grade 5 envisionmath2.0 2017-2018 sy · pdf file · 2017-10-17by gaining comfort...

THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY 2017-2018 1

Grade 5 enVisionmath2.0 2017-2018 SY

Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4

Dat

es

September 5 - October 31 BM Window Nov 1-17

November 2 - January 26 BM Window Jan 29-Feb 13

January 30 - May 8 BM Window May 9-25

May 10 - June 12

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l Te

ach

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Total Days: 39 Including 1 Half Day

Total Days: 50 Days Including 4 Half Days

Total Days Before PSSA: 50 Including 9 Half Days Total Days in Cycle: 60 Including 13 Half Days; Excluding Week of Math PSSA

Total Days: 22 Including 1 Half Day

Top

ics

1 – Understand Place Value 2 – Add and Subtract Decimals to Hundredths 3 – Fluently Multiply Multi-Digit Whole Numbers 4 – Use Models and Strategies to Multiply Decimals

5 – Use Models and Strategies to Divide Whole Numbers 6 – Use Models and Strategies to Divide Decimals 7 – Use Equivalent Fractions to Add and Subtract Fractions 8 – Apply Understanding of Multiplication to Multiply Fractions 9-1 – 9-3 Apply Understanding of Division to Divide Fractions

9-4 – 9-8 – Apply Understanding of Division to Divide Fractions 10 – Understand Volume Concepts 11 – Convert Measurements 12 – Represent and Interpret Data 13 – Algebra: Write and Interpret Numerical Expressions 14 – Graph Points on the Coordinate Plane 15 – Algebra: Analyze Patterns and Relationships

16 – Geometric Measurement: Classify Two-Dimensional Figures

Note: A Benchmark Cycle is defined as the time allotted to teach the content that is on each benchmark, and assumes the benchmark is taken on the first day of the window. This means that though it is fine to give the test later in the window, you should be moving on to new content as of the above listed dates, or you will fall behind.


Table of Contents

Benchmark Cycle 1 Standards ............................................................................................................................................................................................. 3

Benchmark Cycle 1 Scope and Sequence ........................................................................................................................................................................... 4

Benchmark Cycle 2 Standards ............................................................................................................................................................................................. 8

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 11

Benchmark Cycle 3 Standards ........................................................................................................................................................................................... 15

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 19

Cycle 4 Standards .............................................................................................................................................................................................................. 26

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 27

PA Core Standards and Eligible Content by Cycle ............................................................................................................................................................. 30

Document Information Page ............................................................................................................................................................................................ 33


Benchmark Cycle 1 Standards

PA Core Standard PA Eligible Content Common Core State Standard

CC.2.1.5.B.1 Apply place‐value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.

M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place.

5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 & explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Example 1: 4× 102 = 400 Example 2: 0.05 ÷ 103 = 0.00005

5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

M05.A-T.1.1.3 Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)

5.NBT.A.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

M05.A-T.1.1.4 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.

5.NBT.A.3 Read, write, and compare decimals to thousandths. b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

M05.A-T.1.1.5 Round decimals to any place (limit rounding to ones, tenths, hundredths, thousandths place)

5.NBT.4 Use place value understanding to round decimals to any place.

CC.2.1.5.B.2 Extend an understanding of operations with whole numbers to perform operations including decimals.

M05.A-T.2.1.1 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.


Benchmark Cycle 1 Scope and Sequence

Topic 1: Understand Place Value

Suggested Dates

Topic- Lesson

Lesson Title Lesson Objective Eligible Content

9/5

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1-1 Patterns with Exponents and Powers of 10

Use patterns and the properties of multiplication to calculate a product when multiplying by a product of 10; use whole-number exponents to write powers of 10.

M05.A-T.1.1.2

1-2 Understand Whole-Number Place Value

Read and write whole numbers using standard form, expanded form, and number names.

M05.A-T.1.1.1

1-3 Decimals to Thousandths Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals.

M05.A-T.1.1.3

1-4 Understand Decimal Place Value Read and write numbers with decimals through thousandths using standard form, expanded form, and number names; identify equivalent decimals.

M05.A-T.1.1.3

1-5 Compare Decimals Use place value to compare decimals through thousandths. M05.A-T.1.1.4

1-6 Round Decimals Use place value to round decimals to different places. M05.A-T.1.1.5

1-7 Math Practices and Problem Solving: Look for and Use Structure

Use the structure of the decimal place value system in order to solve problems involving patterns.

M05.A-T.1.1.3

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Notes: In 4th grade, students worked with decimals to hundredths. This topic allows them to focus on powers of 10 and its relation to place value. By gaining comfort with decimals and place value in this topic, they can operate in upcoming topics.


Topic 2: Add and Subtract Decimals to Hundredths

Suggested Dates

Topic- Lesson

Lesson Title Lesson Objective Eligible Content 9

/18

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s 2-1 Mental Math Use properties of addition and strategies to solve mentally. M05.A-T.2.1.3

2-2 Estimate Sums and Differences Use rounding or compatible numbers to estimate sums and differences.

M05.A-T.2.1.3

2-3 Use Models to Add and Subtract Decimals

Model sums and differences of decimals. M05.A-T.2.1.3

2-4 Add Decimals Add decimals to the hundredths using the standard algorithm. M05.A-T.2.1.3

2-5 Subtract Decimals Subtract decimals to the hundredths using standard algorithm. M05.A-T.2.1.3

2-6 Add and Subtract Decimals Add and subtract decimals. M05.A-T.2.1.3

2-7 Math Practices and Problem Solving: Model with Math

Use prior math knowledge and equations or bar diagrams to solve problems.

M05.A-T.2.1.3

Notes: Students enter 5th grade with experience adding and subtracting decimals. There are seven lessons in this topic with many strategies and methods, but ultimately students must be able to add and subtract decimals.


Topic 3: Fluently Multiply Multi-Digit Whole Numbers

Suggested Dates

Topic- Lesson


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Multiply Greater Numbers by Powers of 10

Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10.

M05.A-T.1.1.2

3-2 Estimate Products Use rounding and compatible numbers to estimate products. M05.A-T.2.1.1

3-3 Multiply 3-Digit by 2-Digit Numbers

Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products.

M05.A-T.2.1.1

3-4 Multiply Whole Numbers with Zeros

Use knowledge about place value and multiply with 2-digit and 3-digit numbers to multiply with zeros.

M05.A-T.2.1.1

3-5 Multiply Multi-Digit Numbers Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers.

M05.A-T.2.1.1

3-6 Solve Word Problems Using Multiplication

Use models and strategies to solve word problems. M05.A-T.2.1.1

3-7 Math Practices and Problem Solving: Critique Reasoning

Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products.

M05.A-T.2.1.1

Notes: Students have experience multiplying multi-digit numbers in 4th grade. This topic (all 7 lessons) is their opportunity to become fluent using the standard algorithm to multiply and multidigit whole numbers. The first lesson also looks at patterns multiplying with 10.


Topic 4: Use Models and Strategies to Multiply Decimals

Suggested Dates

Topic- Lesson


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4-1 Multiply Decimals by Powers of 10

Use knowledge about place value and patterns to find the product of a decimal number and a power of 10.

M05.A-T.1.1.2

4-2 Estimate the Product of a Decimal and a Whole Number

Use rounding and compatible numbers to estimate the product of a decimal and a whole number.

M05.A-T.2.1.3

4-3 Use Models to Multiply a Decimal and a Whole Number

Use models to represent multiplying a decimal and a whole number.

M05.A-T.2.1.3

4-4 Multiply a Decimal by a Whole Number

Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number.

M05.A-T.2.1.3

4-5 Use Models to Multiply a Decimal and a Decimal

Use grids to model decimals and find the product of a decimal and a decimal.

M05.A-T.2.1.3

4-6 Multiply Decimals Using Partial Products

Multiply decimals using partial products and models. M05.A-T.2.1.3

4-7 Use Properties to Multiply Decimals

Use properties to multiply decimals. M05.A-T.2.1.3

4-8 Use Number Sense to Multiply Decimals

Use number sense and reasoning to place the decimal point in a product.

M05.A-T.2.1.3

4-9 Multiply Decimals Multiply decimals using the standard algorithm for multiplication and multiplication strategies.

M05.A-T.2.1.3


Use previously learned concepts and skills to represent and solve problems.

M05.A-T.2.1.3

Notes: Just like the last Topic, this begins with a lesson about patterns with powers of 10 before moving on to general multiplication. The remaining 9 lessons offer estimation strategies, models, and multiple algorithms. All of this builds to the ultimate goal of them being able to multiply with decimals.

Benchmark 1 Window: 11/1 – 11/17




CC.2.1.5.B.1 Apply place‐value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.

M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Example 1: 4× 102=400 Example 2:0.05÷103=0.00005

5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.


M05.A-T.2.1.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

5.NBT.B.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.


5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

CC.2.1.5.C.1 Use the understanding of equivalency to add and subtract fractions.

M05.A-F.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12

5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (a/b + c/d = (ad + bc)/bd.)

5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.


CC.2.1.5.C.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

M05.A-F.2.1.2 Multiply a fraction (including mixed numbers) by a fraction.

5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

5.NF.B.4 Apply &extend understanding of multiplication to multiply a fraction or whole number by fraction. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.



M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

5.NF.B.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

5.NF.B.5 Interpret multiplication as scaling (resizing), by: b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

M05.A-F.2.1.4 Divide unit fractions by whole numbers and whole numbers by unit fractions.

5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.



Topic 5: Use Models and Strategies to Divide Whole Numbers

Suggested Dates

Topic- Lesson


11

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1/2

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5-1 Use Patterns and Mental Math to Divide

Use place-value patterns and mental math to find quotients. M05.A-T.2.1.2

5-2 Estimate Quotients with 2-Digit Divisors

Use compatible numbers and place-value patterns to estimate quotients.

M05.A-T.2.1.2

5-3 Use Models to Divide with 2-Digit Divisors

Use models to find quotients. M05.A-T.2.1.2

5-4 Use Partial Quotients to Divide Solve division problems using partial quotients. M05.A-T.2.1.2

5-5 Divide by Multiples of 10 Find the quotient when divisor is a multiple of 10. M05.A-T.2.1.2

5-6 Use Estimation to Place the First Digit of the Quotient

Decide where to place the first digit in the quotient when dividing whole numbers.

M05.A-T.2.1.2

5-7 Divide by 2-Digit Divisors Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors.

M05.A-T.2.1.2

5-8 Math Practices and Problem Solving: Make Sense and Persevere

Make sense of problems and keep working. M05.A-T.2.1.2

Notes: Students have experience dividing from 4th grade. Now, all 8 lessons are aimed at students dividing with whole numbers. This understanding builds throughout the Topic as students estimate, use models, and use multiple strategies.


Topic 6: Use Models and Strategies to Divide Decimals

Suggested Dates

Topic- Lesson


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6-1

Patterns for Dividing with Decimals

Use mental math and place-value patterns to divide a decimal by a power of 10.

M05.A-T.1.1.2

6-2 Estimate Decimal Quotients Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals.

M05.A-T.2.1.3

6-3 Use Models to Divide by a 1-Digit Whole Number

Use models to help find quotients in problems involving decimals.

M05.A-T.2.1.3

6-4 Divide by a 1-Digit Whole Number

Use the standard algorithm for division to divide decimals by a whole number.

M05.A-T.2.1.3

6-5 Divide by a 2-Digit Whole Number

Use models to visualize the relationship between division and multiplication to divide decimals by a 2-digit whole number.

M05.A-T.2.1.3

6-6 Use Number Sense to Divide Decimals

Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals.

M05.A-T.2.1.3*

6-7 Divide by a Decimal Use the standard algorithm and place-value patterns to divide a decimal by another decimal.

M05.A-T.2.1.3*

6-8 Continue to Divide with Decimals Use the standard algorithm to divide decimals, annexing zeros as needed.

M05.A-T.2.1.3*

6-9 Math Practices and Problem Solving: Reasoning

Use reasoning to solve problems by making sense of quantities and relationships in the situation.

M05.A-T.2.1.3*

Notes: This Topic starts where the last left off. Now they are dividing with decimals. Note that lessons 6-6 – 6-9 are italicized. They go beyond the level of the standards, which only require students to divide when the dividend is a decimal, not the divisor.


Topic 7: Use Equivalent Fractions to Add and Subtract Fractions

Suggested Dates

Topic- Lesson


2/6

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7-1 Estimate Sums and Differences of Fractions

Estimate sums and differences of fractions by using the nearest half or whole number.

M05.A-F.1.1.1

7-2 Find Common Denominators Find common denominators for fractions with unlike denominators

M05.A-F.1.1.1

7-3 Add Fractions with Unlike Denominators

Add fractions with unlike denominators using M05.A-F.1.1.1

7-4 Subtract Fractions w/ Unlike Den. Subtract fractions with unlike denominators. M05.A-F.1.1.1

7-5 Add and Subtract Fractions Write equivalent fractions to add and subtract fractions with unlike denominators.

M05.A-F.1.1.1

7-6 Estimate Sums and Differences of Mixed Numbers

Estimate sums and differences of fractions and mixed numbers.

M05.A-F.1.1.1

7-7 Use Models to Add Mixed #s Add mixed numbers using models. M05.A-F.1.1.1

7-8 Add Mixed Numbers Add mixed numbers using equivalent fractions and a common denominator.

M05.A-F.1.1.1

7-9 Use Models to Subtract Mixed #s Use models to subtract mixed numbers. M05.A-F.1.1.1

7-10 Subtract Mixed Numbers Subtract mixed numbers using equivalent fractions and a common denominator.

M05.A-F.1.1.1

7-11 Add and Subtract Mixed Numbers Add and subtract mixed numbers using equivalent fractions and a common denominator.

M05.A-F.1.1.1


Represent a problem situation with a mathematical model. M05.A-F.1.1.1

Notes: In 4th grade, students adding and subtracted with like denominators. This entire topic of 12 lessons is aimed at extending that to add and subtract with unlike denominators and mixed numbers. Lessons on models greatly support that, and you may wish to do all of the model lessons first.


Topic 8: Apply Understanding of Multiplication to Multiply Fractions

Suggested Dates

Topic- Lesson


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8-1 Use Models to Multiply a Whole Number by a Fraction

Multiply a whole number by a fraction. M05.A-F.2.1.2

8-2 Use Models to Multiply a Fraction by a Whole Number

Multiply a fraction by a whole number. M05.A-F.2.1.2

8-3 Multiply Fractions and Whole Numbers

Multiply fractions and whole numbers. M05.A-F.2.1.2

8-4 Use Models to Multiply Two Fractions

Use models to multiply two fractions. M05.A-F.2.1.2

8-5 Multiply Two Fractions Multiply two fractions. M05.A-F.2.1.2

8-6 Area of a Rectangle Find the area of a rectangle using fractions and diagrams. M05.A-F.2.1.2

8-7 Multiply Mixed Numbers Use models, equations, and previously learned strategies to multiply mixed numbers.

M05.A-F.2.1.2

8-8 Multiplication as Scaling Compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling.

M05.A-F.2.1.3

8-9 Math Practices and Problem Solving: Make Sense & Persevere

Use previously learned knowledge to make sense of problems and persevere in solving them.

CC.2.1.5.C.2

Notes: In 4th grade, students multiplied whole numbers by fractions and mixed numbers. Now, in this topic, both are fractions. The models are intended to support students’ understanding. You may wish to make informal observations about scaling along the way.






M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).

5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does answer lie?


5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.


5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

CC.2.4.5.A.1 Solve problems using conversions within a given measurement system.

M05.D-M.1.1.1 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Example: Convert 5 cm to meters.

5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

CC.2.4.5.A.4 Solve problems involving computation of fractions using information provided in a line plot.

M05.D-M.2.1.1 Solve problems involving computation of fractions by using information presented in line plots.

5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

CC.2.4.5.A.2 Represent and interpret data using appropriate scale.

M05.D-M.2.1.2 Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs.

CC.2.4.5.A.5 Apply concepts of volume to solve problems and relate volume to multiplication and to addition.

M05.D-M.3.1.1 Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided.

5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. (Not exact match)


5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. (Not exact match)

5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (Not exact match)



5.MD.A.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. (Not exact match)

5.MD.A.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.


M05.D-M.3.1.2 Find volumes of solid figures composed of two non-overlapping right rectangular prisms.

5.MD.A.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

CC.2.2.5.A.1 Interpret and evaluate numerical expressions using order of operations.

M05.B-O.1.1.1 Use multiple grouping symbols (parentheses, brackets, braces) in numerical expressions and evaluate expressions containing these symbols.

5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.


M05.B-O.1.1.2 Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.

5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

CC.2.3.5.A.1 Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.

M05.C-G.1.1.1 Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.

5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). (Not exact match)

M05.C-G.1.1.2 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation.

5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.



Topic 9: Apply Understanding of Division to Divide Fractions

Suggested Dates

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9-1 Fractions and Division Understand how fractions are related to division. M05.A-F.2.1.1

9-2 Fractions and Mixed Numbers as Quotients

Implement division of fractions to show quotients as fractions and mixed numbers.

M05.A-F.2.1.1

9-3 Use Multiplication to Divide Use multiplication to divide a whole number by a unit fraction.

M05.A-F.2.1.4

9-4 Divide Whole Numbers by Unit Fractions

Use models such as pictorial models or a number line to show dividing a whole number by a unit fraction.

M05.A-F.2.1.4

9-5 Divide Unit Fractions by Non-Zero Whole Numbers

Use models to divide unit fractions by non-zero whole numbers.

M05.A-F.2.1.4

9-6 Divide Whole Numbers and Unit Fractions

Use models to divide whole numbers and unit fractions. Check your answer using multiplication.

M05.A-F.2.1.4

9-7 Solve Problems Using Division Solve multi-step problems involving division with unit fractions.

M05.A-F.2.1.4

9-8 Math Practices and Problem Solving: Repeated Reasoning

Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions.

M05.A-F.2.1.4

Notes: This topic is about division of fractions. Think about how to connect to students’ understandings of division as a concept. Notice that according to M05.A-F.2.1.4, students only need to divide whole numbers by unit fractions, and unit fractions by whole numbers. Other fractions are not necessary.


Topic 10: Understand Volume Concepts

Suggested Date

Topic- Lesson


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ays 10-1 Model Volume Find the volume of solid figures. M05.D-M.3.1.1

10-2 Develop a Volume Formula Find the volume of rectangular prisms using a formula. M05.D-M.3.1.1

10-3 Volume of Prisms Find the volume of prisms in different ways. M05.D-M.3.1.1

10-4 Combine Volumes of Prisms Find the volume of a solid figure that is the combination of two or more rectangular prisms.

M05.D-M.3.1.2

10-5 Solve Word Problems Using Volume

Use models, prior knowledge of volumes, and previously learned strategies to solve word problems involving volume.

M05.D-M.3.1.2

10-6 Math Practices and Problem Solving: Use Appropriate Tools

Use previously learned knowledge about volumes to choose the appropriate tools to solve volume problems.

M05.D-M.3.1.2

Notes: In 4th grade, students found area and perimeter, but this is their first exposure to volume. In the next topic, they will continue thinking about volume when they work with capacity, and they will continue to work with it in 6th grade with sides with fractional lengths. Be sure to develop conceptual understanding with modeling before moving to formulas.


Topic 11: Convert Measurements

Suggested Dates

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11-1 Convert Customary Units of Length Convert customary units of length. M05.D-M.1.1.1

11-2 Convert Customary Units of Capacity

Convert customary units of capacity. M05.D-M.1.1.1

11-3 Convert Customary Units of Weight Convert customary units of weight. M05.D-M.1.1.1

11-4 Convert Metric Units of Length Convert metric units of length. M05.D-M.1.1.1

11-5 Convert Metric Units of Capacity Convert metric units of capacity. M05.D-M.1.1.1

11-6 Convert Metric Units of Mass Convert metric units of mass. M05.D-M.1.1.1

11-7 Solve Word Problems Using Measurement Conversions

Solve real-world problems with measurement conversions. M05.D-M.1.1.1

11-8 Math Practices and Problem Solving: Precision

Be precise when solving measurement problems. M05.D-M.1.1.1

Notes: In 4th grade, students converted larger units to smaller ones. Now, they are converting both ways. Help students see the similarities among all of these lessons. Yes, they are different measures, but they are all the same concept. You may want to provide them with the PSSA conversion table so they can get used to using it as a tool.


Topic 12: Represent and Interpret Data

Suggested Dates

Topic- Lesson


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12-1 Analyze Line Plots Read and analyze line plots. M05.D-M.2.1.1

12-2 Make Line Plots Organize and display data in a line plot. M05.D-M.2.1.1

12-3 Solve Word Problems Using Measurement Data

Solve problems using data in a line plot. M05.D-M.2.1.1

12-4 Math Practices and Problem Solving: Critique Reasoning

Critique the reasoning of others using understanding of line plots and fractions.

M05.D-M.2.1.1

PA-1 Display and Interpret Data: Frequency Tables

Write questions that can be addressed with data; collect, organize, and interpret data; make predictions about data.

M05.D-M.2.1.2

PA-2 Display and Interpret Data: Bar Graphs

Represent and interpret numerical and categorical data in a bar graph and make predictions.

M05.D-M.2.1.2

PA-3 Display and Interpret Data: Line Graphs

Create and interpret line graphs, including describing trends and making predictions.

M05.D-M.2.1.2

Notes: The line plot lessons provide additional opportunities to work with fractions. Students have been working with fractions on line plots since 3rd grade. Note the important inclusion of PA lessons that address otherwise ignored eligible content.


Topic 13: Algebra: Write and Interpret Numerical Expressions

Suggested Date

Topic- Lesson


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13-1 Order of Operations Use the order of operations to evaluate expressions. M05.B-O.1.1.1

13-2 Evaluate Expressions Evaluate expressions with parentheses, brackets, and braces. M05.B-O.1.1.1

13-3 Write Numerical Expressions Write simple expressions that show calculations with numbers. M05.B-O.1.1.2

13-4 Interpret Numerical Expressions Interpret numerical expressions without evaluating them. M05.B-O.1.1.2

13-5 Math Practices and Problem Solving: Reasoning

Use reasoning to solve problems by making sense of quantities and relationships in the situation.

M05.B-O.1.1.1

Notes: This is a short topic, and not considered to be part of the major work of 5th grade. Do not focus too much on all of the types of brackets and parentheses, instead focusing on the basic idea of order of operations. Also be careful about using key words to translate expressions as they do not always work.


Topic 14: Graph Points on the Coordinate Plane

Suggested Date

Topic- Lesson


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14-1 The Coordinate System Locate points on a coordinate grid. M05.C-G.1.1.1

14-2 Graph Data Using Ordered Pairs Graph points on a coordinate grid. M05.C-G.1.1.1

14-3 Solve Using Ordered Pairs Solve real-world problems by graphing points. M05.C-G.1.1.2

14-4 Math Practices & Problem Solving Use reasoning to solve problems by making sense of quantities and relationships in the situation.

M05.C-G.1.1.2

Notes: This is again a short topic and not part of the major work of 5th grade. It leads into the next topic where they will be graphing ordered pairs from number sequences. The 5 ELA PSSA days can be spent on this topic or on any other review or extension.

4/16 – 4/20 MATH PSSA


Topic 15 will not be on the benchmark, so its standards are included in Cycle 4. To ensure you have time in Cycle 4 to finish Topic 16 and to review and extend content before the end of the year, it is recommended that you start Topic 15 now.

Topic 15: Algebra: Analyze Patterns and Relationships

Suggested Date

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15-1 Numerical Patterns Analyze numerical patterns. M05.B-O.2.1.1

15-2 More Numerical Patterns Use tables to identify relationships between patterns. M05.B-O.2.1.2

15-3 Analyze and Graph Relationships Analyze patterns and graph ordered pairs generated from number sequences.

M05.B-O.2.1.1

15-4 Math Practices and Problem Solving: Make Sense & Persevere

Make sense of problems and persevere in solving them. M05.B-O.2.1.1

Notes: This topic, and the last couple, have been deepening students’ exposure to algebraic ideas which they will delve into more deeply in 6th grade. Before moving on to Topic 16, you may wish to explore algebraic Step Up lessons at the end of the book to extend this content as a preview for 6th grade.



Cycle 4 Standards


CC.2.2.5.A.4 Analyze patterns and relationships using two rules.

M05.B-O.2.1.1 Generate two numerical patterns using two given rules. Example: Given the rule “add 3” and the starting number 0 and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences.

5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

M05.B-O.2.1.2 Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Example: Given two patterns in which the first pattern follows the rule “add 8” and the second pattern follows the rule “add 2,” observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.

CC.2.3.5.A.2 Classify two‐dimensional figures into categories based on an understanding of their properties.

M05.C-G.2.1.1 Classify two-dimensional figures in a hierarchy based on properties. Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides. Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon.

5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. (Not exact match)

5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties.


Cycle 4 Scope and Sequence

Topic 16: Geometric Measurement: Classify Two-Dimensional Figures

Suggested Dates

Topic- Lesson


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16-1 Classify Triangles Classify triangles by their angles and sides. M05.C-G.2.1.1

16-2 Classify Quadrilaterals Classify quadrilaterals by their properties. M05.C-G.2.1.1

16-3 Continue to Classify Quadrilaterals Classify quadrilaterals using a hierarchy. M05.C-G.2.1.1

16-4 Math Practices and Problem Solving: Construct Arguments

Construct arguments about geometric figures. M05.C-G.2.1.1

Notes: Despite looking at different figures in each lesson, the basic idea of this topic is that we can classify shapes. Geometry is not major work in 5th grade, but it is an opportunity to think critically about how shapes relate and to apply the vocabulary they have been developing about sides and angles in past grades. Geometric content often gets skipped, so try to make time for this Topic.


Remediation and Extension Options

5/21-6/12

16 Days

Option 1: Re-teach Based

on Major Work of 5th Grade

You taught many topics this year. The clusters below represent the major work of 3rd grade, so if you want to revisit something, one or more of these topics would be a good idea.

5.NBT.A Understand the place value system. 5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NF.A Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.MD.C Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Option 2: Pre-Teach

Content for Next Year

Another option is to help prepare students for next year by previewing content. enVisionmath2.0 offers “Step Up” lessons for grades K-5 (see next page). This series of lessons previews a wide range of content for the next year. They go for a breadth over depth approach, so you can choose to follow the lessons as written, or you could select those that target the content you feel is the most important. You may wish to consult with the next grade’s teacher(s) to find out what content they most want you to pre-teach.

Option 3: Revisit STEM

Projects

The Topic Opener page for each Topic features a Math and Science Project. If you did not have time to do them along the way, you might want to do some of them now. The projects require internet access for students to complete research. They provide opportunities for students to read, write, research, do some math, and learn about some science concepts.

Option 4: Financial Literacy

The Federal Reserve Bank of Philadelphia has posted free lesson plans for elementary teachers (including K) on financial literacy at: https://philadelphiafed.org/education/teachers/lesson-plans?tabNum=1. Many of these lessons are tied to early children’s literature, as well. In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: https://www.census.gov/schools/activities/math.html.

https://philadelphiafed.org/education/teachers/lesson-plans?tabNum=1

https://www.census.gov/schools/activities/math.html

https://www.census.gov/schools/activities/math.html


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Step Up Lessons

Lesson 1 Understand Integers Recognize positive numbers and their opposites. M06.A-N.3.1.1 M06.A-N.3.1.2

Lesson 2 Compare and Order Integers Compare and order integers. M06.A-N.3.2.1 M06.A-N.3.2.2

Lesson 3 Rational Numbers on the Coordinate Plane

Identify and graph points with rational number coordinates on the coordinate plane.

M06.A-N.3.1.3

Lesson 4 Understand Ratios Use ratios and ratio language to describe the relationship between two quantities.

M06.A-R.1.1.1

Lesson 5 Understand Rates Use rates to solve problems. M06.A-R.1.1.2

Lesson 6 Understand Percents Represent and find the percent of a whole. M06.A-R.1.1.5

Lesson 7 Fractions, Decimals, Percents Write equivalent values as fractions, decimals, or percents. M06.A-R.1.1.5

Lesson 8 Understand Division of Fractions Use models to divide with fractions. M06.A-N.1.1.1

Lesson 9 Divide Whole Numbers by Fractions

Divide whole numbers by fractions. M06.A-N.1.1.1

Lesson 10 Area of Parallelograms and Rhombuses

Develop and use the formulas for the areas of parallelograms and rhombuses.

M06.C-G.1.1.1


PA Core Standards and Eligible Content by Cycle

PA Core Standard PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

CC.2.1.5.B.1 Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.

M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left. Example: Recognize that in the number 770, the 7 in the tens place is 1/10 the 7 in the hundreds place.

X

M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Example 1: 4 × 102 = 400 Example 2: 0.05 ÷ 103 = 0.00005

X X

M05.A-T.1.1.3 Read and write decimals to thousandths using base-ten numerals, word form, and expanded form. Example: 347.392 = 300 + 40 + 7 + 0.3 + 0.09 + 0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)

X

M05.A-T.1.1.4 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.

X

M05.A-T.1.1.5 Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place).

X


M05.A-T.2.1.1 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).

X

M05.A-T.2.1.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

X


X X

CC.2.1.5.C.1 Use the understanding of equivalency to add and subtract fractions.

M05.A-F.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.) Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12

X



M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).

X

M05.A-F.2.1.2 Multiply a fraction (including mixed numbers) by a fraction. X

M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication. Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

X


X


M05.B-O.1.1.1 Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.

X

M05.B-O.1.1.2 Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them. Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.

X

CC.2.2.5.A.4 Analyze patterns and relationships using two rules.

M05.B-O.2.1.1 Generate two numerical patterns using two given rules. Example: Given the rule “add 3” and the starting number 0 and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences.

X

M05.B-O.2.1.2 Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules. Example: Given two patterns in which the first pattern follows the rule “add 8” and the second pattern follows the rule “add 2,” observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.

X

CC.2.3.5.A.1 Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.

M05.C-G.1.1.1 Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.

X

M05.C-G.1.1.2 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation. X


CC.2.3.5.A.2 Classify two-dimensional figures into categories based on an understanding of their properties.

M05.C-G.2.1.1 Classify two-dimensional figures in a hierarchy based on properties. Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides. Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon.

X

CC.2.4.5.A.1 Solve problems using conversions within a given measurement system.

M05.D-M.1.1.1 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided. Example: Convert 5 cm to meters. X

CC.2.4.5.A.2 Represent and interpret data using appropriate scale.

M05.D-M.2.1.2 Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs.

X

CC.2.4.5.A.4 Solve problems involving computation of fractions using information provided in a line plot.

M05.D-M.2.1.1 Solve problems involving computation of fractions by using information presented in line plots.

X



X

M05.D-M.3.1.2 Find volumes of solid figures composed of two non-overlapping right rectangular prisms. X


Document Information Page

Overview of Contents of Document The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates. The Benchmark Cycle X Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle’s Benchmark. The Benchmark Cycle X Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities. The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught.

What is a Cycle?

We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle.

What If I Fall Behind?

We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and PSSA, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide.

If you are concerned about content that you may not reach before the PSSA, consider implementing number talks and other short routines and games. For example, a lot of Geometry vocabulary and concepts could be taught through Which Once Doesn’t Belong. Rather than pushing to “cover” content, or using test prep resources, content can be infused through short but meaningful structures.

The table below is purely for informational purposes. We used the PSSA Mathematics Blueprint to calculate what percent of tested content you will cover, based on how much of the book you teach before the test. Again, we recommend depth and understanding over coverage, but we wanted to provide this information for your planning purposes.

Percent if Topics 1-12 Are Taught Percent if Topics 1-13 Are Taught Percent if Topics 1-14 Are Taught Percent if Topics 1-15 Are Taught

70 77.5 87.5 95

http://wodb.ca/


Additional Key Considerations in Mathematics

The Standards for Mathematical Practice are:

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

You should try to infuse these Standards into your lessons regularly. Rather than thinking of them as a box to check, think about how you are providing students with opportunities to develop as mathematical thinkers and doers.

The following Common Core Standards have been identified as the major clusters for Grade 5: 5.NBT.A Understand the place value system. 5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NF.A Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.MD.C Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

These do not necessarily reflect what is most tested on the PSSA, but it is the content that is most essential as you prepare students for 6th grade.

The School District of Philadelphia’s Vision for Mathematics Teaching and Learning:

All students think mathematically, and they will be empowered to own, share, and do mathematics.

Our Guiding Principles:

Equitable Discourse Rich + Meaningful Tasks Purpose-Driven Work Questioning and Curiosity Valuing Diverse Thinking

If you have any questions or would like more information, please contact us at [email protected].

grade 5 envisionmath2.0 2017-2018 sy · pdf file · 2017-10-17by gaining comfort...

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