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Curriculum Map

 

5th Grade Math Curriculum Map

2018-2019

BreAnna Coffey

 

B. Coffey

B

Module

Month(s)

week(s)

Lesson

+

Days

Essential Questions

+

Objectives

Common Core State Standard(s)

 

Math Practice

 

Rules, Expectations, Procedures, and Review

 

7 days

 

August 9th – 17th

 

What is my role in the classroom?

 

How do I use math practices?

 

 

Students will understand classroom rules, procedures, expectations, and math practices.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them

CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.

CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.

CCSS.MATH.PRACTICE.MP6 Attend to precision.

CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.

CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.

 

  • Make sense of problems and persevere in solving them

 

  • Reason abstractly and quantitatively.

 

 

  • Construct viable arguments and critique the reasoning of others.

 

  • Model with mathematics.

 

  • Use appropriate tools strategically.

 

  • Attend to precision.

 

  • Look for and make use of structure.

 

  • Look for and express regularity in repeated reasoning.

21st Century Skills

Collaboration

Accountability

Responsibility

Reflection

Decision Making

I CAN Statements

 

Work independently.  

        

Follow directions.    

    

Complete assignments on time.

 

Pay attention in class.    

 

Respectful/considerate/courteous to others.  

 

Work/share/play well with others.

                                 

Do my work neatly and have good penmanship. 

 

 

 

 

Vocabulary

 

  • persevere
  • abstractly
  • quantitatively critique
  • model
  • strategically
  • precision
  • reasoning

Assessments

+ Activities

 

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments

 

Technology

 

 

  • Interactive Projector
  • Chromebooks
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives
  •  

Module 1

Module

Topic

Days

 

Lesson

Days

Objectives

 

[are numbered to correspond with lesson]

Common Core State Standard(s)

 

Math Practice

Module 1

 

Place Value and Decimal Fractions

 

20 Instruction Days

 

August 20h

September 17th

 

Labor Day Sept. 3rd

 

Topic A – Multiplicative Patterns on the Place Value Chart (Lessons 1 – 4)

 

Topic B – Initiating Fluency with Addition and Subtraction Within 100 (Lessons 5 - 6)

 

Topic C – Place Value and Rounding Decimal Fractions (Lessons 7 – 8)

 

Topic D – Adding and Subtracting Decimals (Lessons 9 – 10)

 

Topic E – Multiplying Decimals (Lessons 11 – 12)

 

Topic F – Dividing Decimals (Lessons 13 – 16)

 

8/20 – L1

8/21 – L1

8/22 – L2

8/23 – L3

8/24 – L4

8/27 – A ASSESSMENT

8/28 – L5

8/29 – L6

8/30 – L7

8/31 – L8

9/3

9/4 -  L9

9/5 – L10

9/6 – L11

9/7- L12

9/10 - D ASSESSMENT

9/11 – L13

9/12 – L14

9/13 – L15

9/14 – F ASSESSMENT

9/17 – REVIEW, RETEACH, OR ASSESS

 

 

1 – Reason concretely and pictorially using place value understanding to relate

adjacent base ten units from millions to thousandths.

2 – Reason abstractly using place value understanding to relate adjacent base

ten units from millions to thousandths.

3 – Use exponents to name place value units, and explain patterns in the

placement of the decimal point.

4 – Use exponents to denote powers of 10 with application to metric conversions.

5 – Name decimal fractions in expanded, unit, and word forms by applying place

value reasoning.

6 – Compare decimal fractions to the thousandths using like units, and express

comparisons with >, <, =.

7 – Round a given decimal to any place using place value understanding and the

vertical number line.

8 - Round a given decimal to any place using place value understanding and the

vertical number line.

9 – Add decimals using place value strategies and relate those strategies to a

written method.

10 – Subtract decimals using place value strategies and relate those strategies

to a written method.

 

11 – Multiply a decimal fraction by single-digit whole numbers, relate to a written

method through application of the area model and place value understanding,

and explain the reasoning used.

12 – Multiply a decimal fraction by single –digit whole numbers, including using

estimation to confirm the placement of the decimal point.

13 – Divide decimals by single-digit whole numbers involving easily identifiable

multiples using place value understanding and relate to a written method.

14 – Divide decimals with a remainder using place value understanding and

relate to a written method.

15 – Divide decimals using place value understanding including remainders in

the smallest unit.

16 - Solve word problems using decimal operations.

Topic A

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.

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.

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.

 

Topic B

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10

+ 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

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

comparisons.

 

Topic C

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

 

Topic D

5.NBT. A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 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; justify the reasoning used with a written explanation.

 

Topic E

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.

347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).

 

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; justify the reasoning used with a written explanation.

 

Topic F

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). 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; justify the reasoning used with a written explanation.

MP.6 Attend to precision. Students express the units of the base ten system as they work with

decimal operations, expressing decompositions and compositions with understanding (e.g., “9

hundredths + 4 hundredths = 13 hundredths. I can change 10 hundredths to make 1 tenth”).

 

MP.7 Look for and make use of structure. Students explore the multiplicative patterns of the base

ten system when they use place value charts and disks to highlight the relationships between

adjacent places. Students also use patterns to name decimal fraction numbers in expanded,

unit, and word forms.

 

MP.8 Look for and express regularity in repeated reasoning. Students express regularity in

repeated reasoning when they look for and use whole-number general methods to add and

subtract decimals and when they multiply and divide decimals by whole numbers. Students

also use powers of ten to explain patterns in the placement of the decimal point and

generalize their knowledge of rounding whole numbers to round decimal numbers.

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

 

 

 

 I can demonstrate understanding of the place value system

 

I can use patterns to multiply or divide by a multiple of ten

 

I can write whole numbers using exponents by powers of ten

 

I can read decimals

 

I can write decimals in standard form and word form

 

I can write decimals in expanded form, using scientific notation

 

I can compare two decimals using the symbols >, <, or =

 

I can round decimals to any place

 

I can use drawings/models to show what I know about decimals

 

I can add decimals to hundredths

 

I can subtract decimals to hundredths

 

Vocabulary

 

Thousandths

Hundredths

Tenths

Digit

Place Value Product

Decimal Fraction Factors

Exponents

Equation

Standard Form

Word Form

Unit Form

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

 

  • Interactive Projector
  • Chromebooks
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

 

 

 

Module 2

Module

Days

Topics

Lesson

+

Days

Objectives

Common Core State Standard(s)

 

Math Practice

Module 2

 

Multi-Digit Whole Number and Decimal Fraction Operations

 

 

32 Instruction Days

 

September 19TH – November 12th

 

 

Fall Break October 8th -12th

Halloween Party

October 31st

 

 

Parent Teacher Meetings

November 12th

 

Topic A – Mental Strategies for Multi-Digit Whole Number Multiplication

 

Topic B – The Standard Algorithm for Multi-Digit Whole Number Multiplication

 

Topic C – Decimal Multi-Digit Multiplication

 

Topic D – Measurement Word Problems with Whole Number and Decimal Multiplication

 

Topic E – Mental Strategies for Multi-Digit Whole Number Division

 

Topic G – Partial Quotients and Multi-Digit Decimal Division

 

9/19 – L1

9/20 – L2

9/24 – A ASSESSMENT

9/25 – REVIEW, RETEACH, OR ASSESS

9/26 – L3

9/ 27 –  L4

9/28 – L6 + L7

10/1 – L8 + L9

10/2 – B ASSESSMENT

10/3 – L10

10/4 – L11

10/5 –L12

10/8

10/9

10/10

10/11

10/12

10/15 –C ASSESSMENT

10/16 – L13

10/17 – L14

10/18 – L15

10/19 – D ASSESSMENT

10/22 – L16

10/23 –  L17 + L18

10/24 – L19

10/25 – L20

10/26 – L21

10/29 – REVIEW, RETEACH, OR ASSESS

10/30 – E + F ASSESSMENT

10/31 – HALLOWEEN PARTY

11/1 – L22

11/2 –L 23

11/5 – L24

11/6 – F + G ASSESSMENT

11/7 – L26

11/8 – L27

11/9 – G ASSESSMENT

11/12

 

 

 

 

 

  1. Multiply multi-digit whole numbers and multiples of

10 using place value patterns and the distributive

and associative properties

  1. Estimate multi-digit products by rounding factors to

a basic fact and using place value patterns.

  1. Write and interpret numerical expressions and

compare expressions using a visual model.

  1. Convert numerical expressions into unit form as a

mental strategy for multi-digit multiplication.

  1. Connect visual models and the distributive property

to partial products of the standard algorithm without

  •  
  1. Connect area diagrams and the distributive property

to partial products of the standard algorithm without

  •  
  1. Connect area diagrams and the distributive property

to partial products of the standard algorithm with

  •  
  1.  Fluently multiply multi-digit whole numbers using the

standard algorithm and using estimation to check for

reasonableness of the product.

  1. Fluently multiply multi-digit whole numbers using the

standard algorithm to solve multi-step word

  •  
  1. Multiply decimal fractions with tenths by multi-digit

whole numbers using place value understanding to

record partial products

  1. Multiply decimal fractions by multi-digit whole

numbers through conversion to a whole number

problem and reasoning about the placement of the

  •  
  1. Reason about the product of a whole number and a

decimal with hundredths using place value

understanding and estimation.

  1. Use whole number multiplication to express

equivalent measurements

  1. Use fraction and decimal multiplication to express

equivalent measurements.

  1. Solve two-step word problems involving

measurement conversions.

  1. Use divide by 10 patterns for multi-digit whole number
  2.  
  3. Use basic facts to approximate quotients with two-digit
  4.  
  5. Use basic facts to estimate quotients with two-digit
  6.  
  7. Divide two- and three-digit dividends by multiples of

10 with single-digit quotients and make connections to

a written method.

  1. Divide two- and three-digit dividends by two-digit

divisors with single-digit quotients and make

connections to a written method.

  1. Divide two- and three-digit dividends by two-digit

divisors with single-digit quotients and make

connections to a written method.

  1. Divide three- and four-digit dividends by two-digit

divisors resulting in two- and three-digit quotients,

reasoning about the decomposition of successive

remainders in each place value

  1. Divide three- and four-digit dividends by two-digit

divisors resulting in two- and three-digit quotients,

reasoning about the decomposition of successive

remainders in each place value.

  1. Divide decimal dividends by multiples of 10,

reasoning about the placement of the decimal point

and making connections to a written method.

 

  1. Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the

              placement of the decimal point                                

  1. Divide decimal dividends by two-digit divisors,

estimating quotients, reasoning about the placement

of the decimal point, and making connections to a

written method.

  1. Divide decimal dividends by two-digit divisors,

estimating quotients, reasoning about the placement

of the decimal point, and making connections to a

written method.

Topic A

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

5.NBT.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.

5.NBT.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 power of 10.

 

Topic B

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

5.OA.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.

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

 

Topic C

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

5.OA.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.

5.NBT.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.

5.NBT.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.1

 

Topic D

5.NBT.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.

5.NBT.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 power of 10.

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

5.NBT.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.2

5.MD.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.

 

Topic E

5.NBT.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.

5.NBT.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 power of 10.

5.NBT.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.

 

Topic F

5.NBT.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.

 

 

 

 

 

 

Topic G

5.NBT.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 power of 10.

5.NBT.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.3

 

 

 

MP.1 Make sense of problems and persevere in solving them. Students make sense of problems

when they use place value disks and area models to conceptualize and solve multiplication

and division problems.

 

MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their

relationships when they use both mental strategies and the standard algorithms to multiply

and divide multi-digit whole numbers. Students also decontextualize when they represent

problems symbolically and contextualize when they consider the value of the units used and

understand the meaning of the quantities as they compute.

 

MP.7 Look for and make use of structure. Students apply the times 10, 100, 1,000 and the divide

by 10 patterns of the base ten system to mental strategies and the multiplication and division

algorithms as they multiply and divide whole numbers and decimals.

 

MP.8 Look for and express regularity in repeated reasoning. Students express the regularity they

notice in repeated reasoning when they apply the partial quotients algorithm to divide two-,

three-, and four-digit dividends by two-digit divisors. Students also check the reasonableness

of the intermediate results of their division algorithms as they solve multi-digit division word

problems.

 

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

 

I can multiply multi-digit whole numbers

 

I can express division by using

equations and rectangular arrays

 

I can subtract decimals to hundredths

Multiply

 

I can multiply decimals to hundredths

 

I can divide decimals to hundredths

 

 

Vocabulary

 

Product

Estimate

Associative Property Factor

Commutative Property

Equation

Distributive Property

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

 

  • Interactive Projector
  • Chromebooks
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Module 3

Module

Topic

Days

 

Lesson

Days

Essential Questions

+

Objectives

Common Core State Standard(s)

 

Math Practice

Module 3

 

Addition and Subtraction of Fractions

 

20 Instruction Days

 

November 15th  –

December 18th

 

 

 

Parent Teacher Conferences November 12th

 

 

Thanksgiving Break November 21st  - 23rd

 

 

Christmas Break December 21st – January 2nd

 

 

 

Topic A – Equivalent Fractions

 

Topic B – Making Like Units Pictorially

 

Topic C – Making Like Units Numerically

 

Topic D – Further Applications

11/15 – L2

11/16 – L3

11/19 – L4

11/20 – L5

11/21

11/22

11/23

11/26 – L6

11/27 – L7

11/28 – A + B ASSESSMENT

11/29 – REVIEW, RETEACH, ASSESS

11/30 – REVIEW, RETEACH, OR ASSESS

12/3 – L8

12/4 – L9

12/5 –L10

12/6 – L11

12/7 –L12

12/10 –C ASSESSMENT

12/11 – L13

12/12 – L15

12/13 – D ASSESSMENT

12/14 – REVIEW, RETEACH, ASSESS

12/17 – CHRISTMAS ACTIVITIES

12/18 - CHRISMTAS ACTIVITES

 

 

 

  1. Make equivalent fractions with the number line, the area model, and numbers.
  2. Make equivalent fractions with sums of fractions with like denominators.
  3. Add fractions with unlike units using the strategy of creating equivalent fractions.
  4. Add fractions with sums between 1 and 2.
  5. Subtract fractions with unlike units using the strategy of creating equivalent fractions.
  6. Subtract fractions from numbers between 1 and 2.
  7. Solve two-step word problems.
  8. Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.
  9. Add fractions making like units numerically.
  10. Add fractions with sums greater than 2.
  11. Subtract fractions making like units numerically.
  12. Subtract fractions greater than or equal to 1.
  13. Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations
  14. Strategize to solve multi-term problems.
  15. Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.

 

Topic A

4.NF.1      Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.  Use this principle to recognize and generate equivalent fractions.

4.NF.3      Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

c.             Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

d.            Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

 

Topic B

5.NF.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.  For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.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.  For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

 

Topic C

5.NF.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.  For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.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.  For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

 

Topic D

5.NF.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.  For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.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.  For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

 

MP.1 Make sense of problems and persevere in solving them. Students make sense of problems

when they use number lines, tape diagrams, and fraction models to conceptualize and solve

fraction addition and subtraction problems. Students also check their work and monitor their

progress, assessing their approach and its validity within the given context and altering their

method when necessary.

MP.3 Construct viable arguments and critique the reasoning of others. As students add and

subtract with fractions and mixed numbers, they make choices and reason about which like

unit to choose and draw conclusions about what makes some problems simpler than others.

Students analyze multiple solution strategies for given problems and draw conclusions about

which method is most efficient in each case. Students also critique the reasoning of others

and construct viable arguments during this analysis. They also use their understanding of

fractions to assess the reasonableness of sums and differences and use these assumptions to

justify their conclusions to others.

MP.5 Use appropriate tools strategically. Students use mental computation and estimation

strategies to assess the reasonableness of their answers. They decide which pictorial model

to draw and label and reason about its size relative to the context of the problem. Students

decide on the appropriateness of using special strategies when adding and subtracting mixed

numbers.

MP.7 Look for and make use of structure. Students discern patterns and structures as they draw

fraction models and reason about the number of units represented, the size or length of those

units, and the name of the fraction that each model represents. They identify patterns in

sums and differences when the same fraction is added to or taken from a variety of numbers

and use this understanding to generate predictions about the sums and differences.

MP.8 Look for and express regularity in repeated reasoning. Students express regularity in

repeated reasoning when they look for and use whole number general methods to add and

subtract fractions. Adding and subtracting fractions requires finding like units just as it does

with whole numbers, such as when adding centimeters and meters.

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

 

I can simplify fractions

 

I can convert mixed numbers and improper fractions

 

I can add and subtract fractions

 

I can add and subtract mixed numbers

I can solve real-world problems involving fractions

 

I can determine if my answer is reasonable by using benchmark fractions

 

Vocabulary

 

Equivalent Fractions Numerator

Vertically Denominator

Horizontally

Expression

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

 

  • Interactive Projector
  • Chromebooks
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Module 4

Module

Topic

Days

 

Lesson

Days

Essential Questions

+

Objectives

Common Core State Standard(s)

 

Math Practice

Module 4

 

Multiplication and Division of Fractions and Decimal Fractions

 

41 Days

 

January 3rd  –

March 1st

 

Weeks 1 – 6

 

Martin Luther King, Jr. Day

January 21st

 

Presidents’ Day February 18th

 

Topic A – Line Plots of Fraction Measurements

 

Topic B – Factions as Division

 

Topic C – Multiplication of a Whole Number by a Fraction

 

Topic D – Fraction Expressions and Word Problems

 

Topic E – Multiplication of a Fraction by a Fraction

 

Topic F – Multiplication with Fractions and Decimals as Scaling and Word Problems

 

Topic G – Division of Fractions and Decimal Fractions

 

Topic H – Interpretation of Numerical Expressions

1/3 – L1

1/4 – L2

1/7 – L3

1/8 –L4

1/9 – A + B ASSESSMENT

1/10 –REVIEW, RETEACH, ASSESS

1/11 – REVIEW. RETEACH. ASSESS

1/14 – L5

1/15 – L6

1/16 – L7

1/17 – L9

1/18 – B + C ASSESSMENT

1/21

1/22 –L10

1/23 – L11 + L12

1/24 –D ASSESSMENT

1/25 – L13

1/28 – L14

1/29 – L15

1/30 – L16

1/31 – E ASSESSMENT

2/1 – L17

2/ 4 – L18

2/5 – L19

2/6 – L20

2/7 – E ASSESSMENT

2/8 – L21

2/11 – L22

2/12 – L23

2/13 – L24

2/14 – REVIEW, RETEACH, OR ASSESS

2/15 – F ASSESSMENT

2/18

2/19 – L25

2/20 – L26

2/21 – L27

2/22 – L29

2/23 – G ASSESSMENT

2/25 – L30

2/26 – L31

2/27 – L32

2/28 – G + H ASSESSMENT

3/1 – REVIEW, RETEACH, OR ASSESS

 

 

 

 

 

 

  1. Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch and analyze the data through line plots.
  2. Interpret a fraction as division.
  3. Interpret a fraction as division
  4. Use tape diagrams to model fractions as division
  5. Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers.
  6. Relate fractions as division to fraction of a set.
  7. Multiply any whole number by a fraction using tape diagrams.
  8. Relate fraction of a set to the repeated addition interpretation of fraction multiplication.
  9. Find a fraction of a measurement and solve word problems.
  10. Compare and evaluate expressions with parentheses.
  11. Solve and create fraction word problems involving addition, subtraction, and multiplication.
  12. Solve and create fraction word problems involving addition, subtraction, and multiplication.
  13. Multiply unit fractions by unit fractions
  14. Multiply unit fractions by non-unit fractions.
  15. Multiply non-unit fractions by non-unit fractions.
  16. Solve word problems using tape diagrams and fraction-by-fraction multiplication.
  17. Relate decimal and fraction multiplication.
  18. Relate decimal and fraction multiplication.
  19. Convert measures involving whole numbers, and solve multi-step word problems.
  20. Convert mixed unit measurements, and solve multi-step word problems.
  21. Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.
  22. Compare the size of the product to the size of the factors.
  23. Compare the size of the product to the size of the factors.
  24. Solve word problems using fraction and decimal multiplication.
  25. Divide a whole number by a unit fraction.
  26. Divide a unit fraction by a whole number.
  27. Solve problems involving fraction division.
  28. Write equations and word problems corresponding to tape and number line diagrams.
  29. Connect division by a unit fraction to division by 1 tenth and 1 hundredth.
  30. Divide decimal dividends by non-unit decimal divisors.
  31. Divide decimal dividends by non-unit decimal divisors.
  32. Interpret and evaluate numerical expressions including the language of scaling and fraction division.
  33. Create story contexts for numerical expressions and tape diagrams, and solve word problems.

Topic A

5.MD.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.

Topic B

5.NF.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 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4.  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 your answer lie?

Topic C

5.NF.4      Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product of (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.)

Topic D

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

5.OA.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.

5.NF.4      Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product of (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.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.

Topic E

5.NBT.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.

5.NF.4      Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a.            Interpret the product of (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.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.

5.MD.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.

Topic F

5.NF.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.

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.

5.NF.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.

Topic G

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

5.NBT.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.

5.NF.7      Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.  (Students able to multiple fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division.  But division of a fraction by a fraction is not a requirement at this grade level.)

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.

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.

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?

Topic H

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

5.OA.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.

MP.2 Reason abstractly and quantitatively. Students reason abstractly and quantitatively as they

interpret the size of a product in relation to the size of a factor, as well as interpret terms in a multiplication sentence as a quantity and scaling factor. Then, students create a coherent

representation of the problem at hand while attending to the meaning of the quantities.

 

MP.4 Model with mathematics. Students model with mathematics as they solve word problems

involving multiplication and division of fractions and decimals, as well as identify important

quantities in a practical situation and map their relationships using diagrams. Students use a

line plot to model measurement data and interpret their results with respect to context of the

situation, reflecting on whether results make sense, and possibly improve the model if it has not served its purpose.

 

MP.5 Use appropriate tools strategically. Students use rulers to measure objects to the 1/2,

1/4, and 1/8

-inch increments, recognizing both the insight to be gained and limitations of this tool as they

learn that the actual object may not match the mathematical model precisely.

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

 

I can solve expressions using order of operations

 

I can write an expression

 

I can interpret numerical expressions

 

I can find the area of a rectangle with fractional side lengths

 

I can solve real-world problems

involving multiplication of fractions

I can divide whole numbers and fractions

 

I can identify the division symbol in fractions

 

I can solve and explain real-world problems involving mixed numbers

 

I can solve real-world problems with division of fractions and whole number

 

I can create a line plot to display fractional data

 

 

Vocabulary

 

Line Plot

Frequency

 

 

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

 

  • Interactive Projector
  • Chromebooks
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Module 5

Module

Topic

Days

 

Lesson

Days

Essential Questions

+

Objectives

Common Core State Standard(s)

 

Math Practice

Module 5

Addition and Multiplication with Volume and Area

 

25 Instruction Days

 

March 4th – April 12th

 

 

Spring Break April 1st – 5th

 

Topic A – Concepts of Volume

 

Topic B – Volume and the Operations of Multiplication and Addition

 

Topic C – Area of Rectangular Figures with Fractional Side Lengths

 

Topic D – Drawing, Analysis, and Classification of Two-Dimensional Shapes

3/4-L1

3/5-L2

3/6 – L3

3/7 –A ASSESSMENT

3/8 –L4

3/11 –L6

3/12 –L7

3/13 –REVIEW, RETEACH, ASSESS

3/14 –B ASSESSMENT

3/15 –L10

3/18 –L11

3/19 –L12

3/20 –L13

3/21 –L14 + L15

3/22 – C ASSESSMENT

3/25 – REVIEW, RETEACH, ASSESS

3/26 –L16

3/27 – L17

3/28 – L18

3/29 – L19

4/1

4/2

4/3

4/4

4/5

4/8 – L20

4/9 – L21

4/10 – D ASSESSMENT

4/11 – REVIEW, RETEACH, OR ASSESS

4/12 – REVIEW, RETEACH, OR ASSESS

 

  1. Explore volume by building with and counting unit cubes.
  2. Find the volume of a right rectangular prism by packing with cubic units and counting.
  3. Compose and decompose right rectangular prisms using layers.
  4. Use multiplication to calculate volume.
  5. Use multiplication to connect volume as packing with volume as filling.
  6. Find the total volume of solid figures composed of two non-overlapping rectangular prisms.
  7. Solve word problems involving the volume of rectangular prisms with whole number edge lengths.
  8. Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.
  9. Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.
  10. Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.
  11. Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths by tiling, record by drawing, and relate to fraction multiplication.
  12. Measure to find the area of rectangles with fractional side lengths.
  13. Multiply mixed number factors, and relate to the distributive property and area model.
  14. Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.
  15. Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.
  16. Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.
  17. Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes.
  18. Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.
  19. Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.
  20. Classify two-dimensional figures in a hierarchy based on properties.
  21. Draw and identify varied two-dimensional figures from given attributes.

Topic A

5.MD.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.

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.

5.MD.4    Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

 

Topic B

5.MD.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.

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.

5.MD.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.

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.

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

 

Topic C

5.NF.4      Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a 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.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.

 

Topic D

5.G.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.

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

MP.1 Make sense of problems and persevere in solving them. Students work toward a solid

understanding of volume through the design and construction of a three-dimensional

sculpture within given parameters.

 

MP.2 Reason abstractly and quantitatively. Students make sense of quantities and their

relationships when they analyze a geometric shape or real life scenario and identify,

represent, and manipulate the relevant measurements. Students decontextualize when they

represent geometric figures symbolically and apply formulas.

MP.3 Construct viable arguments and critique the reasoning of others. Students analyze shapes,

draw conclusions, and recognize and use counterexamples as they classify two-dimensional

figures in a hierarchy based on properties.

 

MP.4 Model with mathematics. Students model with mathematics as they make connections

between addition and multiplication as applied to volume and area. They represent the area

and volume of geometric figures with equations (and vice versa) and represent fraction

products with rectangular areas. Students apply concepts of volume and area and their

knowledge of fractions to design a sculpture based on given mathematical parameters.

Through their work analyzing and classifying two-dimensional shapes, students draw

conclusions about their relationships and continuously see how mathematical concepts can be

modeled geometrically.

 

MP.6 Attend to precision. Mathematically proficient students try to communicate precisely with

others. They endeavor to use clear definitions in discussion with others and their own

reasoning. Students state the meaning of the symbols they choose, including using the equal

sign (consistently and appropriately). They are careful about specifying units of measure and

labeling axes to clarify the correspondence with quantities in a problem. They calculate

accurately and efficiently express numerical answers with a degree of precision appropriate

for the problem context. In the elementary grades, students give carefully formulated

explanations to each other. By the time they reach high school, students have learned to

examine claims and make explicit use of definitions.

 

MP.7 Look for and make use of structure. Students discern patterns and structures as they apply

additive and multiplicative reasoning to determine volumes. They relate multiplying two of

the dimensions of a rectangular prism to determining how many cubic units would be in each

layer of the prism, as well as relate the third dimension to determining how many layers there

are in the prism. This understanding supports students in seeing why volume can be

computed as the product of three length measurements or as the product of one area by one

length measurement. Additionally, recognizing that volume is additive allows students to find

the total volume of solid figures composed of more than one non-overlapping right

rectangular prism

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

I can show attributes of two-dimensional figures

 

I can classify two-dimensional figures

 

I can compare and contrast two-dimensional figures

 

I can find the area of a rectangle with fractional side lengths

 

I can find the volume by counting unit cubes

 

I can apply volume formula to solve real-world problem

 

I can show volume of a rectangular prism with whole number sides

 

I can find the volume of a figure by finding the volume of its parts

 

Vocabulary

 

cube

cubic units

unit cubes

base

right rectangular prism

volume of a solid

solid figure

face

 

 

 

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

  • Interactive Projector
  • Chromebook
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

Module 6

Module

Topic

Days

 

Lesson

Days

Essential Questions

+

Objectives

Common Core State Standard(s)

 

Math Practice

Module 6

Problem Solving with the Coordinate Plane

 

12 Instruction Days

 

April 15th – April 30th

 

Weeks 1 – 6

 

Topic A – Coordinate Systems

 

Topic B – Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

 

Topic C – Drawing Figures in the Coordinate Plane

 

Topic D – Problem Solving in the Coordinate Plane

4/15 – L2

4/16 –A ASSESSMENT

4/17 – L7, L8, L9

4/18 – TOPICS C + D

4/19 – TOPICS C + D

4/22 – TOPICS C + D

4/23 – REVIEW

4/24 – REVIEW

4/25 –REVIEW

4/26 – REVIEW

4/29 – REVIEW

4/30 – REVIEW

 

  1. Construct a coordinate system on a line.
  2. Construct a coordinate system on a plane.
  3. Name points using coordinate pairs, and use the coordinate pairs to plot points.
  4. Name points using coordinate pairs, and use the coordinate pairs to plot points.
  5. Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.
  6. Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.
  7. Plot points, using them to draw lines in the plane, and describe patterns within the coordinate pairs.
  8. Generate a number pattern from a given rule, and plot the points.
  9. Generate two number patterns from given rules, plot the points, and analyze the patterns.
  10. Compare the lines and patterns generated by addition rules and multiplication rules.
  11. Analyze number patterns created from mixed operations. 
  12. Create a rule to generate a number pattern, and plot the points.
  13. Construct parallel line segments on a rectangular grid.
  14. Construct parallel line segments, and analyze relationships of the coordinate pairs.
  15. Construct perpendicular line segments on a rectangular grid.
  16. Construct perpendicular line segments, and analyze relationships of the coordinate pairs.
  17. Draw symmetric figures using distance and angle measure from the line of symmetry.
  18. Draw symmetric figures on the coordinate plane.
  19. Plot data on line graphs and analyze trends.
  20. Use coordinate systems to solve real world problems.

Topic A

5.G.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.,  -axis and  -coordinate,  -axis and  -coordinate).

 

Topic B

5.OA.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.

5.OA.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.

5.G.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.,  -axis and  -coordinate,  -axis and  -coordinate).

 

Topic C

5.G.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.,  -axis and  -coordinate,  -axis and  -coordinate).

5.G.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 D

5.OA.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.

5.G.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.

MP.1 Make sense of problems and persevere in solving them. Students make sense of problems

as they use tape diagrams and other models, persevering to solve complex, multi-step word

problems. Students check their work and monitor their own progress, assessing their

approaches and their validity within the given context and altering their methods when

necessary.

 

MP.2 Reason abstractly and quantitatively. Students reason abstractly and quantitatively as they

interpret the steepness and orientation of a line given by the points of a number pattern.

Students attend to the meaning of the values in an ordered pair and reason about how they

can be manipulated to create parallel, perpendicular, or intersecting lines.

 

MP.3 Construct viable arguments and critique the reasoning of others. As students construct a

coordinate system on a plane, they generate explanations about the best place to create a

second line of coordinates. They analyze lines and the coordinate pairs that comprise them

and then draw conclusions and construct arguments about their positioning on the coordinate

plane. Students also critique the reasoning of others and construct viable arguments as they

analyze classmates’ solutions to lengthy, multi-step word problems.

 

MP.6 Attend to precision. Mathematically proficient students try to communicate precisely to

others. They endeavor to use clear definitions in discussion with others and in their own

reasoning. These students state the meaning of the symbols they choose, including using the

equal sign, consistently and appropriately. They are careful about specifying units of measure

and labeling axes to clarify the correspondence with quantities in a problem. Students

calculate accurately and efficiently, expressing numerical answers with a degree of precision

appropriate for the problem context. In the elementary grades, students give carefully

formulated explanations to each other. By the time they reach high school, they have learned

to examine claims and make explicit use of definitions.

 

MP.7 Look for and make use of structure. Students identify and create patterns in coordinate pairs

and make predictions about their effects on the lines that connect them. Students also

recognize patterns in sets of coordinate pairs and use those patterns to explain why a line is

parallel or perpendicular to an axis. They use operational rules to generate coordinate pairs

and, conversely, generalize observed patterns within coordinate pairs as rules.

 

21st Century Skills

  • Collaboration
  • Accountability
  • Responsibility
  • Reflection
  • Decision Making
  • Self-Direction
  • Social and Cross-Cultural Skills
  • Productivity
  • Metacognition
  • Reflection
  • Evaluation
  • Explanation
  • Problem Solving
  • Media Skills

I CAN Statements

 

I can name and label the parts of a coordinate plane

 

I can graph points on a positive coordinate plane

I can represent real-world problems by graphing points on coordinate plane

 

I can generate numerical patterns

 

I can determine the relationship, given a numerical pattern

Vocabulary

coordinate plane

coordinate

coordinate pair or ordered pair

origin

midpoint

x-axis

y-axis

 

 

Assessments

+ Activities

  • Sprints – are designed to develop math fluency. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving on the second part, even if only by one more. Students receive one minute per part.
  • Application Problem – application problems use literacy strategies to assess students understanding of mathematics.
  • Choral Response Assessments
  • Study Island Assessments
  • Exit Slips [reflection of lesson]
  • Center-based Activities
  • Formative Assessments
  • Summative Assessments
  • Gradual Release of Responsibility Model

Technology + Resources + Materials

 

  • Interactive Projector
  • Chromebook
  • Accelerated Math
  • Zearn – web-based learning
  • Study Island Exact Path
  • Study Island
  • SownToGrow – web-based reflection
  • Flocabulary
  • Kahoot
  • YouTube
  • Kiddle
  • Personal White Boards – with template inserted
  • Manipulatives

 

 

Review of 5th Grade Math Concepts

 

+

 

K-Prep Testing

 

12 Instruction Days

 

May 1st – May 16th

 

Closing Day May 17th

 

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