HHH Curriculum Guide Math Grade 5

Math Curriculum Guide th

5 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

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.

Previous Content 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 Exposure Content for Future Study 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 7, 9 and 10) together with district colleagues.

5th Grade

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HHH Math Curriculum Guide

Topic 1: Numeration

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Sept. 6 & Sept. 12, 7 Days Essential Understandings

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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. Numbers can be used to tell how many.

Place value can be used to compare and order numbers.

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

Lesson Number and Title

1-1

Place Value

1-2

Comparing and Ordering Whole Numbers Mixed Problem Solving

1-3

Decimal Place Value

1-4

Comparing and Ordering Decimals

1-5

Problem Solving Look for a Pattern

Content Key

Essential understandings or items that need supplementation or adjustment Place value in the billions is beyond grade level standards. Expose students to place value in the billions.

Decimal place value in the millionths place is beyond grade level standards. Expose students to decimal place value in the millionths.

Some students may need a decimal place value chart in order to complete the lesson.

5th Grade

HHH Math Curriculum Guide

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Topic 2: Adding and Subtracting Whole Numbers and Decimals

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Sept. 12, Sept. 19 & Sept.26, 10 Days Essential Understandings

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There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expression so the calculation is easy to do mentally.

Rounding whole numbers is a process for finding the multiple of 10, 100, etc, or of 0.1, 0.01, etc., closest to a given number.

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 sequences of numbers or objects repeat or grow in predictable ways.

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.

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.

Adding or subtracting multi-digit decimals is similar to adding or subtracting multi-digit whole numbers.

Some problems can be solved by first finding and solving a subproblem(s) and then using that answer(s) to solve the original problem.

Lesson Number and Title

2-1

Mental Math Mixed Problem Solving

2-2

Rounding Whole Numbers and Decimals

2-3

Estimating Sums and Diffferences

2-4

Problem Solving Draw a Picture and Write an Equation

2-5

Adding and Subtracting Mixed Problem Solving

2-6

Adding Decimals

Content Key

Some students may have difficulty with the concept of compatible numbers.

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2-8

Rounding whole numbers should be a brief review as it is prior content. Focus of the lesson should be on rounding decimal numbers.

Be ready to accept multiple answers as this lesson asks students to use a variety of estimation strategies. It also does not give students a specific place to round to.

Before teaching this lesson, teachers should review models of bar diagrams. Students will have exposure to this problem solving strategy from prior grades.

Lessons 2-6 and 2-7 may be combined depending on readiness level of the students.

& 2-7

Essential understandings or items that need supplementation or adjustment

Subtracting Decimals

Problem Solving Multiple-Step Problems

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Before teaching this lesson, teachers should review models of bar diagrams. They can be reviewed with students if necessary. Students will have exposure to this problem solving strategy from prior grades.

5th Grade

HHH Math Curriculum Guide

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Topic 3: Multiplying Whole Numbers

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 3 & Oct. 14, 9 Days Essential Understandings

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The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms.

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

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

The standard multiplication algorithm breaks the calculation into simpler calculations using place values starting with the ones, then the tens, and so on. Operations are done in a numerical expression in an agreed upon order.

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

Different numerical expressions can have the same value. Or, the value of the one expression can be less than (or greater than) the value of the other expressions.

Some numbers can be represented using a base number and an exponent.

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 or equation.

Lesson Number and Title

3-1

Multiplication Properties

3-2

Using Mental Math to Multiply

3-3

Estimating Products

3-4

Multiplying by 1-Digit Numbers

3-5

Multiplying 2-Digit by 2-Digit Numbers

3-6

Multiplying Greater Numbers

3-7

Exponents

3-8

Problem Solving Draw a Picture and Write and Equation

Content Key

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Essential understandings or items that need supplementation or adjustment

Patterns of multiplication were taught in prior grades. Patterns of multiplication with 3 digits are grade level content.

Some students may have difficulty with the concept of compatible numbers.

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The Partial Products Method is introduced in fourth grade. Students may need to review this method prior to the lesson. A variety of methods may be introduced at this time (traditional, lattice, etc.)

Teachers should supplement problems containing 3 digit by 3 digit multiplication.

This content can be moved to Post May. However this content is part of the CCSS and will be assessed in the future.

Teachers may have to supplement extra problems if students require extra practice.

5th Grade

HHH Math Curriculum Guide

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Topic 4: Dividing with 1-Digit Divisors

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 17 & Oct. 24, 10 Days Essential Understandings

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Basic facts and place-value patterns can be used to divide multiples of 10, 100 and so forth by one-digit numbers.

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

Answers to problems should always be checked for reasonableness, and this can be done in different ways. Two ways are to use estimation when appropriate and to check the answer against the question and conditions in the problem.

Different numerical expressions can have the same value. Or, the value of the one expression can be less than or greater than the value of another expression. The sharing interpretation of division and money can be used to model the standard division algorithm.

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

Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

Every counting number is divisible by 1 and itself, an some numbers are also divisible by other numbers. There are rules that help to determine if a number is divisible by another.

Operations are done in a numerical expression in an agreed upon order.

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 or equation.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

4-1

Dividing Multiples of 10 and 100

4-2

Estimating Quotients

Some students may have difficulty with the concept of compatible numbers.

4-3

Problem Solving Reasonableness

Teachers may have to supplement extra problems if students require extra practice.

4-4

Connecting Models and Symbols

4-5

Dividing by 1-Digit Divisors

4-6

Zeros in the Quotient

4-7

Understanding Factors

4-8

Prime and Compsite Numbers

4-9

Problem Solving Draw a Picture and Write and Equation

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Students are exposed to connecting models and symbols in prior grades. Students are using amounts appropriate for their grade level.

All content in this lesson is grade level. Lesson may need to be taught on separate days so that more time can spent understanding divisibility rules and their importance in prime factorization.

5th Grade

HHH Math Curriculum Guide

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Topic 5: Dividing with 2-Digit Divisors

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Oct. 31, Nov. 7 & Nov. 14, 5 Days Essential Understandings

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Patterns can be used to mentally multiply decimals by 10, 100, and 1000.

There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.

Some problems can be solved by first finding and solving a subproblem(s) and then using that answer(s) to solve the original problem.

Dividing by 2-digit divisors is just an extension of the steps for dividing with1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

Patterns can sometimes be used to identify the relationship between quantities. Dividing by 2-digit divisors is just an extension of the steps for dividing with1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients.

Dividing with multi digit divisors is just an extension of the steps for dividing with1 and 2-digit divisors. Estimation and place value can help determine the placement of digits in the quotient.

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

Lesson Number and Title

5-1

Using Patterns to Divide

5-2

Estimating Quotients with 2-Digit Divisors

5-3

Problem Solving Multiple-Step Problems

5-4

Dividing by Multiples of 10

5-5

1-Digit Quotients

5-6

2-Digit Quotients

5-7

Estimating and Dividing with Greater Numbers

5-8

Problem Solving Missing or Extra Information

Content Key

Essential understandings or items that need supplementation or adjustment

Some students may have difficulty with the concept of compatible numbers.

The lesson requires students to use a calculator.

Teachers must have a set of class calculators for this lesson. Also, the lesson requires the students to complete several steps. Teachers may skip the 1st step and begin with the calculators instead of rounding first.

Homework will need to be modified as well.

Students must also have calculators to complete the homework.

5th Grade

HHH Math Curriculum Guide

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Topic 7: Multiplying and Dividing Decimals

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Nov. 14, Nov. 21 & Nov. 28, 10 Days Essential Understandings

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Patterns can be used to mentally multiply decimals by 10, 100, and 1,000.

The steps for multiplying whole numbers by decimals are similar to the steps for multiplying two whole numbers. Place value determines the placement of the decimal point in a product.

Rounding and compatible numbers can be used to estimate the product of a whole number and a decimal.

Steps for multiplying decimals are similar to steps for multiplying whole numbers. Place value determines the placement of the decimal point in a product. The product of two decimals less than one is less than either factor.

Place-value patterns can be used to mentally divide decimals by 10, 100, and 1,000.

Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity.

Patterns can sometimes be used to identify the relationship between quantities. The standard division algorithm, which involves using place value to break the calculation into smaller simpler calculations, can be extended to dividing decimals by whole numbers.

Substituting compatible numbers is an efficient technique for estimating quotients.

To divide decimals by decimals, change to an equivalent calculation by multiplying the dividend and the divisor by a power of 10 so the divisor is a whole number. Then divide using the standard algorithm.

Some problems can be solved by first finding and solving a subproblem(s) and then using that answer(s) to solve the original problem.

Lesson Number and Title

7-1

Multiplying Decimals by 10, 100, or 1,000

7-2

Multiplying a Decimal by a Whole Number

7-3

Estimating the Product of a Decimal and a Whole Number

7-4

Multiplying Two Decimals

7-5

Dividing Decimals by 10,100 or 1,000

7-6

Dividing a Decimal by a Whole Number

7-7

Estimation: Decimals Divided by Whole Numbers

7-8

Dividing a Decimal by a Decimal

7-9

Problem Solving Multiple-Step Problems

Content Key

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Essential understandings or items that need supplementation or adjustment

5th Grade

HHH Math Curriculum Guide

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Topic 6: Variables and Expressions

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Nov. 28, Dec. 5 & Dec. 12, 8 Days Essential Understandings • •

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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 that results.

Some mathematical phrases can be represented using a variable in an algebraic expression.

Numerical and algebraic expressions can involve more than one operation. The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation that results. The value of an algebraic expression can be found by replacing the variable(s) with given number(s) and doing the calculation that results.

The distributive property of multiplication over addition lets you multiply a sum by multiplying each addend separately and then finding the sum of the products.

To simplify a numerical expression, first compute within parentheses.

Then do any multiplication and division calculations followed by any addition and subtraction calculations.

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

6-1

Variables and Expressions

6-2

Patterns and Expressions

6-3

More Patterns and Expressions

6-4

Distributive Property

6-5

Order of Operations Mixed Problem Solving

6-6

Problem Solving Act it Out and Use Reasoning

Content Key

Essential understandings or items that need supplementation or adjustment

Teachers may need to supplement with more input/output tables for students to practice this skill.

Many of the examples in this lesson are too similar. Teachers may want to give a variety of examples so that students can see how the format of expressions can change.

Subtraction with compensation may be challenging for some students. Expose students to this strategy so that they are able to use a variety of methods.

Teachers may want to move this lesson to the beginning of the topic so that students are familiar with the use of parenthesis

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5th Grade

HHH Math Curriculum Guide

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Topic 8: Shapes

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Dec. 12 & Dec. 19, 8 Days Essential Understandings

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Point, line, line segment, and plane are the core attributes of space objects, and real-world situations can be used to think about these attributes. Some sequences of numbers or objects repeat or grow in predictable ways.

Rays are sets of points that can be used to describe parts of lines. Angles are formed by two intersecting lines or by two rays with a common end point and angles are classified by size.

Plane shapes have any 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

8-1

Basic Geometric Ideas

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8-2

Measuring and Classifying Angles

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8-3

Polygons

8-4

Triangles

8-5

Quadrilaterals

8-6

Problem Solving Make and Test Generalizations

Essential understandings or items that need supplementation or adjustment

5th Grade

HHH Math Curriculum Guide

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Topics 9 & 10: Fractions and Decimals, Adding and Subtracting Fractions and Mixed Numbers

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 3, Jan. 10 & Jan 17, 13 Days Essential Understandings

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A fraction describes to 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 what is the whole.

Fractions greater than 1 can be named using a whole number of an improper fraction.

Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number.

There is more than one way to compare and order fractions and mixed numbers. Number sense and equivalent fractions can be used to compare and order fractions and mixed numbers.

One is a common factor of any two counting numbers. Some counting numbers have more than two factors. The greatest common factor (GCF) is the largest number that divides two or more numbers.

A fraction is the simplest form when 1 is the only common factor of the numerator and denominator.

A fraction and the related decimal can be associated with a unique point on the number line.

Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand To add or subtract fractions with like denominators, add or subtract the numerators and write the sum or difference over the common denominator All non-zero whole numbers have common multiples, including a least one. Sometimes the least common multiple of two numbers is one of the numbers.

Lesson Number and Title

Content Key

9-1

Meanings of Fractions

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9-2

Fractions and Division

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9-3

Mixed Numbers and Improper Fractions

9-4

Equivalent Fractions

9-5

Comparing and Ordering Fractions and Mixed Numbers

9-6

Common Factors and Greater Common Factor

9-7

Fractions in Simplest Form Mixed Problem Solving

9-10

Fractions and Decimals on the Number Line

9-11

Problem Solving Writing to Explain

10-1

Adding and Subtracting Fractions with Like Denominators

10-2

Common Multiples and Least Common Multiple

Essential understandings or items that need supplementation or adjustment

5th Grade

HHH Math Curriculum Guide

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Topic 12: Perimieter and Area

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 23, 5 Days Essential Understandings

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Length can be measured in different systems (customary, Metric) and using different units in each system that are related to each other. Using smaller units of measure results in greater accuracy when measuring length. Length can be estimated in different measurement systems.

The distance around a figure is its perimeter. Formulas exist for finding the perimeter of some polygons.

Lesson Number and Title

12-1

Using Customary Units of Length

12-2

Using Metric Units of Length

12-3

Perimeter

Content Key

Essential understandings or items that need supplementation or adjustment

5th Grade

HHH Math Curriculum Guide

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Topic 13: Solids

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Jan. 30, 5 Days Essential Understandings

Lesson Number and Title 13-1

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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 have flat surfaces in the shape of a polygon.

The shape of a solid can sometimes be determined by analyzing different views of the solid.

Some problems can be solved by breaking apart or changing the problem into simpler ones, solving the simpler ones, and using those solutions to solve the original problem.

Content Key

Essential understandings or items that need supplementation or adjustment

Solids

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13-1 and 13-2 were combined in 2011

13-2

Relating Shapes and Solids

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13-1 and 13-2 were combined in 2011

13-4

View of Solids

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13-7

Problem Solving Use Objects and Solve a Simpler Problem

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5th Grade

HHH Math Curriculum Guide

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Topic 14: Measurement Units, Time and Temperature

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Feb. 6 & Feb. 13, 9 Days Essential Understandings

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Capacity is a measure of the amount of liquid a container can hold.

Different units can be used to estimate and measure capacity.

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

Relationships between customary measurement units of length, between units of capacity, and between units of weight/mass can be expressed as a ratio (e.g., 12 inches to 1ft or 12 in. = 1ft) and used to convert between units.

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

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

Lesson Number and Title

14-1

Customary Units of Capacity

14-3

Units of Weight and Mass

14-4

Converting Customary Units

14-5

Converting Metric Units

14-6

Elapsed Time Mixed Problem Solving

14-7

Elapsed Time in Other Units

14-9

Problem Solving Make a Table

Content Key

Essential understandings or items that need supplementation or adjustment 14-1 and 14-3 were combined in 2011

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14-1 and 14-3 were combined in 2011

14-6 and 14-7 were combined in 2011

14-6 and 14-7 were combined in 2011

5th Grade

HHH Math Curriculum Guide

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Topic 15: Solving and Writing Equations and Inequalities

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Feb. 27 & Mar. 5, 7 Days Essential Understandings •

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Properties of equality and inverse operations can be used to solve addition and subtraction (or multiplication and division) equations. The solutions can be checked by substitution. The value of an equation containing unknowns can be true or false depending on the replacement values of the unknowns.

Inequalities involving addition or subtraction can be solved using the same process as solving equations involving addition or subtraction.

Solutions to inequalities can be graphed on a number line.

Some quantities have a mathematical relationship so that the value of the one quantity can be found if you know the value of the other quantity.

Patterns can sometimes help identify the relationship between quantities.

The value of an equation containing unknowns can be true or false depending on the replacement values of the unknowns. Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence.

Lesson Number and Title

15-1

Solving Addition and Subtraction Equations

15-3

Inequalities and the Number Line

15-4

Patterns and Equations

15-5

Problem Solving Draw a Picture and Write and Equation

Content Key

Essential understandings or items that need supplementation or adjustment 15-1 and 15-2 were combined in 2011

Optional if time allows 15-4 and 15-5 were combined in 2011

15-4 and 15-5 were combined in 2011

5th Grade

HHH Math Curriculum Guide

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Topic 16: Ratio and Percent

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Mar. 5 & Mar. 12, 5 Days Essential Understandings • • •

A ratio is a special relationship between two quantities where for every x units of one quantity there are y units of another quantity. The quantities being compared in a ratio are called terms.

A percent is a special kind of ratio in which a part is compared to a whole with 100 parts. The whole is 100%. Percent is relative to the size of the whole.

A part of a whole or a part of a set can be represented by a fraction, a decimal, and a percent.

Lesson Number and Title

16-1

Understanding Ratios

16-2

Understanding Percent

16-3

Percent, Fractions, and Decimals

Content Key

Essential understandings or items that need supplementation or adjustment

5th Grade

HHH Math Curriculum Guide

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Topic 18: Graphs and Data

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Mar. 12, Mar. 19 & Mar. 26, 10 Days Essential Understandings •

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Some questions can be answered using a survey. An appropriately selected sample can be used to make predictions about a population.

Sample size determines how close data from the sample mirrors the population.

Each type of graph is most appropriate for certain kinds of data. Picture graphs and bar graphs make it easy to compare data.

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.

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

Each type of graph is most appropriate for certain kinds of data.

Histograms make it easy to compare categorical continuous numerical data.

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.

Different measures can be used to describe the center of a numerical data set. Each measure is most appropriate depending on characteristics of the data Some problems can be solved by making, reading, and analyzing a graph.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

18-1

Data from Surveys

18-2

Bar Graphs and Picture Graphs

18-3

Line Graphs

18-4

Stem-and-Leaf Plots

The goal of this lesson is to formulate conclusions and make predictions from graphs.

Focus on 18-2, but expose to 18-4 and 18-5.

18-5

Histograms

The goal of this lesson is to formulate conclusions and make predictions from graphs.

Focus on 18-2, but expose to 18-4 and 18-5.

18-6

Circle Graphs

18-7

Mean

18-9

Problem Solving Make a Graph

The goal of this lesson is to formulate conclusions and make predictions from graphs.

Focus on 18-2, but expose to 18-4 and 18-5.

If you are making line graphs and bar graphs with students throughout the topic, this lesson does not need to be done.

5th Grade

HHH Math Curriculum Guide

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Topic 19: Transformations, Congruence and Symmetry

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of Mar. 26 & Apr. 2, 6 Days Essential Understandings

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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.

Some problems can be solved by using objects to act the actions in the problems.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

19-1

Translations

To be discussed after the assessment

19-2

Reflections

19-2 and 19-3 were combined in 2011

19-3

Rotations

19-2 and 19-3 were combined in 2011

19-4

Congruence

* Use Coach Book lesson 28 with this lesson to ensure that all performance indicators are met.

19-5

Symmetry

* Use Coach book lesson 31 with this lesson to ensure that all performance indicators are met.

19-6

Problem Solving Use Objects

5th Grade

HHH Math Curriculum Guide

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Post NYS Assessment Topics: 9, 10, 11 & 16

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of May 14, May 21 & May 28, 12 Days Essential Understandings • • • • • • •

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A decimal is another name for a fraction.

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

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

One way to add mixed numbers is to add the fractional parts and then add the whole number parts. Sometimes whole numbers or fractions need to be renamed.

One way to subtract mixed numbers is to subtract the fractional parts and then subtract the whole number parts. Sometimes whole numbers or fractions need to be renamed.

Some problems can be solved by making a reasoned first try at guessing the answer and then checking whether the answer is correct.

The product of a whole number and a fraction can be interpreted in different ways. One interpretation is repeated addition. Multiplying a whole number by a fraction involves division as well as multiplication.

The product is a fraction of the whole number.

A unit square can be used to show the area meaning of fraction multiplication. When you multiply two fractions that are both less than 1, the product is smaller than either fraction. To multiply fractions, write the product of the numerators over the product of the denominators.

One way to find the product of mixed numbers is to change the calculation to an equivalent one involving improper facts.

One way to find the quotient of mixed numbers is to change the calculation to an equivalent one involving multiplication of improper fractions.

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

Finding a percent of a whole is like finding a fractional part of a whole.

You can find the percent of a number by changing the percent to a decimal and multiplying or using a proportion.

Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in the table.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

9-8

Tenths and Hundredths

To be discussed after the assessment

9-9

Thousandths

To be discussed after the assessment

10-3 10-4

Adding Fractions with Unlike Denominators Subtracting Fractions with Unlike Denominators

To be discussed after the assessment To be discussed after the assessment

10-5

Adding Mixed Numbers

To be discussed after the assessment

10-6

Subtracting Mixed Numbers

To be discussed after the assessment

10-7

Problem Solving Try, Check, and Revise

To be discussed after the assessment

11-1

Multiplying Fractions and Whole Numbers

To be discussed after the assessment

11-2

Multiplying Two Fractions

To be discussed after the assessment

11-3 11-4 11-5 16-4 16-5

Multiplying Mixed Numbers Relating Division to Multiplication of Fractions Problem Solving Draw a Picture and Write an Equation Finding Percent of a Whole Number Problem Solving Make a Table and Look for a Pattern

To be discussed after the assessment To be discussed after the assessment To be discussed after the assessment To be discussed after the assessment To be discussed after the assessment

5th Grade

HHH Math Curriculum Guide

√

Post NYS Assessment Topics: 12, 13 & 14

Grade Level Content Previous Content Exposure Content for Future Study

Weeks of May 28 & June 4 9 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. 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. Area can be estimated in square units.

The formula for the area of a triangle is derived from the formula for the area of a parallelogram. Area can be estimated in square units.

The perimeter of a circle is called its circumference. A formula exists for finding the circumference of a circle.

Information in a problem can be represented using a diagram and used to solve the problem. Some problems can be solved by generating a list of outcomes organized in a systematic way.

A polyhedron is a three-dimensional figure made of flat surfaces. The surface area of a polyhedron is sum of the areas of the faces.

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.

The area of some irregular shapes and the volume of some irregular solids can be estimated by breaking apart the shape or solid into shapes or solids for which the area and volume can be estimated.

Capacity is a measure of the amount of liquid a container can hold.

Different units can be used to estimate and measure capacity.

Temperature can be expressed using degrees Fahrenheit or Celsius.

Temperature change can be found using addition or subtraction.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

12-4

Areas of Squares and

To be discussed after the assessment

12-5

Area of Parallelograms

To be discussed after the assessment

12-6

Area of Triangles

To be discussed after the assessment

12-7

Circles and Circumference

To be discussed after the assessment

12-8

Problem Solving Draw a Picture and Make an Organized List

To be discussed after the assessment

13-3

Surface Area

To be discussed after the assessment

13-5

Volume

To be discussed after the assessment

13-6

Irregular Shapes and Solids

To be discussed after the assessment

14-2

Metric Units of Capacity

To be discussed after the assessment

14-8

Temperature Change

To be discussed after the assessment

5th Grade

HHH Math Curriculum Guide

Post NYS Assessment Topic: 17

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Grade Level Content Previous Content Exposure Content for Future Study

Week of June 11, 5 Days Essential Understandings

• • •

• •

Integers are the whole numbers and their opposites where zero is its own opposite.

The Cartesian coordinate system is a scheme that uses perpendicular number lines intersecting at zero to tell the location of points in the plane.

The distance between two points on the number line is the number of unit segments between the points. Finding the length of vertical and horizontal line segments is the same as finding the distance between two points on the number line.

A graph of linear equation contains all of the points on the coordinate grid whose x and y coordinates satisfy the equation.

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

17-1

Understanding Integers

To be discussed after the assessment

17-2

Ordered Pairs

To be discussed after the assessment

17-3

Distances on Number Lines and the Coordinate Plan

To be discussed after the assessment

17-4

Graphing Equations

To be discussed after the assessment

17-5

Problem Solving Work Backward

To be discussed after the assessment

5th Grade

HHH Math Curriculum Guide

√

Post NYS Assessment Topics: 18 & 20

Grade Level Content Previous Content Exposure Content for Future Study

Week of June 18, 5 Days Essential Understandings

• •

• • •

Different measures can be used to describe the center of a numerical data set. Each measure is most appropriate depending on characteristics of the data 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 can be expressed as a number between 0 and 1 inclusive.

Experiments can be used to estimate the likelihood of an event occurring and used to make predictions related to that event.

Some problems can be solved by breaking apart or changing the problem into simpler ones, solving the simpler ones, and using those solutions to solve the original problem.

Lesson Number and Title

Content Key

Essential understandings or items that need supplementation or adjustment

18-8

Median, Mode, and Range

To be discussed after the assessment

20-1

Outcomes

To be discussed after the assessment

20-2

Writing Probability as a Fraction

To be discussed after the assessment

20-3

Experiments and Predictions

To be discussed after the assessment

20-4

Problem Solving Solve a Simpler Problem

To be discussed after the assessment