HHH Curriculum Guide Math Grade 4

Math Curriculum Guide th

4 Grade 2011 – 2012 School Year

Dear Colleague, Please use this curriculum guide to assist in your unit, lesson and assessment plans as you progress through the school year. As additional guidance, included below is further clarrification regarding the “Content Key” symbols used throughout this document: Content Key √ Grade Level Content

Previous Content

Exposure Content for Future Study

Description Content that is part of the current grade level set of standards.

Students should be assessed fully on their ability to demonstrate an understanding of these concepts.

Content that was part of a previous grade level set of standards.

Students should be assessed fully on their ability to demonstrate an understanding of these concepts. You may be able to condense material here based upon your students maintained knowledge of this information.

Content that is part of a future grade level set of standards. Students should be assessed, at an exposure level, on their ability to demonstrate an understanding of these concepts. It is not expected that all students develop a mastery level of understanding of these concepts at this time.

Additionally, in preparation for the upcoming implementation and transistion into the Common Core State Standards (CCSS), it is imperitative that we begin fostering the mathematical mindsets and practices of our students that are embodied within these new standards. Also within these standards, there will be a stronger emphasis placed on specific areas of study. In following the guidance of the New York State Education Department, as a district, we have decided to plan for an intensive focus of study to occur within the topics of the meaning and understanding of fractions and decimals. Time will be made available to develop these units of study (topics 10, 11 and 12) together with district colleagues.

4th Grade

HHH Math Curriculum Guide

Topic 1: Numeration

√

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Sept. 6 & Sept. 12, 5 Days

Essential Understandings

• A number in the thousands can be represented with place-value blocks or a number line. A number can be written in standard form using digits only, expanded form by writing the sum of the value of the digits, or word form using periods from a place-value chart.

• Our number system is based on groups of ten.

Whenever we get 10 in one place value, we move to the next greater place value.

• Place value can be used to compare and order numbers.

• Rounding whole numbers is a process for finding the multiple of 10, 100, and so on closest to a given number.

• Relationships among dollars, dimes, and pennies are a good model for decimal numeration.

• When counting money, it is often easiest to start with the bills or coins that have the greatest value. Counting up is usually an efficient way to make change.

• Some problems can be solved by generating a list of outcomes and organizing that list in a systematic way so all outcomes are accounted for.

Lesson Number and Title

1-1

Thousands

Content Key

3

Essential understandings or items that need supplementation or adjustment Be mindful of the increments on the number line. This can be confusing for students.

& 1-2

Millions

1-3

Comparing and Ordering Whole Numbers

1-4

Rounding Whole Numbers

1-5

Using Money to Understand Decimals

This lesson is a preview to 5.N.1. To address all lesson objectives, be sure to add expanded form to the Interactive Learning Lesson.

3 3

A portion of this lesson previews 5.N.24. When teaching rounding, slowly build to rounding to Millions. Be aware, that some supplementation may be necessary.

3

1-6

Counting Money and Making Change

3

The focus of this lesson is counting up to make change. The focus of this lesson does not include the subtraction algorithm. Students should be encouraged to use money manipulatives to assist them when making change. Supplementation may be necessary. Consider utilizing the center activities for this lesson. Allow opportunities for students to demonstrate an understanding of this concept before moving on.

1-7

Problem Solving: Make and Organized List

3

Need more opportunities to practice combinations and organized lists.

Consider assessing topics 1 and 2 together.

4th Grade

HHH Math Curriculum Guide

√

Topic 2: Adding and Subtracting Whole Numbers

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Sept. 12, Sept. 19 & Sept. 26, 8 Days

Essential Understandings

Lesson Number and Title

3

Since the addition properties were discussed in Third Grade, students should have a foundation for this topic.

3

No Changes

3

Use Center Activities and Intervention Kit for extra practice.

3

No Change

Subtracting Whole Numbers

3

No Changes

2-6

Subtracting Across Zeros

3

More practice problems needed with subtracting with zero’s (larger numbers with zero’s)

2-7

Problem Solving Draw a Picture and Write an Equation

3

No Changes

2-1 • Representing numbers and numerical expressions in equivalent forms can make some calculations easy to do mentally. There is more than one way to do a mental calculation.

• There is more than one way to estimate a sum or difference. Each estimation technique gives a way to replace numbers with other numbers that are close and easy to compute with mentally.

• Some problems have data missing needed to find the answer, and some problems have extra data not needed to solve the problem.

• The standard addition and subtraction algorithms for multi-digit numbers break the calculation into simpler calculations using place value starting with the ones, then the tens, and so on.

• Information can often be shown using a picture or diagram and by writing and completing a number sentence or equation.

Using Mental Math to Add and Subtract

Essential understandings or items that need supplementation or adjustment

Content Key

2-2

2-3

2-4 & 2-5

Consider assessing topics 1 and 2 together.

Estimating Sums and Differences of Whole Numbers Problem Solving Missing or Extra Information Adding Whole Numbers Mixed Problem Solving

4th Grade

√

HHH Math Curriculum Guide

Topic 3: Multiplication Meanings and Facts

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Sept. 26 & Oct. 3, 6 Days Essential Understandings

• Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Repeated addition and arrays are two ways to think about multiplication.

• There are patterns in the products for multiplication facts with factors of 2 and 5.

• Two numbers can be multiplied in any order. The product of any number and 0 is zero. The product of any number and 1 is that number.

• Basic multiplication facts with 3,4,6,7,8,10,11 or 12 as a factor can be found by breaking apart the unknown fact into known facts. The answers to the known facts are added to get the final product. Patterns can be used to find products involving factors of 10, 11, and 12 • Information can often be shown using a picture or diagram and by writing and completing a number sentence or equation.

Lesson Number and Title

Essential understandings or items that need supplementation or adjustment

Content Key

3-1

Meaning of Multiplication Mixed Problem Solving

3

Connecting cubes not provided with 4th grade kit Look at pacing. Possibility of combining lessons within this topic.

3-2

Patterns for Facts

3

No Changes

3-3

Multiplication Problems

3

No Changes

3-4

3 and 4 as Factors

3

No Changes

3-5

6,7 and 8 as Factors

3

No Change

3-6

10,11 and 12 as Factors

3

No Change

3-7

Problem Solving Draw a Picture and Write an Equation

3

No Change

&

Consider assessing topics 3 and 4 together.

4th Grade

HHH Math Curriculum Guide

√

Topic 4: Division Meanings and Facts

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 3, 10 & Oct.17, 7 Days Essential Understandings • Some real-world problems can be solved using division. Sharing and repeated subtraction are two ways to think about division.

• Multiplication and division have an inverse relationship. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact.

• Any number (except 0) divided by itself is equal to 1. Any number divided by 1 is that number.

Zero divided by any number (except 0) is zero.

Zero cannot be a divisor.

• Information in a problem can often be shown using a picture or diagram and by writing and completing a number sentence or equation.

Lesson Number and Title

Essential understandings or items that need supplementation or adjustment

Content Key

4-1

Meanings of Division

3

No Change

4-2

Relating Multiplication and Division

3

Can possibly be combined with 4-3 and 4-4

4-3

Special Quotients

3

No Change

3

No Change

3

No Change

4-4

4-5

Consider assessing topics 3 and 4 together.

Using Multiplication Facts to Find Division Facts Problem Solving Draw a Picture and Write an Equation

4th Grade

HHH Math Curriculum Guide

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Topic 5: Multiplying by 1-Digit Numbers

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 17 & Oct. 24, Oct. 31, 9 Days Essential Understandings

• Basic facts and place-value patterns can be used to find products when a factor is 10 or 100.

• There is more than one way to do a mental calculation.

• Rounding and substituting compatible numbers are two ways to estimate products.

• Answers to problems should always be checked for reasonableness. This can be done with estimation when appropriate and checking the answer against the question and conditions in the problem.

• There is an expanded algorithm for multiplying where numbers are broken apart using place value and the parts are used to find partial products. The partial products are then added together to find the product.

• The standard algorithm for multiplying three-digit by one-digit numbers is just an extension to the hundreds place of the algorithm for multiplying twodigit by one-digit numbers.

• Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Some problems can be solved by writing and completing a number sentence.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

5-1

Multiplying by 3 Multiples of 10 and 100

No Change

5-2

Using Mental Math to Multiply

3

Emphasize the definition of a Compatible Number as numbers that are easy to work with mentally.

5-3

Using Rounding to Estimate

3

Answers may vary. Create guidelines with your students when using rounding to estimate.

5-4

Problem Solving Reasonableness

3

Answers may vary. Create guidelines with your students when using rounding to estimate.

5-5

Using and Expanded Algorithm

3

Represent partial products both vertically and horizontally to make connections to previous “break-apart” lessons.

5-6

Multiplying 2-Digit by 1-Digit Numbers

3

No Change

5-7

Multiplying 3-Digit by 1-Digit Numbers

3

No Change

5-8

Problem Solving Draw a Picture and Write an Equation

3

No Change

4th Grade

HHH Math Curriculum Guide

√

Topic 6: Patterns and Expressions

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 31 & Nov. 7, 5 Days

Essential Understandings • Some mathematical phrases can be represented using a variable in an algebraic expression. The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation.

• Patterns can sometimes be used to identify a relationship between two quantities. Some realworld quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

• Some problems can be solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem.

Lesson Number and Title

Essential understandings or items that need supplementation or adjustment

Content Key

6-1

Variables and Expressions

3

Carefully monitor practice questions for this topic. Students can use inverse operations when asked to divide with two-digit divisors.

6-2

Addition and Subtraction Expressions

3

No Change

6-3

Multiplication and Division Expressions

3

Supplementation may be necessary. Expose children to “Input/Output” examples.

6-4

Problem Solving Use Objects and Reasoning

3

No Change

4th Grade

HHH Math Curriculum Guide

√

Topic 7: Multiplying by 2-Digit Numbers

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Nov. 14 & Nov. 21, 8 Days

Essential Understandings • Basic facts and place-value patterns can be used to mentally multiply a 2-digit number by a multiple of 10, 100, or 1,000.

• Rounding and substituting compatible numbers are two ways to estimate products.

• The expanded algorithm for multiplying by 2digit numbers is just an extension of the expanded algorithm for multiplying with 1-digit numbers.

• The standard algorithm for multiplying 2-digit by 2-digit numbers is just an extension of the algorithm for multiplying multi-digit numbers by one-digit numbers.

• The standard algorithm for multiplying 2-digit by 2-digit numbers is just an extension of the algorithm for multiplying multi-digit numbers by one-digit numbers.

• The standard multiplication algorithm is a shortcut for the expanded algorithm. Regrouping is used rather than showing all partial products.

• Sometimes the answer to one problem/question is needed to find the answer to another problem/question.

Lesson Number and Title

Essential understandings or items that need supplementation or adjustment

Content Key

7-1

Using Mental Math to Multiply 2-Digit Numbers

3

No Change

7-2

Estimating Products

3

Answers may vary. Use reasonableness when rounding.

7-3

Arrays and an Expanded Algorithm

3

Extra time may be necessary. A variety of methods are introduced in one lesson.

7-4

Multiplying 2-Digit Numbers by Multiples of Ten

3

No Change

7-5

Multiplying 2-Digit by 2-Digit Numbers

3

No Change

7-6

Special Cases

3

No Change

7-7

Problem Solving Two-Question Problems

3

No Change

4th Grade

HHH Math Curriculum Guide

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Topic 8: Dividing by 1-Digit Divisors

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Nov. 28 & Dec. 5, 10 Days

Essential Understandings

• Basic facts and place-value patterns can be used to divide multiples of 10 and 100 by 1-digit numbers • Substituting compatible numbers is an efficient technique for estimating quotients.

• The remainder when dividing must be less than the divisor. The nature of the question asked determines how to interpret and use the remainder.

• The sharing interpretation of division can be used to model the standard division algorithm.

• The standard division algorithm breaks the calculation into simpler calculations using basic facts, place value, the relationship between multiplication and division, and estimation.

• The relationship between multiplication, division, and estimation can help determine the place value of the largest digit in a quotient.

• Every counting number is divisible by 1 and itself, and some counting numbers are also divisible by other numbers.

• Some counting numbers have exactly two factor; others have more than two.

• Some problems can be solved by first find and solving a sub-problem(s) and then using that answer(s) to solve the original problem.

Lesson Number and Title

Essential understandings or items that need supplementation or adjustment

Content Key

8-1

Using Mental Math to Divide

3

No Change

8-2

Estimating Quotients

3

Compatible numbers are numbers that are easier to work with.

8-3

Dividing with Remainders

3

No Change

8-4

Connecting Models and Symbols

3

No Change

8-5

Dividing 2-Digit by 1-Digit Numbers

3

No Change

8-6

Dividing 3-Digit by 1-Digit Numbers

3

No Change

8-7

Deciding Where to Start Dividing

3

No Change

8-8

Factors

3

No Change

8-9

Primate and Composite Numbers

3

No Change

8-10

Problem Solving Multiple-Step Problems

3

No Change

4th Grade

HHH Math Curriculum Guide

Topic 9: Lines, Angles and Shapes

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Dec. 12 & Dec. 19, 8 Days Essential Understandings • Point, line and plane are the core attributes of space objects, and real-world situations can be used to think about these attributes.

• Line segments and rays are sets of points that describe parts of lines, shapes, and solids.

Angles are formed by two intersecting lines or by rays with a common endpoint and are classified by size.

• Then unit for measuring the size of the opening of an angle is 1 degree.

• Two-dimensional or plan shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles.

• Two-dimensional or plan shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles.

• Two-dimensional or plan shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles.

• Commonalities in attributes of objects or situations can be found and used to make generalizations about relationships.

Lesson Number and Title

Content Key

9-1

Points, Lines, and Planes

3

9-2

Line Segments, Rays, and Angles

3

9-3

Measuring Angles

3

9-4

Polygons

3

9-5

Triangles

3

9-6

Quadrilaterals

3

9-7

Problem Solving Make and Test Generalizations

3

Essential understandings or items that need supplementation or adjustment

4th Grade

HHH Math Curriculum Guide

Topic 14: Area and Perimeter

√

Grade Level Content Previous Content Exposure Content for Future Study

Week of Dec. 19, 2 Days

Essential Understandings • The amount of space inside a shape is its area, and area can be estimated or found using square units.

• The distance around a figure is its perimeter.

Formulas exist for finding the perimeter of some polygons.

Lesson Number and Title

Content Key

14-1

Understanding Area

3

14-6

Perimeter

3

Essential understandings or items that need supplementation or adjustment

4th Grade

HHH Math Curriculum Guide

Topic 15: Solids

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 2 & Jan. 9, 5 Days

Essential Understandings • Three-dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and vertices. Many everyday objects closely approximate standard geometric solids.

• Some solids can be shown as a plane shape made up of other shapes. The plane shape can be folded to construct the solid.

• Views of solids from different perspectives can sometimes be used to completely describe the solid.

• Some problems can be solved by identifying elements that repeat in a predictable way.

Lesson Number and Title

Content Key

15-1

Solids

15-2

Views of Solids: Nets 3

15-3

Views of solids: Perspective

3

15-5

Problem Solving Look for a Pattern

3

Essential understandings or items that need supplementation or adjustment

3

Students should be exposed to these understandings only

4th Grade

HHH Math Curriculum Guide

Topic 19: Transformations, Congruence and Symmetry

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan.9 & Jan. 16, 6 Days

Essential Understandings

• Shapes in the plane can be translated to another position in the plane. The translated image is the same size and shape as the original figure.

• Shapes in the plane can be reflected across a line.

The reflected image is the same size and shape as the original figure.

• Shapes in the plane can be rotated around a point.

The rotated image is the same size and shape as the original figure.

• Congruent figures remain congruent through translations, reflections, and rotations.

• Some shapes can be reflected across one or more lines passing through the shape so the shape folds onto itself exactly.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

19-1

Translations

3

19-1, 19-2, & 19-3 were combined in 2011

19-2

Reflections

3

19-1, 19-2, & 19-3 were combined in 2011

19-3

Rotations

3

19-1, 19-2, & 19-3 were combined in 2011

19-4

Congruent Figures

19-4 & 19-5 were combined in 2011

19-5

Line Symmetry

19-4 & 19-5 were combined in 2011

4th Grade

HHH Math Curriculum Guide

Topic 10: Understanding Fractions

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 16 & Jan. 23, 7 Days Essential Understandings • A fraction describes the division of a whole (region, set, segment) into equal parts. A fraction is relative to the size of the whole.

• A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided.

• The relationship between multiplication, division, and estimation can help determine the place value of the largest digit in a quotient.

• The same fractional amount can be represented by an infinite set of different by equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.

• If two fractions have the same denominator, the fraction with the greater numerator is the greater fraction. If two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.

• Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to the other numbers.

• Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

10-1

Regions and Sets

3

10-2

Fractions and Division

3

10-3

Estimating Fractional Amounts

3

10-3, 10-7, & 10-8 were combined in 2011

10-4

Equivalent Fractions

3

10-4 & 10-9 were combined in 2011

10-7

Comparing Fractions

3

10-3, 10-7, & 10-8 were combined in 2011

10-8

Ordering Fractions

3

10-3, 10-7, & 10-8 were combined in 2011

10-9

Problem Solving Writing to Explain

3

10-4 & 10-9 were combined in 2011

10-1 & 10-2 were combined in 2011

&

4th Grade

HHH Math Curriculum Guide

Topic 11: Adding and Subtracting Fractions

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Grade Level Content Previous Content Exposure Content for Future Study

Week of Jan. 30, 1 Day Essential Understandings

Lesson Number and Title

• To add or subtract fractions with like denominators, add or subtract the numerators and write the sum or difference over the common denominator

Adding and Subtracting Fractions 11-1 with Like Denominators

Content Key

3

Essential understandings or items that need supplementation or adjustment

4th Grade

HHH Math Curriculum Guide

Topic 12: Understanding Decimals

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 30 & Feb. 6, 6 Days Essential Understandings

• Decimal numeration is just an extension of whole number numeration.

• Place value can be used to compare and order numbers.

• A decimal is another name for a fraction.

• Each fraction, mixed number, and decimal can be associated with a unique point on the number line.

• Information in a problem can often be shown using a diagram and used to solve the problem.

Lesson Number and Title 12-1

Decimal Place Value

12-2

Comparing and Ordering Decimals

12-3

Fractions and Decimals

Fractions and 12-4 Decimals on the Number Line Mixed Numbers and 12-5 Decimals on the Number Line 12-6

Problem Solving Draw a Picture

Content Key

Essential understandings or items that need supplementation or adjustment

3

Read and write decimals – compare only to hundredths

3

3

3

3

4th Grade

HHH Math Curriculum Guide

Topic 13: Operations with Decimals

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Feb. 6 & Feb. 13, 5 Days

Essential Understandings

• Rounding decimals is a process for finding the multiple of 0.1, 0.01, etc., closest to a given number.

• Models and algorithms for adding or subtracting multi-digit decimals are just an extension of models and algorithms for adding or subtracting multi-digit whole numbers.

Lesson Number and Title

Rounding Decimals Mixed Problem Solving Modeling Addition 13-3 and Subtraction of Decimals 13-1

13-4

Adding and Subtracting Decimals

Content Key

Essential understandings or items that need supplementation or adjustment

3

3

13-3 & 13-4 were combined in 2011

3

13-3 & 13-4 were combined in 2011

4th Grade

HHH Math Curriculum Guide

√

Topic 16: Measurement, Time and Temperature

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Feb. 27 & Mar. 5, 9 Days Essential Understandings

• Length can be estimated and measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Capacity is a measure of the amount of liquid a container can hold. Capacity can be measured in different systems (customary, metric) and using different units in each system that are related to each other.

• The weight of an object is a measure of how heavy an object is.

• Relationships between customary measurements units can be expressed as a ratio (e.g., 12 inches to 1ft or 12 in. = 1ft).Relationships exist that enable you to convert between customary units of the same attribute by multiplying or dividing.

• Length can be estimated and measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Capacity is a measure of the amount of liquid a container can hold. Capacity can be measured in different systems (customary, metric) and using different units in each system that are related to each other.

• Mass is a measure of the quantity of matter in an object.

Weight and mass are different measures.

• Time can be expressed using different units that are related to each other.

• The duration of an event can be measured if one knows that start and end times for the event.

Lesson Number and Title

Content Key

16-1

Using Customary Units of Length

16-2

Customary Units of Capacity

16-3

Units of Weight

16-4

Changing Customary Units

16-5

Using Metric Units of Length

16-6

Metric Units of Capacity

3

16-7

Units of Mass

3

3

Review of 3rd grade measurement

3

3 16-9

Units of Time

16-10 Elapsed Time

Essential understandings or items that need supplementation or adjustment

3

Equivalents without memorizing (know inches & feet)

16-9 & 16-10 were combined in 2011. Don’t cross AM and PM. 16-9 & 16-10 were combined in 2011. Don’t cross AM and PM.

4th Grade

HHH Math Curriculum Guide

Topic 17: Data and Graphs

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Grade Level Content Previous Content Exposure Content for Future Study

Week of Mar. 5 & Mar. 12, 4 Days Essential Understandings

• Some questions can be answered using a survey.

An appropriately selected sample can be used to make predictions about a population.

• Each type of graph is most appropriate for certain kinds of data. Line graphs made from ordered pairs can be used to show a relationship between two sets of data.

• Some problems can be solved by making, reading, and analyzing a graph.

Lesson Number and Title

Content Key

17-1

Data from Surveys

3

17-2

Interpreting Graphs

3

17-5

Line Graphs

3

17-10

Problem Solving Making a Graph

3

Essential understandings or items that need supplementation or adjustment

Coach resources may be helpful

4th Grade

HHH Math Curriculum Guide

Topic 18: Adding and Subtracting Fractions

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Grade Level Content Previous Content Exposure Content for Future Study

Week of Mar. 12, 1 Day Essential Understandings • A solution to an inequality is a value that makes the inequality true.

Lesson Number and Title 18-4

Understanding Inequalities

Content Key

3

Essential understandings or items that need supplementation or adjustment

4th Grade

HHH Math Curriculum Guide

Topic 20: Probability

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Mar. 12 & Mar. 19, 7 Days

Essential Understandings

• Counting techniques exist for finding the number of possible combinations.

• The outcomes of an event can be represented pictorially using a tree diagram and counted to find the number of possible outcomes.

• The chance or likelihood of an event occurring, called its probability, can be expressed as a number between 0 and 1 inclusive.

• Some problems can be solved by reasoning about the conditions in the problem.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

20-1

Finding a Combination

3

20-1 and 20-2 were combined in 2011

20-2

Outcomes and Tree Diagrams

3

20-1 and 20-2 were combined in 2011

20-3

Writing Probability as a Fraction

3

20-4

Problem Solving Use Reasoning

3

4th Grade

HHH Math Curriculum Guide

Post NYS Assessment Topics: 14, 15 & 19

√

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of May 14 & May 21, 8 Days Essential Understandings • The amount of space inside a shape is its area, and area can be estimated or found using square units. Formulas exist for finding the area of some polygons.

• The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found. Area can be estimated in square units.

• The formula for the area of a parallelogram is derived from the formula for the area of a rectangle.

• The formula for the area of a triangle is derived from the formula for the area of a parallelogram.

• There are relationships between the perimeter and area of a polygon.

• There are relationships between the perimeter and area of a polygon.

• Some problems can be solved by breaking apart or changing the problem into simpler ones.

Recording information in a table can help one understand and solve some problems.

• Volume is the amount of space inside a solid figure. Volume can be measured by counting the number of cubic units needed to fill a threedimensional object.

• Some shapes can be rotated around a point in less than one complete turn and turn onto itself exactly • Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

14-2

Area of Squares and Rectangles

3

Information to be discussed after the assessment

14-3

Area of Irregular Shapes

3

Information to be discussed after the assessment

14-4

Area of Parallelograms

3

Information to be discussed after the assessment

14-5

Area of Triangles

Information to be discussed after the assessment

14-7

Same Perimeter, Different Area

Information to be discussed after the assessment

14-8

Same Area, Different Perimeter

3

Information to be discussed after the assessment

Problem Solving Solve a Simpler 14-9 Problem and Make a Table

3

Information to be discussed after the assessment

15-4

Volume

Information to be discussed after the assessment

19-6

Rotational Symmetry

Information to be discussed after the assessment

19-7

Problem Solving Draw a Picture

3

Information to be discussed after the assessment

4th Grade

HHH Math Curriculum Guide

Post NYS Assessment Topics: 10, 11 & 13

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of May 21 & May 28, 6 Days Essential Understandings • A fraction can be expressed in its simplest form by dividing the numerator and denominator by common factors until there are no common factors other than 1.

• Fractional amounts greater than 1 can be represented using a whole number and a fraction.

Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction equals 1.

• Line segments and rays are sets of pints that describe parts of lines, shapes, and solids.

Angles are formed by two intersecting lines or by rays with a common endpoint and are classified by size.

• To subtract with unlike denominators, change to an equivalent calculation with like denominators.

• Information can often be shown using a diagram by writing and completing a number sentence or equation.

• Techniques for estimating calculations with whole numbers can also be used to estimate calculations with decimals.

• Multiplying a whole number by a decimal is similar to multiplying two whole numbers.

Estimation and place value can determine the location of the decimal point in the product.

• Dividing a decimal by a whole number is similar to dividing two whole numbers. Estimation and place value can determine the location of the decimal point in the quotient.

• Some problems can be solved by making a reasoned first try for what the answer might be, and then by using additional reasoning to arrive at the correct answer.

Lesson Number and Title 10-5

10-6

11-2

11-3

11-4

13-2

13-5

Content Key

Fractions in Simplest Form Improper Fractions and Mixed Numbers Mixed Problem Solving Adding Fractions with Unlike Denominators Subtracting Fractions with Unlike Denominators Problem Solving Draw a Picture and Write an Equation Estimating Sums and Difference of Decimals Multiplying a Whole Number by a Decimal

Essential understandings or items that need supplementation or adjustment Information to be discussed after the assessment

Information to be discussed after the assessment

Information to be discussed after assessment

Information to be discussed after assessment

3

Information to be discussed after the assessment

3

Information to be discussed after the assessment

3

Information to be discussed after the assessment

13-6

Dividing a Decimal by a Whole Number

3

Information to be discussed after the assessment

13-7

Problem Solving Try, Check, and Revise

3

Information to be discussed after the assessment

4th Grade

HHH Math Curriculum Guide

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Post NYS Assessment Topics: 16 & 17

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of June 4 & June 11, 8 Days

Essential Understandings • Relationships between metric units can be expressed as a ratio (e.g., 10mm to 1 cm or 1 mm = 1 cm). Relationships exist that enable you to convert between metric units of the same attribute by multiplying or dividing.

• Temperature can be expressed using degrees Fahrenheit or Celsius. Temperature change can be found using addition or subtraction.

• Some problems with the initial data point unknown can be solved by starting the end result and by reversing the steps and processes work backward to find the initial data point.

• Each type of graph is most appropriate for certain kinds of data. A line plot organizes data on a number line and is useful for showing visually how data are distributed.

• The Cartesian Coordinate System is a scheme that uses perpendicular number lines intersecting at zero on each axis to name the location of points in the plane.

• There is more than one way to describe the center or typical number in a numerical data set. The mean is the average of a set of numerical data.

• There is more than one way to describe the center or typical number in a numerical data set; median and mode are two ways. Range is one way to describe how data are distributed.

• Each type of graph is most appropriate for certain kinds of data. Stem-and-leaf plots can be used to show how data are distributed.

• Each type of graph is most appropriate for certain kinds of data. A circle graph is most appropriate for certain kinds of data. A circle graph shows how portions of a set of data compare with the whole.

Lesson Number and Title 16-8

Content Key

Changing Metric Units

16-11 Temperature

Essential understandings or items that need supplementation or adjustment Information to be discussed after the assessment

3

Information to be discussed after the assessment

16-12

Problem Solving Work Backwards

3

Information to be discussed after the assessment

17-3

Line Plots

3

Information to be discussed after the assessment

17-4

Ordered Pairs

3

Information to be discussed after the assessment

17-6

Mean

Information to be discussed after the assessment

17-7

Median, Mode, and Range

Information to be discussed after the assessment

17-8

Stem-and-Leaf Plot

Information to be discussed after the assessment

17-9

Reading Circle Graphs

3

Information to be discussed after the assessment

4th Grade

HHH Math Curriculum Guide

Post NYS Assessment Topic 18

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Grade Level Content Previous Content Exposure Content for Future Study

Weeks of June 11 & June 18, 4 Days Essential Understandings • Two algebraic expressions are equal if the value of each expression is the same when each variable is replaced with its assigned number and the resulting calculations are completed.

• A solution to an equation is a value of the unknown (or unknowns) that makes the equation true. Equations of the form x + a = b or x - a = b can be solved using properties of equality and inverse operations.

• Equations of the form ax = b or ______ = b (a ≠ 0) can be solved using properties of equality and inverse operations.

• Some problems with the initial data point unknown can be solved by starting with the end result and, by reversing the steps and processes, work backward to find the initial data point.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

18-1

Equal or Not Equal

Information to be discussed after the assessment

18-2

Solving Addition and Subtraction Equations

Information to be discussed after the assessment

18-3

Solving Multiplication and Division Equations

Information to be discussed after the assessment

18-5

Problem Solving Work Backward

3

Information to be discussed after the assessment