Grade 4 Math Scaffolding - The Mississippi Department of ...

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document

Grade 4

College- and Career-Readiness Standards for Mathematics

GRADE 4 Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 ? 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Desired Student Performance

A student should know

A student should understand A student should be able to do

? How to fluently multiply and ? A multiplicative comparison ? Use a tape diagram model to

divide within 100.

compares two quantities by

make and illustrate

? How to fluently recall basic

showing that one quantity is a

multiplicative comparisons.

multiplication facts.

specific number "times less

? Write an equation to represent

? The answer to a multiplication

than" or "greater than" the

a multiplicative comparison.

problem is called the product.

other quantity.

? Identify unknown quantities in

? The two numbers that are

? Determine the factor by which

multiplicative comparison

being multiplied in a

to multiply one quantity in

equations.

multiplication equation are

order to result in another.

? Use a symbol for an unknown

called factors.

? The meaning of "times as

number

? How to compare numbers in

many."

? Identify which number is being

an additive sense (what

? The difference in the situations

multiplied and which number

amount would be added to a

in which you would multiply to

tells "how many times as

quantity in order to result in

find the unknown or divide to

much."

another).

find the unknown.

? How to explain patterns in

? Reasoning abstractly and

arithmetic.

quantitatively.

? How to interpret products of ? Modeling with mathematics.

whole numbers.

? Interpretation means to

communicate symbolically,

numerically, abstractly, and/or

with a model.

September 2016

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College- and Career-Readiness Standards for Mathematics

GRADE 4 Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

Desired Student Performance

A student should know

A student should understand A student should be able to do

? How to fluently multiply and divide within 100.

? How to fluently recall basic multiplication facts.

? The answer to a multiplication problem is called the product.

? The two numbers that are being multiplied in a multiplication equation are called factors.

? The answer to a division problem is called the quotient.

? The number being divided is called the dividend and the number being divided into the dividend is called the divisor.

? How to compare numbers in an additive sense (what amount would be added to a quantity in order to result in another).

? How to interpret products and quotients of whole numbers.

? Interpretation means to communicate symbolically,

? An additive comparison is the ? Solve multiplication and

difference between two

division problems that involve

quantities.

the following comparison

? A multiplicative comparison compares two quantities by

situations: unknown product, group size unknown, number

showing that one quantity is a

of groups unknown.

specific number "times less

? Use a tape diagram model to

than" or "greater than" the

make and illustrate

other quantity.

multiplicative comparisons.

? Determining the factor by

? Write an equation to represent

which to multiply one quantity

a multiplicative comparison

in order to result in another.

using a symbol to represent

? The meaning of "times as

the unknown.

many."

? Determine if a word problem is

? The difference in the situations in which you would multiply to

additive comparison or multiplicative comparison.

find the unknown or divide to ? Identify differences among

find the unknown.

additive comparison and

? Reason abstractly and quantitatively.

multiplicative comparison word problems.

? Modeling with mathematics.

? Looking for and making use of

structure.

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College- and Career-Readiness Standards for Mathematics

numerically, abstractly, and/or with a model.

September 2016

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College- and Career-Readiness Standards for Mathematics

GRADE 4 Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems

4.OA.3 Solve multistep (two or more operational steps) word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

A student should know

? A variable represents an unknown quantity.

? How to write one-step equations using variables.

? How to write two-step equations using addition and subtraction (easy to medium difficulty level).

? How to explain the difference between an expression and an equation.

? Equal sign means "is the same as."

? How to add, subtract, divide, and multiply with multi-digit whole numbers.

? How to define multiplication and division.

? How to describe the inverse relationship between multiplication and division and addition and subtraction.

? How to fluently multiply and divide within 100.

Desired Student Performance

A student should understand A student should be able to do

? Use of parenthesis in an

? Identify the differences among

equation.

addition, subtraction,

? Reading an expression or

multiplication, and division

equation that has more than

word problems.

one step.

? Perform addition, subtraction,

? Rounding whole numbers to

division, and multiplication with

find an estimate that can be

whole numbers.

used to assess the

? Interpret remainders and how

reasonableness of the

they affect the whole number

answer.

answer in a division problem.

? Remainders can be

? Write equations using

interpreted as:

variables to represent the

o a leftover.

unknown for multi-step word

o fractions or decimals.

problems.

o discards, leaving only ? Evaluate the reasonableness

the whole number

of an answer by using

quotient.

estimation strategies or mental

o increasing the whole

math strategies.

number quotient by one. ? Write an equation consisting of

o rounding to the nearest

multiple operations to reflect

whole number for an

the situation(s) in a word

approximate result.

problem.

? Substitute * or for the "x" in a ? Select a word problem that

multiplication equation.

matches a specific equation.

? Making sense of problems

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College- and Career-Readiness Standards for Mathematics

? How to fluently recall basic multiplication facts.

? How to fluently add and subtract numbers up to 1,000.

and persevering in solving them. ? Attending to precision. ? Modeling with mathematics. ? Reasoning abstractly and quantitatively.

? Solve addition and subtraction word problems that include the following situations: result unknown, total unknown, both addends unknown, change unknown, difference unknown, greater unknown, and lesser unknown (refer to table in Progressions document).

? Solve multiplication and division word problems that include the following situations: equal groups, arrays of objects, and comparison (refer to table in Progressions Document).

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College- and Career-Readiness Standards for Mathematics

GRADE 4 Operations and Algebraic Thinking (OA)

Gain familiarity with factors and multiples

4.OA.4 Find all factor pairs for a whole number in the range 1?100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1?100 is a multiple of a given onedigit number. Determine whether a given whole number in the range 1? 100 is prime or composite.

A student should know

? How to fluently multiply and divide within 100.

? Describe the inverse relationship between multiplication and division.

? A factor is a number that is multiplied with another number to get a product.

? A product is the answer to a multiplication problem when two factors are multiplied.

? The words multiple and product are interchangeable.

? Division can be used to find an unknown factor.

Desired Student Performance

A student should understand A student should be able to do

? Any whole number is a

? List factors for a given whole

multiple of each of its factors.

number.

? A prime number only has two ? Classify numbers as prime or

factors, one and itself.

composite.

? A composite number has two ? List multiples of a given single

or more factor pairs.

digit number.

? A factor pair is two factors that ? Decide if a number is a

create a specific product.

multiple of a given one-digit

? A multiple is divisible by its

number.

factors.

? Divisibility means that a

multiple can be divided evenly

by its factor with no remainder.

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College- and Career-Readiness Standards for Mathematics

GRADE 4 Operations and Algebraic Thinking (OA)

Generate and analyze patterns

4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. 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. Explain informally why the numbers will continue to alternate in this way.

A student should know

? A pattern is a set of numbers or objects which relate to each other according to a specific rule.

? How to identify patterns in a multiplication table.

? How to identify patterns in an addition table.

? How to fluently add and subtract single digit numbers.

? How to fluently multiply and divide within 100.

Desired Student Performance

A student should understand A student should be able to do

? Patterns can grow or repeat. ? Construct shape patterns that

? Division can be used to help

express a given rule.

identify properties of repeating ? Construct number patterns

patterns when finding the "nth"

that express a given rule.

figure in a pattern (for

? Connect a rule for a given

example: find the 100th figure

pattern with its sequence of

in the pattern circle, square,

numbers or shapes.

triangle, triangle?since there ? Extend a given pattern after

are four figures in the pattern

determining the rule that the

before the pattern repeats,

pattern follows.

divide 100 by 4. This tells you ? Make generalizations about

that there will be 25 full

patterns that are not apparent

repeats so the 100th figure

within the given rule.

would be the last shape in the ? Determine the rule for a given

pattern.)

pattern that can be used to

? Reasoning abstractly and

find the "" number or object

quantitatively.

in the pattern.

? Attending to precision.

? Look for and make use of

? Looking for and expressing

structure.

regularity in repeated

reasoning.

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