Content Standard(s):
Mathematics MA2019 (2019) Grade: 2 2. Fluently add and subtract within 20 using mental strategies such as counting on, making ten, decomposing a number leading to ten, using the relationship between addition and subtraction, and creating equivalent but easier or known sums.

a. State automatically all sums of two one-digit numbers.

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Evidence Of Student Attainment:

Students:

find sums and differences of basic facts through sums of 20.
use an efficient mental strategy (recall, inverse to addition, derived facts) to find the difference (large minus small) of two numbers less than twenty.
show fluency (efficiency and accuracy based on understanding) with sums of 20.
when given two one-digit numbers can state their sum with minimal hesitation (by the end of 2nd grade). Teacher Vocabulary:

Knowledge:

Students know:

how to use mental strategies to add and subtract within 20. Skills:

Students are able to:

use addition and subtraction strategies efficiently. Understanding:

Students understand that:

fluency involves a mixture of "just knowing" answers, knowing answers from patterns, and knowing answers from the use of strategies. The word fluently is used in the standards to mean accurately, efficiently, and flexibly. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.2.2.1: Recall single-digit subtraction facts with minuends of 10 or less.
M.2.2.2: Recall single-digit addition facts with sums up to 10.
M.2.2.3: Apply addition and subtraction strategies.
Examples: doubles, doubles plus one, doubles minus one.
M.2.2.4: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:

Define addition and subtraction.
Recognize properties of operations.
Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
Apply signs +, -, = to actions of joining and separating sets.
Identify fact families to ten.
Recognize the value of zero.
Decompose numbers up to 5 using objects or drawings.
Compose numbers up to 5 using objects or drawings.
Count backward from 5.
Count forward to 5.
Write numerals from 0 to 10.
Represent a given numeral 1 to 10 with objects or drawings.
Count forward from a given number 1 to 10.
Model joining sets of objects to total 10.
Identify plus, minus, and equal signs.
Match numerals to objects or drawings.
Identify numerals 1 to 10.
Count 0 to 10.
Add and subtract numbers within 20 using objects, pictures and fingers.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.2.2 Represent addition as "add to/put together" and subtraction as "take from/take apart" with objects, drawings, fingers, or sounds (within 30).

Mathematics MA2019 (2019) Grade: 3 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

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Evidence Of Student Attainment:

Students:

Relate three whole numbers to determine an unknown number in a multiplication equation.
Example: 8 x ? = 48 or ? x 8 = 48.
Relate three whole numbers to determine an unknown whole number in a division equation.
Example: 5 = ? ÷ 3 or ? ÷ 3 = 5.
Relate missing factor multiplication equations to division equations using both symbols ? or ÷ for division. Teacher Vocabulary:

Unknown
Multiplication
Division
Divisor
Dividend
Equation
Product Knowledge:

Students know:

how to use the meaning of multiplication and division and the relationship between the two operations to determine an unknown number in a given equation. Skills:

Students are able to:

Relate three whole numbers to determine the unknown factor in a multiplication equation.
Relate three whole numbers to determine the unknown whole number in a division equation. Understanding:

Students understand that:

the unknown number in a multiplication or division equation is the number that makes the equation true. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.3.4.1: Use arrays to show equal groups in multiplication and division.
M.3.4.2: Recall basic multiplication facts.
M.3.4.3: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
M.3.4.4: Represent repeated addition, repeated subtraction, and equal groups using manipulatives.

Prior Knowledge Skills:

Distinguish between rows and columns.
Use repeated addition to solve problems with multiple addends Pulled up from first grade.
Represent addition and subtraction with objects, pictures, fingers, or sounds within twenty.
Understand addition as putting together and subtraction as taking from.
Establish one-to-one correspondence between numbers and objects.
Rote count to 20.
Notice same/different and some/all.
Establish one-to-one correspondence between numbers and objects.
Point to matching or similar objects.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.3.3 Use strategies (arrays, equal groups, manipulatives, etc.) to model multiplication and division equations to find an unknown number.

Mathematics MA2019 (2019) Grade: 3 7. Use strategies based on properties and patterns of multiplication to demonstrate fluency with multiplication and division within 100.

a. Fluently determine all products obtained by multiplying two one-digit numbers.

b. State automatically all products of two one-digit numbers by the end of third grade

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Evidence Of Student Attainment:

Students:

When given any single digit multiplication problem, use an efficient strategy (recall, inverse operations, arrays, derived facts, properties of operations, doubling, skip counting, square numbers) to name the product.
When given a division problem with a single digit divisor and an unknown single digit quotient, use an efficient strategy (recall, inverse operations, arrays, derived facts, properties of operations, doubling, skip counting, square numbers) to name the quotient. Teacher Vocabulary:

Fluently
Properties of operations
Product
Digit
Divisor
Dividend
Inverse operation
Derived fact Knowledge:

Students know:

Strategies for finding products and quotients.
How to use multiplication facts in terms of a missing factor to learn division facts. Skills:

Students are able to:

Use strategies based on properties of operations and patterns of multiplication to find products and quotients.
Use efficient multiplication and division strategies based on the numbers in the problems.
-Use multiplication facts in terms of a missing factor to learn division facts. Understanding:

Students understand that:

they can use the meaning of the numbers in multiplication and division situations to determine strategies to become fluent with multiplication and division facts. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.3.7.1: Name the first 10 multiples of each one-digit natural number.
M.3.7.2: Recognize multiplication as repeated addition, and division as repeated subtraction.
M.3.7.3: Apply properties of operations as strategies to add and subtract.
M.3.7.4: Recall basic addition and subtraction facts.

Prior Knowledge Skills:

Recall single-digit subtraction facts.
Recall single-digit addition facts.
Add and subtract two two-digit numbers with and without regrouping.
Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
Alabama Alternate Achievement Standards

AAS Standard: M.AAS.3.7 Demonstrate fluency of multiplication using skip counting, multiples of numbers, number charts, arrays, etc.

Mathematics MA2019 (2019) Grade: 4 4. For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.

a. Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.

b. Determine whether a whole number in the range 1 to 100 is prime or composite.

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Evidence Of Student Attainment:

Students:

When given a number in the range 1-100,

Find all factor pairs and recognize that a whole number is a multiple of each of its factors.
Determine whether the whole number in the range 1-100 is a multiple of a given one-digit number.
Determine whether a whole number in the range 1-100 is prime or composite. Teacher Vocabulary:

Multiple
Factor
Prime
Composite
Whole number
Factor pair Knowledge:

Students know:

Factor pairs include two numbers that when multiplied result in a particular product.
Multiples are the result of multiplying two whole numbers. How to identify a prime or composite number. Skills:

Students are able to:

Find all factor pairs of a given number.
Identify a number as a multiple of each of its factors.
Determine whether a number is prime or composite. Understanding:

Students understand that:

A whole number is a multiple of each of its factors.
Numbers can be classified as prime, composite, or neither, based on their properties and characteristics. Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.4.1: Define factors, prime number, and composite number.
M.4.4.2: Apply properties of operations as strategies to multiply and divide.
M.4.4.3: Identify all factor pairs for a whole number in the range 1-20.
M.4.4.4: Name the first ten multiples of each one-digit natural number.
M.4.4.5: Recall basic multiplication facts.
M.4.4.6: Count within 1000; skip-count by 5s, 10s, and 100s.

Prior Knowledge Skills:

Represent equal groups using manipulatives.
Identify and define the parts of a multiplication problem including factors, multiplier, multiplicand and product.
Use multiplication to find the total number of objects arranged in rectangular arrays based on columns and rows.
Write an equation to express the product of the multipliers (factors).
Relate multiplication to repeated addition and skip counting.
Define pair, odd and even.
Recall doubles addition facts with sums to 20.
Apply sign+ and = to actions of joining sets.
Model written method for composing equations.
Skip count by 2s.