Waterloo School Community Unit School District #5
Curriculum Map of the New Illinois Learning Standards
Fifth Grade Mathematics
How to Read the Grade Level Content Standards
Standards define what students should understand and be able to do.
Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because
mathematics is a connected subject.
Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.
1
Standards for Mathematical Practice
The Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all
students Grades K-12. Below are a few examples of how these Practices may be integrated into tasks students complete.
1.
Make sense of problems and persevere in solving them.
Mathematically proficient students in grade 5 should solve problems by applying their understanding of operations with whole numbers,
decimals, and fractions including mixed numbers. They solve problems related to volume and measurement
conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their
thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the
problem in a different way?”.
2. Reason abstractly and quantitatively.
Mathematically proficient students in grade 5should recognize that a number represents a specific quantity. They connect
quantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved
and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students
write simple expressions that record calculations with numbers and represent or round numbers using place value concepts.
3. Construct viable arguments and critique the reasoning of others.
In fifth grade mathematical proficient students may construct arguments using concrete referents, such as objects, pictures, and
drawings. They explain calculations based upon models and properties of operations and rules that generate patterns. They
demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as
they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their
thinking to others and respond to others’ thinking.
4. Model with mathematics.
Mathematically proficient students in grade 5 experiment with representing problem situations in multiple ways including
numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc.
Students need opportunities to connect the different representations and explain the connections. They should be able to use all of
these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results
make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve
problems.
2
5. Use appropriate tools strategically.
Mathematically proficient fifth graders consider the available tools (including estimation) when solving a mathematical probl em and
decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to
measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real wor ld
data.
6. Attend to precision.
Mathematically proficient students in grade 5 continue to refine their mathematical communication skills by using clear and precise
language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to
expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the
meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answe rs in
cubic units.
7. Look for and make use of structure.
In fifth grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use
properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine
numerical patterns and relate them to a rule or a graphical representation.
8. Look for and express regularity in repeated reasoning.
Mathematically proficient fifth graders use repeated reasoning to understand algorithms and make generalizations about patterns.
Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and
perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate
generalizations.
3
Fifth Grade Mathematics Curriculum Map
Waterloo School District Scope and Sequence Overview
Unit of Study
Domain and Standards
1
Domain: Numbers and Operations in Base Ten, Operations and Algebraic Thinking, Numbers and Operations - Fraction
Standards: 5.OA.1, 5.OA.2, 5.NBT.2, 5.NF.5a
2
Domain: Measurement and Data, Numbers and Operations in Base Ten
Standards: 5.MD.1, 5.NBT.1, 5.NTB.2, 5.NBT.3a, 5.NBT.4, 5.NBT.7
3
Domain: Operations and Algebraic Thinking, Number and Operations in Base Ten, Geometry
Standards: 5.OA.2, 5.NBT.2, 5.NBT.3a, 5.G.3, 5.G.4
4
Domain: Numbers and Operations in Base Ten, Operations and Algebraic Thinking
Standards: 5.OA.2, 5.NBT.2, 5.NBT.6, 5.NBT.7
5
Domain: Numbers and Operations - Fractions, Numbers and Operations Base Ten
Standards: 5.NF.1, 5.NF.2, 5.NF.3, 5.NBT.3a, 5.NBT.4, 5.NBT.7
6
7
8
9
10
Domain: Numbers and Operations in Base Ten, Measurement and Data, Numbers and Operations - Fractions
Standards: 5.NBT.4, 5.MD.1, 5.MD.2, 5.NF.1, 5.NF.2, 5.NF.3
Domain: Numbers and Operations in Base Ten, Operations and Algebraic Thinking, Measurement and Data
Standards: 5.NBT.1, 5.NBT.2, 5.OA.1, 5.OA.2, 5.MD.2
Domain: Numbers and Operations - Fractions
Standards: 5.NF.1, 5.NF.2, 5.NF.4, 5.NF.5b, 5.NF.6
Domain: Numbers and Operations – Fractions, Geometry, Measurement and Data
Standards: 5.NF.4, 5.NF.7a, 5.NF.7b, 5.NF.7c, 5.G.1, 5.G.2, 5.MD.1, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b, 5.MD.5c, 5.G.1, 5.G.2,
5.MD.1, 5.MD.3a, 5.MD.3b, 5.MD.5a, 5.MD.5b, 5.MD.5c
Domain: Measurement and Data, Geometry, Operations and Algebraic Thinking
Standards: 5.MD.1, 5.MD.2, 5.MD.3a, 5.MD.4, 5.MD.5b, 5.G.1, 5.G.2, 5.OA.2, 5.OA.3
11
Domain: Measurement and Data
Standards: 5.MD.1, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b
12
Domain: Numbers and Operations – Fractions, Numbers and Operations Base Ten
Standards: 5.NF.7a, 5.NF.7b, 5.NF.7c, 5.NBT.7
4
Fifth Grade
Instruction and Assessment Schedule
Assessment
Unit of
Study
2
Unit of
Study
3
Ch. 1
Test
Ch. 2
Test
Ch. 3
Test
??
??
Unit of
Study
4
Unit of
Study
5
Unit of
Study
6
Ch. 4
Test
Ch. 5
Test
Ch. 6
Test
??
??
??
Unit of
Study
7
Unit of
Study
8
Unit of
Study
9
Ch. 7
Test
Ch. 8
Test
Ch. 9
Test
??
??
??
Unit of
Study
10
Unit of
Study
11
Unit of
Study
12
Ch. 10
Test
Ch. 11
Test
Ch. 12
Test
End of
Year
Benchmark 3
Unit of
Study
1
??
Common Assessment D
??
Common Assessment C
??
Benchmark 2
??
Common Assessment B
Instructional
Content
Benchmark 1
Approx.
Number of
Days of
Instruction
Common Assessment A
It is expected that the units will be taught consecutively. The table below reflects which units are assessed on each benchmark. It is
possible to begin a new unit prior to the quarter in which it is being assessed.
Getting
Ready
for Gr.
1 Unit
5
Unit of Study 1
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Operations and Algebraic Thinking
Standard(s):
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 the numerical expressions without evaluating them. For example, express the calculation “add
8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or
product.
Domain: Number and Operations in Base Ten
Standard(s):
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 multiplies or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Domain: Number and Operations - Fractions
Standard(s):
5.NF.5a – Interpret multiplication as scaling (resizing) by: 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.
6
Math Content Objectives
5.OA.1
I can use the order of operations to solve numerical
expressions.
5.OA.2
I can write simple numerical expressions
I can use words to interpret numerical expressions
5.NBT.2
I can multiply by powers of ten
I can divide by powers of ten
5.NF.5a
I can predict the size of a product when one factor doesn’t
change when comparing two equations
Example: 225 * 60 and 225 * 30)
Vocabulary
Composite Number
Commutative Property of Multiplication
Difference
Divisible by
Divisibility rule
Even number
Exponent
Exponent key
Exponential notation
Factor
Factor pair
Factor rainbow
Factor string
Length of factor string
Name Collection Box
Name/collection box
Number model
Number Sentence
Numerical Expressions
Odd number
Order of operations
Prime
Prime factorization
Prime number
Product
Quotient
Rectangular array
Remainder
Square array
Square number
Square Root
Square-root key
Sum
Turn-around rule (for multiplication)
Unsquaring a number
Teacher’s Resources and Notes
5.NF.5a
Teachers Manual Page 36
7
Everyday Math
Common Core
Alignment
Lesson 1-1*
5.OA.2
5.NBT.2
Unit of Study 1 – Additional Resources
Lesson 1-1 – No Study Link Worksheet
Lesson 1-5 – Teach Mental Strategies 2,3,5,10. Use calculator for all other divisors
Lesson 1-10 – Do not do Math Box problem #2
Lesson 1-2
5.NBT.2
Lesson 1-3
5.OA.2
Lesson 1-4
5.OA.2
5.NF.5a
Lesson 1-5*
5.NBT.2
Lesson 1-6
5.NBT.2
Lesson 1-7
5.OA.2
Lesson 1-8
5.OA.2
5.NBT.2
Lesson 1-9
5.OA.2
5.NBT.2
8
Unit of Study 2
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Measurement and Data
Standard(s):
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 multistep, real world problems.
Domain: Number and Operations in Base Ten
Standard(s):
5.NBT.1 – Recognize that in a multi-digit number, a digit in one place represents 10 times as much as ir 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 multiplies or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.3a – Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
5.NBT.4 – Use place value understanding to round decimals to any place.
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.
9
Math Content Objectives
5.MD.1
I can do measurement conversions within the same
system
I can use these conversion to solve multi-step real world
problems
5.NBT.1
I can determine that a digit represents ten times what it
would be in the place to its right and 1 tenth to its left
5.NBT.2
I can multiply by powers of ten
I can divide by powers of ten
5.NBT.3a,
I can read and write decimals to thousandths place using
numerals, number names, and expanded forms
5.NBT.4
I can round place value to decimals to anyplace
5.NBT.7
I can add, subtract, multiply, and divide decimals to the
hundredths using various methods using a variety of
strategies
I can explain the answer was found
Vocabulary
Teacher’s Resources and Notes
Algorithm
Certain
Colum-addition method
Difference
Digit
Expanded notation
Impossible
Magnitude estimate
Minuend
Number sentence
Open number
Operation symbol
Partial-differences method
Partial-products method
Partial-sums method
Place value
Probability meter
Relation symbol
Solution
Subtrahend
Trade-first method
Variable
10
Everyday Math
Common Core
Alignment
Unit of Study 2 – Additional Resources
Lesson 2-1*
5.MD.1
*Lesson 2-1 – Replace Lesson to meet to meet 5.MD.1
*Add Journal Page 56a & 56b
Lesson 2-2
5.NBT.1
5.NBT.3a
5.NBT.7
**Lesson 2-9 – Add Partial Products in a Box
Lesson 2-10 – Study Link could be enrichment
Lesson 2-3
5.NBT.7
Lesson 2-4
5.NBT.7
Lesson 2-6
Covers Standards of
Mathematical Practices
Lesson 2-7
5.NBT.2
Lesson 2-8
5.NBT.4
5.NBT.7
Lesson 2-9**
Covers Standards of
Mathematical Practices
Lesson 2-11
Assessment
11
Unit of Study 3
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Operations and Algebraic Thinking
Standard(s):
5.OA.2 – Write simple expressions that record calculations with numbers, and interpret the numerical expressions without evaluating them. For example, express the calculation “add
8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or
product.
Domain: Number and Operations in Base Ten
Standard(s):
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 multiplies or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.3a – Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
Domain: Geometry
Standard(s):
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.
12
Math Content Objectives
5.OA.2
I can write simple numeric expressions
I can explain simple numeric expressions without finding
the answer
5.NBT.2
I can multiply by powers of ten
I can divide by powers of ten
5.NBT.3a
I can read and write decimals to thousandths place using
numerals, number names, and expanded forms
5.G.3
I can identify attributes and categories of two dimensional
figures
Vocabulary
Teacher’s Resources and Notes
Acute angle
Obtuse angle
Right angle
Straight angle
Straight angle
Reflex angle
Geometry template
Arc
Equilateral triangle
Isosceles triangle
Scalene triangle
Congruent
Polygon
Quadrangle
Regular polygon
5.G.4
I can classify two dimensional figures in a hierarchy
according to the attributes
13
Everyday Math
Common Core
Alignment
Lesson 3-2*
5.OA.2
5.NBT.2
Unit of Study 3 – Additional Resources
*Lesson 3-2 – Take out Journal Lesson Pages 62-63
**Lesson 3-6 – Keep Journal Page 7. Exclude 76-78 (Supplement).
***Lesson 3-7 – Use Math Master 440A
Lesson 3-4
5.G.3
Lesson 3-6**
5.G.3
Lesson 3-7***
5.G.3
5.G.4
Lesson 3-9
5.NBT.2
5.NBT.3a
Lesson 3-11
Assessment
14
Unit of Study 4
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Operations and Algebraic Thinking
Standard(s):
5.OA.2 – Write simple expressions that record calculations with numbers, and interpret the numerical expressions without evaluating them. For example, express the calculation “add
8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or
product.
Domain: Number and Operations in Base Ten
Standard(s):
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 multiplies or divided by a power of 10. Use whole-number exponents to denote powers 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.
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.
15
Math Content Objectives
5.OA.2
I can write simple numeric expressions
I can explain simple numeric expressions without finding
the answer
5.NBT.2
I can multiply by powers of ten
I can divide by powers of ten
Vocabulary
Teacher’s Resources and Notes
Dividend
Divisor
Quotient
Multiple(s)
Remainder
Partial quotient
Decimal point
Variable
5.NBT.6
I can divide four digit whole numbers by two digit whole
numbers using a variety of strategies
I can show the results of division using equations, arrays,
or area models
I can explain the results of division using equations,
arrays, or area models
5.NBT.7
I can add, subtract, multiply, and divide decimals to the
hundredths using various methods using a variety of
strategies
I can explain the answer was found
16
Everyday Math
Common Core
Alignment
Lesson 4-1*
5.OA.2
5.NBT.2
5.NBT.6
Unit of Study 4 – Additional Resources
*Move Math Masters 440a to Unit 3 Lesson 3-7
**Lesson 4-3 Keep Finding Factors Journal Page 104
Lesson 4-2
5.NBT.6
Lesson 4-3**
Covers Standards of
Mathematical Practices
Lesson 4-4
5.NBT.6
Lesson 4-5
5.NBT.7
Lesson 4-6
5.OA.2
5.NBT.6
5.NBT.7
Lesson 4-7
5.OA.2
5.NBT.2
Lesson 4-8
Assessment
17
Unit of Study 5
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Number and Operations - Fractions
Standard(s):
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 + ½ = 3/7, by observing that 3/7 < ½.
5.NF.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of who numbers leading to answers I in the form of
fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret ¾ t of dividing 3 by 4, noting that ¾ multiplied
by 4 equals 3 and that when 3 wholes are shared equally among 4 people, each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by
weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Domain: Number and Operations in Base Ten
Standard(s):
5.NBT.3a – Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x
(1/1000).
5.NBT.4 – Use place value understanding to round decimals to any place.
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.
18
Math Content Objectives
5.NF.1
I can use equivalent fractions to add fractions with unlike
denominators (including mixed numbers)
I can use equivalent fractions to subtract fractions to
subtract fractions with unlike denominators (including
mixed numbers)
5.NF.2
I can solve word problems involving addition and
subtraction of fractions
I can use benchmark fractions and number sense to
estimate and assess the reasonableness of answers
5.NF.3
I can explain a fraction as division of the numerator by the
denominator
I can solve word problems involving division and write the
remainder as a fraction or mixed numbers using a variety
of strategies.
Vocabulary
Teacher’s Resources and Notes
Whole
Denominator
Numerator
Unit fraction
Improper fraction
Mixed number
Benchmark
Fraction stick
Equivalent fractions
Round down
Round up
Round to the nearest
Repeating decimal
Percent
5.NBT.3a
I can read and write decimals to thousandths place using
numerals, number names, and expanded forms
5.NBT.4
I can place value to round decimals to anyplace
5.NBT.3a
Read and write decimals to thousandths place using
numerals, number names, and expanded forms
5.NBT.4
Place value to round decimals to anyplace
19
Everyday Math
Common Core
Alignment
Lesson 5-1
5.NF.3
Unit of Study 5 – Additional Resources
*Lesson 5-5 – Skip Journal page 139 and #2 on page 140
**Skip Filling in a Table of Decimal Equivalents for Fractions Section
Lesson 5-2
Covers Standards of
Mathematical Practices
Lesson 5-3
5.NF.1
5.NF.2
Lesson 5-4
5.NF.2
Lesson 5-5*
5.NBT.3a
5.NBT.4
Lesson 5-6**
5.NBT.3a
5.NBT.4
5.NF.3
Lesson 5-7
5.NBT.3a
Lesson 5-8
5.NBT.3a
5.NBT.4
Lesson 5-13
Assessment
20
Unit of Study 6
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Numbers and Operation in Base Ten
Standard(s):
5.NBT.4 – Use place value understanding to round decimals to any place.
Domain: Measurement and Data
Standard(s):
5.MD.1 – Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multistep, real world problems.
5.MD.2 – Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 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.
Domain: Number and Operations - Fractions
Standard(s):
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 answer. For
example, recognize an incorrect result 2/5 + ½= 3/7, by observing that 3/7 < ½.
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 ¾ as the result of dividing 3 by 4, noting
that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of ¾. If 9 people want to share a 50 pound sack of
rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
21
Math Content Objectives
5.NBT.4
I can round place value to decimals to anyplace
5.MD.1
I can do measurement conversions within the same
system
I can use these conversions to solve multi-step real world
problems
5.MD.2
I can make a line plot to display a set of measurements in
fractions of a unit
Solve problems with the information on the line plot
5.NF.1
I can use equivalent fractions to add fractions with unlike
denominators (including mixed numbers)
I can use equivalent fractions to subtract fractions to
subtract fractions with unlike denominators (including
mixed numbers)
Vocabulary
Teacher’s Resources and Notes
Common denominator
Fathom
Cubit
Fair game
Frequency table
Great span
Landmark
Leaf
Line plot
Maximum
Median
Mode
Population
Quick common denominator
Sample
Simplest Form
Span
Stem-and-leaf plot
Survey
Unlike denominator
5.NF.2
I can solve word problems involving addition and
subtraction of fractions
I can use benchmark fractions and number sense to
estimate and assess the reasonableness of answers
5.NF.3
I can explain a fraction as division of the numerator by the
denominator
I can solve word problems involving division and write the
remainder as a fraction or mixed numbers using a variety
of strategies
22
Everyday Math
Common Core
Alignment
Lesson 6-1*
5.NBT.4
5.MD.2
Unit of Study 6 – Additional Resources
*In lesson 6-1 be sure to teach journal pages 166 and MM 186A and 186B
*Skip 6-3, 6-7
Lesson 6-2
5.MD.1
Lesson 6-4
SMP 1-4, 6
Lesson 6-5
SMP 1-6
Lesson 6-6
SMP 1-6
Lesson 6-8
5.NF.1
5.NF.2
5.NF.3
Lesson 6-9
5.NF.1
5.NF.2
Lesson 6-10
5.NF.1
5.NF.2
Lesson 6-11
Assessment
23
Unit of Study 7
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Numbers and Operations in Base Ten
Standard(s):
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 powers of 10.
Domain: Operations and Algebraic Thinking
Standard(s):
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 x (8+ 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product .
Domain: Measurement and Data
Standard(s):
5.MD.2 – Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 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.
24
Math Content Objectives
5.NBT.1
I can determine that a digit represents ten times what it
would be in the place to its right and 1 tenth to its left
5.NBT.2
I can multiply by powers of ten
I can divide by powers of ten
5.OA.1
I can use the order of operations to solve numerical
expressions.
5.OA.2
I can write simple numerical expressions
Use words to interpret numerical expressions
5.MD.2
I can make a line plot to display a set of measurements in
fractions of a unit solve problems with the information on
the line
Vocabulary
Teacher’s Resources and Notes
Account Balance
Ambiguous
Axis
Base
Change-Sign Key
Debt
Expanded notation
Exponent
Exponential notation
Expression
Factor
In the black
In the red
Line graph
Negative number
Nested parenthesis
Number-word notation
Opposite
Order of operations
Powers of 10
Power of a number
Scientific notations
Standard notation
25
Everyday Math
Common Core
Alignment
Unit of Study 7 – Additional Resources
Lesson 7-1
5.NBT.2
Lesson 7-2
5.NBT.1
5.NBT.2
Lesson 7-3
5.NBT.2
Lesson 7-4
5.OA.1
5.OA.2
Lesson 7-5
5.OA.1
5.OA.2
Lesson 7-7
SMP1-4, 6-8
Lesson 7-8
SMP2-8
Lesson 7-9
SMP2-4, 6-8
Lesson 7-10
5.MD.2
Lesson 7-11
SMP1-6
Lesson 7-12
Assessment
26
Unit of Study 8
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Numbers and Operations - Fractions
Standard(s):
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 answer.
For example, recognize an incorrect result 2/5 + ½= 3/7, by observing that 3/7 < ½.
5.NF.4 – Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. – Interpret the product (a/b) x q as a parts of the partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷b. For example, use a visual
fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd).
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.5b – Explaining why multiplying a given number by fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers
greater than 1 as a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (nxa)/(nxb) to the effect of
multiplying a/b by 1.
5.NF.6 – Solve real work problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
27
Math Content Objectives
5.NF.1
I can use equivalent fractions to add fractions with unlike
denominators (including mixed numbers)
I can use equivalent fractions to subtract fractions to
subtract fractions with unlike denominators (including
mixed numbers)
Vocabulary
Teacher’s Resources and Notes
Area model
Discount
Horizontal
Quick common denominator
Unit fraction
Unit percent
Vertical
5.NF.2
I can solve word problems involving addition and
subtraction of fractions
I can use benchmark fractions and number sense to
estimate and assess the reasonableness of answers
5.NF.4a
I can represent a whole number as a fraction
5.NF.4b
I can multiply fractional side lengths to find the area of
rectangles
5.NF.5b
I can compare the size of a product to the size of one
factor based on the size of the other factor without
multiplying
5.NF.6
I can solve real-world problems involving multiplication of
fractions and mixed numbers using visual fraction models
or equations
28
Everyday Math
Common Core
Alignment
Unit of Study 8 – Additional Resources
Lesson 8-1
5.NF.1
5.NF.2
Lesson 8-2
5.NF.1
5.NF.2
Lesson 8-3
5.NF.1
5.NF.2
Lesson 8-4
5.NF.1
Lesson 8-5*
5.NF.4a
5.NF.6
Lesson 8-6
5.NF.4a
5.NF.5b
5.NF.6
Lesson 8-7
5.NF.4a
5.NF.5b
Lesson 8-8
5.NF.4a
5.NF.4b
5.NF.6
Lesson 8-9
SMP 1-6
Lesson 8-10
SMP 1-6
Lesson 8-12
5.NF.7a
5.NF.7b
5.NF.7c
Lesson 8-13
Assessment
29
Unit of Study 9
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Numbers and Operations - Fractions
Standard(s):
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.7 – Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a - Interpret division of a unit fraction by a non-zero whole number, and computer 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) x 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 to show the quotient. Use the
relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (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 ½ lb of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?
Domain: Geometry
Standard(s):
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 ) 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 (3.g., x-axis and x coordinate,
y-axis and y-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.
Domain: Measurement and Data
Standard(s):
5.MD.1 – Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real world
problems.
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 a “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.
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 x w x h and V = b x 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.
30
Math Content Objectives
5.NF.4b
I can multiply fractional side lengths to find the area of
rectangles
5.G.1
I can identify the parts of a coordinate plane and plot a given
point on the plane using ordered pairs.
5.G.2
I can represent and interpret real world and math problems by
graphing points on the coordinate plane
5.NF.7a
I can explain division of a unit fraction by a whole number and
find the quotient of a division problem for a unit fraction and
whole number
5.NF.7b
I can explain division of a whole number by a unit fraction and
find the quotient of a division problem for a whole number and a
unit fraction
5.NF.7c
I can solve real-world problems involving division of unit
fractions by whole numbers and solve real-world problems
involving division of whole numbers by unit fractions
5.MD.1
I can measure conversions within the same system and use
these conversions to solve multi-step, real-world problems
5.MD.3a
I can recognize a unit cube and know that it can be used to
measure volume
5.MD.3b
I can identify the volume of a solid figure in cubic units
5.MD.4
I can measure volume by counting unit cubes
5.MD.5a
I can find the volume of a right rectangular prism using unit
cubes, show its volume by multiplying the edge lengths, and
show its volume by multiplying the height by the area of the
base
Vocabulary
Teacher’s Resources and Notes
Reflection
Square Units
Translation
Variable
Vertical axis
Volume
31
Math Content Objectives (cont.)
Vocabulary
Teacher’s Resources and Notes
5.MD.5b
Use l * w * h and b * h to find volume for right rectangular prisms
in real-world problems
5.MD.5c
Find the volume of a solid figure made of two non overlapping
parts by adding volumes of the two right rectangular prisms in
real-world problems
32
Everyday Math
Common Core
Alignment
Lesson 9-1
5.G.1
5.G.2
Lesson 9-2
5.G.1
5.G.2
Lesson 9-3
5.G.1
5.G.2
Lesson 9-4
5.NF.4b
5.NF.7a
5.NF.7b
5.NF.7c
Lesson 9-5
SMP1-3, 5, 6, 8
Lesson 9-6
SMP5, 5-8
Lesson 9-8
5.MD.3a
5.MD.3b
5.MD.4
5.MD.5a
5.MD.5b
Lesson 9-9
5.MD.5c
Lesson 9-10
5.NF.4b
5.MD.1
5.MD.3a
5.MD.3b
5.MD.5a
5.MD.5b
Unit of Study 9 – Additional Resources
* Skip lesson 9-7, but use math journal pages 317, 318, and 319 for enrichment. Use math boxes and math masters page 278 for extra practice.
* Skip lesson 9-9, but do math journal pages 325A and 325B. Also, number 19 and 20 should be extra credit or eliminated on the unit test.
* Skip journal page 329 in lesson 9-10
* Number 19 and 20 should be extra credit or eliminated on the unit test.
33
Unit of Study 10
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Measurement and Data
Standard(s):
5.MD.1 – Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real world
problems.
5.MD.2 – Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 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.
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 a “one cubic unit” of volume, and can be used to measure volume.
5.MD.4 – Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.5 – Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
b. – Apply the formulas V = l x w x h and V = b x 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.
Domain: Geometry
Standard(s):
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 ) 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 (3.g., x-axis and x
coordinate, y-axis and y-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
Domain: Operations and Algebraic Thinking
Standard(s):
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 x (8+ 7). Recognize that 3 x (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.
34
Math Content Objectives
Vocabulary
Teacher’s Resources and Notes
5.MD.3a
I can recognize a unit cube and know that it can be used to
measure volume
5.MD.4
I can measure volume by counting unit cubes
5.MD.5b
I can use l * w * h and b * h to find volume for right
rectangular prisms in real-world problems
5.G.1
I can identify the parts of a coordinate plane and plot a given
point on the plane using ordered pairs.
5.G.2
I can represent and interpret real world and math problems
by graphing points on the coordinate plane
5.OA.2
I can write simple numerical expressions
Use words to interpret numerical expressions
5.OA.3
I can create a function table and explain a rule
I can use a rule to graph ordered pairs on a coordinate plane
I can compare sets of data that are related and recognize the
relationship between them
5.MD.1
I can do measurement conversions within the same system
I can use these conversions to solve multi-step real world
problems
5.MD.2
I can make a line plot to display a set of measurements in
fractions of a unit solve problems with the information on the
line
35
Everyday Math
Common Core
Alignment
Lesson 10-1
5.MD.3a
5.MD.4
5.MD.5b
Lesson 10-2
5.MD.2
Lesson 10-3
5.MD.2
5.OA.2
5.OA.3
Unit of Study 10 – Additional Resources
*Be sure to complete math masters p. 303
*Skip lesson 10-5
*Skip lesson 10-8
*Don’t teach part one of lesson 10-9, but use journal pages 366A and 366B to reinforce converting units of measure.
*Remove page 202 from the test
Lesson 10-4*
5.OA.3
5.G.1
5.G.2
Lesson 10-6
5.G.1
5.G.2
5.OA.3
Lesson 10-7
5.G.1
Lesson 10-9*
5.MD.1
Lesson 10-10
Assessment
36
Unit of Study 11
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Measurement and Data
Standard(s):
5.MD.1 – Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multistep, real world problems.
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 a “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.
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 x w x h and V = b x 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.
37
Math Content Objectives
5.MD.1
I can do measurement conversions within the same
system
I can use these conversions to solve multi-step real world
problems
5.MD.3a
I can recognize a unit cube and know that it can be used
to measure volume
Vocabulary
Teacher’s Resources and Notes
Base
Cylinder
Edge
Face
Geometric Solid
Prism
Vertex
5.MD.3b
I can identify the volume of a solid figure in cubic units
5.MD.4
I can measure volume by counting unit cubes
5.MD.5a
I can find the volume of a right rectangular prism using unit
cubes, show its volume by multiplying the edge lengths,
and show its volume by multiplying the height by the area
of the base
5.MD.5b
I can use l * w * h and b * h to find volume for right
rectangular prisms in real-world problems
38
Everyday Math
Common Core
Alignment
Lesson 11-1*
5.MD.3a
5.MD.3b
5.MD.4
5.MD.5a
5.MD.5b
Unit of Study 11 – Additional Resources
*Include journal pages 384A & 384B into lesson 11-1 (from lesson 11-5)
*Eliminate journal pages 369 – 370 in lesson 11-1
*No assessment of unit 11
Lesson 11-6
5.MD.1
Lesson 11-8
Assessment
39
Unit of Study 12
Fifth Grade
Quarter ??
Approx. ?? days
Domain: Number and Operations - Fractions
Standards:
5.NF.7 – Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a - Interpret division of a unit fraction by a non-zero whole number, and computer 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) x 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 to show the
quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (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 ½ lb of chocolate equally? How many 1/3 cup servings are
in 2 cups of raisins?
Domain: Number and Operations in Base Ten
Standards:
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.
40
Math Content Objectives
5.NF.7a
I can explain division of a unit fraction by a whole number
and find the quotient of a division problem for a unit
fraction and whole number
5.NF.7b
I can explain division of a whole number by a unit fraction
and find the quotient of a division problem for a whole
number and a unit fraction
5.NF.7c
I can solve real-world problems involving division of unit
fractions by whole numbers and solve real-world problems
involving division of whole numbers by unit fractions
Vocabulary
Teacher’s Resources and Notes
Common Factor
Equally likely
Factor Tree
Greatest common factor
Least common multiple
Prime Factorization
Probability
Rate
Ratio
Ration comparison
Tree Diagram
5.NBT.7
I can add,subtract, multiply, and divide decimals to the
hundredths using a variety of strategies and explain how
the answer was found.
41
Everyday Math
Common Core
Alignment
Lesson 12-1
SMP 1-3, 5-8
Lesson 12-2
5.NBT.7
Unit of Study 12 – Additional Resources
*Do not teach lesson 12-3, 12-6, 12-7, 12-8
* Can use the whole assessment 12-9
Lesson 12-4
SMP 1,2, 4-6
Lesson 12-5
5.NF.7a
5.NF.7b
5.NF.7c
42