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Mississippi College and Career Readiness Standards for

Mathematics Scaffolding Document

Grade 5

September 2016 Page 1 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Operations and Algebraic Thinking (OA)

Write and interpret numerical expressions

5.OA.1

Use parentheses,

brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Desired Student Performance

A student should know

operations of addition, subtraction, multiplication, and division. write the different operations and some situations require different mathematical symbols. when working with multiplication and can be used to illustrate the

Associative Property of

Multiplication and the

A student should understand

keep numeric expressions organized. numbers and operation symbols together and can also represent the operation of multiplication.

A student should be able to do

solving within parentheses first, within brackets second, and finally within the braces. problems will contain all the mathematical symbols, but when they are present, an order of operations must be followed to complete the problem. appropriately to organize numerical expressions.

September 2016 Page 2 of 65

College- and Career-Readiness Standards for Mathematics

Distributive Property of

Multiplication.

expression and an equation. expressions and evaluate them. numerical expressions.

September 2016 Page 3 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Operations and Algebraic Thinking (OA)

Write and interpret numerical expressions

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.

Desired Student Performance

A student should know

group expressions together. given expression by another quantity. of Multiplication can be written as an expression.

A student should understand

situations and can be represented using numerical expressions. same as (14)3, (10 + 4) x 3, or (10 + 4) + (10 + 4) + (10 + 4). (There are many other ways to write the expression as well.) and organizing the information into a numeric expression is a necessary part of mathematics.

A student should be able to do

real-world situation as a numeric expression. equivalent expressions. mathematical symbols appropriately. symbols appropriately to organize numerical expressions. numerical expressions.

September 2016 Page 4 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Operations and Algebraic Thinking (OA)

Analyze patterns and relationships

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

Desired Student

Performance

A student should know

pattern that follows a given rule. For example: given the rule “Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.

A student should understand

the relationship between the coordinates and the coordinate plane. relationships between numbers. regularity in repeat ed reasoning. of structure.

A student should be able to do

mathematical problems that require graphing points in

Quadrant I of a coordinate

plane. points in the context of the situation. pair given a rule that must be followed. between two sets of patterns, i.e., Given the rule “Add 2" and a starting number 0, and given

September 2016 Page 5 of 65

College- and Career-Readiness Standards for Mathematics corresponding terms in the other sequence.

Explain informally why

this is so. the rule "Add 6" and a starting number 0, explain why the terms in the second sequence are three times greater than the numbers in the first sequence.

September 2016 Page 6 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Number and Operations in Base Ten (NBT)

Understand the Place Value System

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 (e.g., "In the number 3.

33, the

underlined digit represents 3/10, which is 10 times the amount represented by the digit to its right (3/100) and is

1/10 the amount

represented by the digit to its left (3)).

Desired Student Performance

A student should know

columns for whole numbers. different tens compose a hundred, and ten different hundreds compose a thousand. the tenths or hundredths place. place value because it is a positional notat ion system.

The numerals 0, 1, 2, 3, 4, 5,

6, 7, 8, and 9 can represent

A student should understand

a different value than a nine in the hundred"s position. a given column have a greater value than columns located to the right of that column. division. equivalents for fractions of

1/10, 1/100, 1/1000, etc.

is the same as dividing by 10,

A student should be able to do

what value each digit holds.

For example, in 245, the 2 is in

the hundreds place and has a value of 200.

Base Ten System (each

position is 10 times the position to its right and 1/10 of the position to its left multi-digit number to show the quantity of each digit. For example: 345.67 is equivalent

September 2016 Page 7 of 65

College- and Career-Readiness Standards for Mathematics different values depending upon their position within a group of numerals. This is an efficient way to represent many quantities with few numeric symbols. multiplying by 1/100 is the same as dividing by 100, etc. to (3 x 100) + (4 x 10) + (5 x 1) + (6 x 1/10) + (7 x 1/100). equivalent to multiplying by 1/10.

September 2016 Page 8 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Number and Operations in Base Ten (NBT)

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 powe rs of 10.

Desired Student Performance

A student should know

of the multiplication of whole numbers. of the Distributive Property of

Multiplication.

multiplication. patterns. has a value 10 times that of the column to the right of it.

Each column has a value

A student should understand

operation of multiplication. being multiplied, while the exponent is the number of times the base is multiplied. referred to as powers. meaning without actually evaluating. For example: 10 2 = 10 x 10 = 100 10 3 = 10 x 10 x 10 = 1,000 10 4 = 10 x 10 x 10 x 10 =

10,000

A student should be able to do

powers of ten relate to numbers being multiplied by them. 2 is the same as multiplying by 10 x 10, and the product of this is 100. 6.2 x 10 2 is the same as

6.2 x 100.

place a decimal in a product or quotient. For example: The product of 3.1 x 10 2 must be close to 300 because 3.1 is

September 2016 Page 9 of 65

College- and Career-Readiness Standards for Mathematics

1/10 of the column to the left

of it. nu mbers by a single digit number as well as multi-digit numbers by a two digit number. close to 3 and 3 x 100 = 300, therefore the logical placement of the decimal is between the ones place and the tenths place.

September 2016 Page 10 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Number and Operations in Base Ten (NBT)

Understand the Place Value System

5.NBT.3a

Read, write, and

compare decimals to thousandths.

Read and write decimals

to thousandths using base ten numerals, number names, and expanded form, e.g.,

347.392 = 3 × 100 + 4 ×

10 + 7 × 1 + 3 × (1/10) + 9

× (1/100) + 2 × (1/1000).

Desired Student Performance

A student should know

numbers using base ten numerals, number names, and expanded form. fractions and their base ten decimal equivalents.

For example: 0.6 is equivalent

to 0.60. the hundredths. hundredths using modeling.

A student should understand

value system can be extended beyond hundredths. value of a hundredth, 1/100 the value of a tenth, and

1/1000 the value of one whole.

represent any given amount. separate hundredths and thousandths.

A student should be able to do

thousandths using base -ten numerals, number names, and expanded form. and expanded form. in the various forms and with varying decimal place values.

September 2016 Page 11 of 65

College- and Career-Readiness Standards for Mathematics

GRADE 5

Number and Operations in Base Ten (NBT)

Understand the Place Value System

5.NBT.3b

Read, write, and

compare decimals to thousandths.

Compare two decimals

to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Desired Student Performance

A student should know

numbers using base ten numerals, number names, and expanded form. numbers based on the meanings of the digits in each place. fractions and their base ten decimal equivalents.

For example: 0.6 is equivalent

to 0.60

A student should understand

value system can be extended beyond hundredths. value of a hundredth, 1/100 the value of a tenth, and

1/1000 the value of one whole.

represent any given amount. separate hundredths and thousandths. base ten decimal number does not determine its value.

A student should be able to do

thousandths place by using the symbols >, =, and < value of each digit in a base ten decimal number. by using visual models and/or fractional equivalence line to demonstrate an understanding of value. Use number lines that show tenths, hundredths, and thousandths.

September 2016 Page 12 of 65

College- and Career-Readiness Standards for Mathematics the hundredths place. hundredths using modeling. >, =, and <.

For example: 0.7 > 0.299

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