.3.8 Use customary and metric tools and units and non-standard units to estimate, measure, and solve problems involving length and perimeter to the nearest quarter-inch or half-centimeter, area, capacity, weight, temperature and volume.

3.3.9 Use estimation strategies to predict reasonable answers to measurement problems and explain the reasoning used orally and in writing.

Measure to the nearest quarter-inch. Add and subtract units of length. Convert among customary units of length, capacity,

and weight. Apply customary units of length to calculate area. Compare units of measure. Identify appropriate units of measure for a given

situation. Use benchmarks, estimate length, capacity, and

weight to explain quantity. Solve problems involving customary units of

measure. Read Fahrenheit temperatures on the thermometer. Solve problems involving Fahrenheit temperatures. Calculate elapsed time.






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Common Vocabulary:inch, foot, yard, mile, square inch (foot, yard, milk), cubic inch (foot, yard), acre, ounce, pound, ton, benchmark, fluid ounce, cup, pint, quart, gallon, Fahrenheit, integer, capacity, weight, volume, area, units of measure, minutes, hours, quarter-hour, half-hour




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Teacher Resources


LESSON PLANS

FLIP CHARTS


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