California Common Core State Standards Comparison- FIFTH GRADE

California Common Core State Standards Comparison-

FIFTH GRADE

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

5. Use appropriate tools strategically

2. Reason abstractly and quantitatively.

6. Attend to precision.

3. Construct viable arguments and critique the reasoning of others

7. Look for and make use of structure.

4. Model with mathematics.

8. Look for and express regularity in repeated reasoning.

Current CA Math Content Standards

NUMBER SENSE:

NS 1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.

NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

# of Items

29 49%

1

CST Released Items #

California Common Core State Standards Mathematics

Notes

1,2 Understand the place value system.

CCS does not reference estimation

5.NBT.1: Recognize that in a multi-digit number, a digit in directly. In the Mathematical Practice

one place represents 10 times as much as it represents in standards, CCS implies a thorough

the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.3: Read, write, and compare decimals to

understanding of the concepts so students could develop strong estimation skills as a by-product of the depth of understanding.

thousandths.

a. Read and write decimals to thousandths using

base-ten numerals, number names, and

expanded form, e.g., 347.392 = 3 x 100 + 4 x 10

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

b. Compare two decimals to thousandths based on

meaning of the digits in each place, using >, =, and

< symbols to record the results of comparisons.

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

to any place.

Adapted from Analysis by Sacramento County Office of Education, June 2010 1

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

NS 1.2 Interpret percents as a part of a

5

3-9

hundred; find decimal and percent

equivalents for common fractions and

explain why they represent the same

value; compute a given percent of a

whole number.

NS 1.3 Understand and compute positive

1

10

integer powers of nonnegative integers;

compute examples as repeated

multiplication.

Understand the place value system.

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.

Notes

6.RP.3c: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity): solve problems involving finding the whole, given a part and the percent.

6.EE.1: Write and evaluate numerical expressions involving whole-number exponents

NS 1.4 Determine the prime factors of all

3

numbers through 50 and write the

numbers as the product of their prime

factors by using exponents to show

multiples of a factor (e.g., 24 = 2 x 2 x 2 x

3 = 2? x 3).

NS 1.5 Identify and represent on a number 2 line decimals, fractions, mixed numbers, and positive and negative integers.

NS 2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and

11-16

Write and interpret numerical expressions

5.OA.2.1: Express a whole number in the range 2-50 as a product of its prime factors. For example, find the prime factors of 24 and express 24 as 2x2x2x3.

17-19

6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on the coordinate plane.

Adapted from Analysis by Sacramento County Office of Education, June 2010 2

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

Notes

NS 2.1 Add, subtract, multiply, and divide 7 with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

20-27

Perform Operations with multi-digit whole numbers and with decimals to hundredths. 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; related the strategy to a written method and explain the reasoning used.

6.NS.3: Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation. 7.NS.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

NS 2.2 Demonstrate proficiency with

3

division, including division with positive

decimals and long division with

multidigit divisors.

28-31

Perform Operations with multi-digit whole numbers and with decimals to hundredths. 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.

Adapted from Analysis by Sacramento County Office of Education, June 2010 3

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

NS 2.3 Solve simple problems including

5

ones arising in concrete situations,

involving the addition and subtraction of

fractions and mixed numbers (like and

unlike denominators of 20 or less), and

express answers in the simplest form.

32-37

Use equivalent fractions as a strategy to add and subtract fractions 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.

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.

Notes

Adapted from Analysis by Sacramento County Office of Education, June 2010 4

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

NS 2.4 Understand the concept of

1

38-40 Apply and extend previous understanding s of multiplication

multiplication and division of fractions.

and division to multiply and divide fractions

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) ? 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) 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.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.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 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 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.

Notes

Students able to multiply 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.

Adapted from Analysis by Sacramento County Office of Education, June 2010 5

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

NS 2.5 Compute and perform simple

1

41, 42 Apply and extend previous understanding s of

multiplication and division of fractions

multiplication and division to multiply and divide

and apply these procedures to solving

fractions

problems.

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.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 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 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.

Notes

Adapted from Analysis by Sacramento County Office of Education, June 2010 6

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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

ALGEBRA AND FUNCTIONS:

17

26%

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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.

Notes

Adapted from Analysis by Sacramento County Office of Education, June 2010 7

California Common Core State Standards Comparison-

FIFTH GRADE

Current CA Math Content Standards

# of Items

CST Released Items #

California Common Core State Standards Mathematics

AF 1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.

AF 1.1 Use information taken from a graph 1 or equation to answer questions about a problem situation.

43, 44

AF 1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

6

45-53

AF 1.3 Know and use the distributive

1

54-56

property in equations and expressions

with variables

Notes

6.EE: (Cluster Statement) Apply and extend previous understandings of arithmetic to algebraic expressions

6.EE.9: Use variables to represent two quantities in a real world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and table, and relate these to the equation. 6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.3: Apply the properties of operations to generate equivalent expressions.

Adapted from Analysis by Sacramento County Office of Education, June 2010 8

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