5^{th} Grade Math Curriculum Map
20182019
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 9^{th} – 17^{th}


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.
 Use appropriate tools strategically.
 Look for and make use of structure.
 Look for and express regularity in repeated reasoning.

21^{st} 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 – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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 20^{h} –
September 17^{th}
Labor Day Sept. 3^{rd}
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 singledigit 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 singledigit 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 multidigit 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 wholenumber exponents to denote powers of 10.
5.MD.A.1 Convert among differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use
these conversions in solving multistep, real world problems.
Topic B
5.NBT.A.3a Read and write decimals to thousandths using baseten 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 baseten 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 baseten 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 baseten 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 wholenumber 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.

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural 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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebooks
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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
MultiDigit Whole Number and Decimal Fraction Operations
32 Instruction Days
September 19^{TH} – November 12^{th}
Fall Break October 8^{th} 12^{th}
Halloween Party
October 31^{st}
Parent Teacher Meetings
November 12^{th}
Topic A – Mental Strategies for MultiDigit Whole Number Multiplication
Topic B – The Standard Algorithm for MultiDigit Whole Number Multiplication
Topic C – Decimal MultiDigit Multiplication
Topic D – Measurement Word Problems with Whole Number and Decimal Multiplication
Topic E – Mental Strategies for MultiDigit Whole Number Division
Topic G – Partial Quotients and MultiDigit 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

 Multiply multidigit whole numbers and multiples of
10 using place value patterns and the distributive
and associative properties
 Estimate multidigit products by rounding factors to
a basic fact and using place value patterns.
 Write and interpret numerical expressions and
compare expressions using a visual model.
 Convert numerical expressions into unit form as a
mental strategy for multidigit multiplication.
 Connect visual models and the distributive property
to partial products of the standard algorithm without
 Connect area diagrams and the distributive property
to partial products of the standard algorithm without
 Connect area diagrams and the distributive property
to partial products of the standard algorithm with
 Fluently multiply multidigit whole numbers using the
standard algorithm and using estimation to check for
reasonableness of the product.
 Fluently multiply multidigit whole numbers using the
standard algorithm to solve multistep word
 Multiply decimal fractions with tenths by multidigit
whole numbers using place value understanding to
record partial products
 Multiply decimal fractions by multidigit whole
numbers through conversion to a whole number
problem and reasoning about the placement of the
 Reason about the product of a whole number and a
decimal with hundredths using place value
understanding and estimation.
 Use whole number multiplication to express
equivalent measurements
 Use fraction and decimal multiplication to express
equivalent measurements.
 Solve twostep word problems involving
measurement conversions.
 Use divide by 10 patterns for multidigit whole number

 Use basic facts to approximate quotients with twodigit

 Use basic facts to estimate quotients with twodigit

 Divide two and threedigit dividends by multiples of
10 with singledigit quotients and make connections to
a written method.
 Divide two and threedigit dividends by twodigit
divisors with singledigit quotients and make
connections to a written method.
 Divide two and threedigit dividends by twodigit
divisors with singledigit quotients and make
connections to a written method.
 Divide three and fourdigit dividends by twodigit
divisors resulting in two and threedigit quotients,
reasoning about the decomposition of successive
remainders in each place value
 Divide three and fourdigit dividends by twodigit
divisors resulting in two and threedigit quotients,
reasoning about the decomposition of successive
remainders in each place value.
 Divide decimal dividends by multiples of 10,
reasoning about the placement of the decimal point
and making connections to a written method.
 Use basic facts to approximate decimal quotients with twodigit divisors, reasoning about the
placement of the decimal point
 Divide decimal dividends by twodigit divisors,
estimating quotients, reasoning about the placement
of the decimal point, and making connections to a
written method.
 Divide decimal dividends by twodigit 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 multidigit 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 wholenumber 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 multidigit 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 multidigit 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 multidigit 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 wholenumber exponents to denote power of 10.
5.NBT.5 Fluently multiply multidigit 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 differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use
these conversions in solving multistep, real world problems.
Topic E
5.NBT.1 Recognize that in a multidigit 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 wholenumber exponents to denote power of 10.
5.NBT.6 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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 wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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 wholenumber 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 multidigit 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 fourdigit dividends by twodigit divisors. Students also check the reasonableness
of the intermediate results of their division algorithms as they solve multidigit division word
problems.

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural Skills
 Productivity
 Metacognition
 Reflection
 Evaluation
 Explanation
 Problem Solving
 Media Skills

I CAN Statements
I can multiply multidigit 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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebooks
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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 15^{th} –
December 18^{th}
Parent Teacher Conferences November 12^{th}
Thanksgiving Break November 21^{st}  23^{rd}
Christmas Break December 21^{st} – January 2^{nd}
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

 Make equivalent fractions with the number line, the area model, and numbers.
 Make equivalent fractions with sums of fractions with like denominators.
 Add fractions with unlike units using the strategy of creating equivalent fractions.
 Add fractions with sums between 1 and 2.
 Subtract fractions with unlike units using the strategy of creating equivalent fractions.
 Subtract fractions from numbers between 1 and 2.
 Solve twostep word problems.
 Add fractions to and subtract fractions from whole numbers using equivalence and the number line as strategies.
 Add fractions making like units numerically.
 Add fractions with sums greater than 2.
 Subtract fractions making like units numerically.
 Subtract fractions greater than or equal to 1.
 Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations
 Strategize to solve multiterm problems.
 Solve multistep 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.

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural 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 realworld 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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebooks
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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 3^{rd} –
March 1^{st}
Weeks 1 – 6
Martin Luther King, Jr. Day
January 21^{st }
Presidents’ Day February 18^{th}
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

 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.
 Interpret a fraction as division.
 Interpret a fraction as division
 Use tape diagrams to model fractions as division
 Solve word problems involving the division of whole numbers with answers in the form of fractions or whole numbers.
 Relate fractions as division to fraction of a set.
 Multiply any whole number by a fraction using tape diagrams.
 Relate fraction of a set to the repeated addition interpretation of fraction multiplication.
 Find a fraction of a measurement and solve word problems.
 Compare and evaluate expressions with parentheses.
 Solve and create fraction word problems involving addition, subtraction, and multiplication.
 Solve and create fraction word problems involving addition, subtraction, and multiplication.
 Multiply unit fractions by unit fractions
 Multiply unit fractions by nonunit fractions.
 Multiply nonunit fractions by nonunit fractions.
 Solve word problems using tape diagrams and fractionbyfraction multiplication.
 Relate decimal and fraction multiplication.
 Relate decimal and fraction multiplication.
 Convert measures involving whole numbers, and solve multistep word problems.
 Convert mixed unit measurements, and solve multistep word problems.
 Explain the size of the product, and relate fraction and decimal equivalence to multiplying a fraction by 1.
 Compare the size of the product to the size of the factors.
 Compare the size of the product to the size of the factors.
 Solve word problems using fraction and decimal multiplication.
 Divide a whole number by a unit fraction.
 Divide a unit fraction by a whole number.
 Solve problems involving fraction division.
 Write equations and word problems corresponding to tape and number line diagrams.
 Connect division by a unit fraction to division by 1 tenth and 1 hundredth.
 Divide decimal dividends by nonunit decimal divisors.
 Divide decimal dividends by nonunit decimal divisors.
 Interpret and evaluate numerical expressions including the language of scaling and fraction division.
 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 50pound 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 differentsized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, 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 nonzero 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 nonzero 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 1/3cup 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.

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural 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 realworld 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 realworld problems involving mixed numbers
I can solve realworld 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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebooks
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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 4^{th} – April 12^{th}
Spring Break April 1^{st} – 5^{th}
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 TwoDimensional Shapes

3/4L1
3/5L2
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

 Explore volume by building with and counting unit cubes.
 Find the volume of a right rectangular prism by packing with cubic units and counting.
 Compose and decompose right rectangular prisms using layers.
 Use multiplication to calculate volume.
 Use multiplication to connect volume as packing with volume as filling.
 Find the total volume of solid figures composed of two nonoverlapping rectangular prisms.
 Solve word problems involving the volume of rectangular prisms with whole number edge lengths.
 Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.
 Apply concepts and formulas of volume to design a sculpture using rectangular prisms within given parameters.
 Find the area of rectangles with wholebymixed and wholebyfractional number side lengths by tiling, record by drawing, and relate to fraction multiplication.
 Find the area of rectangles with mixedbymixed and fractionbyfraction side lengths by tiling, record by drawing, and relate to fraction multiplication.
 Measure to find the area of rectangles with fractional side lengths.
 Multiply mixed number factors, and relate to the distributive property and area model.
 Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.
 Solve real world problems involving area of figures with fractional side lengths using visual models and/or equations.
 Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.
 Draw parallelograms to clarify their attributes, and define parallelograms based on those attributes.
 Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombuses based on those attributes.
 Draw kites and squares to clarify their attributes, and define kites and squares based on those attributes.
 Classify twodimensional figures in a hierarchy based on properties.
 Draw and identify varied twodimensional 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 wholenumber 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 wholenumber 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 wholenumber 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 nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping 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 twodimensional 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 twodimensional 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 threedimensional
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 twodimensional
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 twodimensional 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 nonoverlapping right
rectangular prism

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural Skills
 Productivity
 Metacognition
 Reflection
 Evaluation
 Explanation
 Problem Solving
 Media Skills

I CAN Statements
I can show attributes of twodimensional figures
I can classify twodimensional figures
I can compare and contrast twodimensional 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 realworld 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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebook
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased 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 15^{th} – April 30^{th}
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

 Construct a coordinate system on a line.
 Construct a coordinate system on a plane.
 Name points using coordinate pairs, and use the coordinate pairs to plot points.
 Name points using coordinate pairs, and use the coordinate pairs to plot points.
 Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.
 Investigate patterns in vertical and horizontal lines, and interpret points on the plane as distances from the axes.
 Plot points, using them to draw lines in the plane, and describe patterns within the coordinate pairs.
 Generate a number pattern from a given rule, and plot the points.
 Generate two number patterns from given rules, plot the points, and analyze the patterns.
 Compare the lines and patterns generated by addition rules and multiplication rules.
 Analyze number patterns created from mixed operations.
 Create a rule to generate a number pattern, and plot the points.
 Construct parallel line segments on a rectangular grid.
 Construct parallel line segments, and analyze relationships of the coordinate pairs.
 Construct perpendicular line segments on a rectangular grid.
 Construct perpendicular line segments, and analyze relationships of the coordinate pairs.
 Draw symmetric figures using distance and angle measure from the line of symmetry.
 Draw symmetric figures on the coordinate plane.
 Plot data on line graphs and analyze trends.
 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, multistep 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, multistep 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.

21^{st} Century Skills
 Collaboration
 Accountability
 Responsibility
 Reflection
 Decision Making
 SelfDirection
 Social and CrossCultural 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 realworld 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
xaxis
yaxis

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]
 Centerbased Activities
 Formative Assessments
 Summative Assessments
 Gradual Release of Responsibility Model

Technology + Resources + Materials
 Interactive Projector
 Chromebook
 Accelerated Math
 Zearn – webbased learning
 Study Island Exact Path
 Study Island
 SownToGrow – webbased reflection
 Flocabulary
 Kahoot
 YouTube
 Kiddle
 Personal White Boards – with template inserted
 Manipulatives

Review of 5^{th} Grade Math Concepts
+
KPrep Testing
12 Instruction Days
May 1^{st} – May 16^{th}
Closing Day May 17^{th}
