Module 3, Topic D gives students the opportunity to apply their new multiplication skills (4.NBT.5). In Lesson 12, students extend their work with multiplicative comparison from Topic A to solve real-world problems(4.OA.2). As shown on the next page, students use a combination of addition, subtraction, and multiplication to solve multi-step problems in Lesson 13(4.OA.3).

Content Standard(s):

Mathematics MA2019 (2019) Grade: 4

1. Interpret and write equations for multiplicative comparisons.

Unpacked Content

Evidence Of Student Attainment:

Students:

When given a multiplication equation, create and explain a corresponding verbal multiplicative comparison statement. Example: interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 35 is 7 times as many as 5.

When given a verbal (written or oral) representation of a multiplicative comparison, write and solve the related multiplication equation.

Example: Sue has 7 cards and Joe has 5 times as many cards as Sue. The student will write 5 x 7 and accurately find the number of cards Joe has to be 35.

Teacher Vocabulary:

Multiplicative comparison

Multiplier

Equation

Times as many

Times as much

Verbal statement

Factor

Product

Quantity

Multiple

Scale factor

Knowledge:

Students know:

How to write an equation to represent a word situation.

Which quantity is being multiplied and which factor is telling how many times.

Varied language that describes multiplicative comparisons.

Skills:

Students are able to:

Interpret equations for multiplicative comparisons.

Write equations for multiplicative comparisons.

Understanding:

Students understand that:

Multiplicative comparisons relate the size of two quantities and a scale factor.

Factors in multiplication problems have different roles from each other in the context of comparison problems.

Explanations and drawings show ways multiplicative comparisons are similar to and different from equal groups and arrays.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.1.1: Use arrays to show equal groups in multiplication.
M.4.1.2: Recall basic multiplication facts.
M.4.1.4: Demonstrate computational fluency, including quick recall of addition and subtraction facts.
M.4.1.5: Recognize multiplication as repeated addition.

Prior Knowledge Skills:

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.

Apply concepts of multiplication through the use of manipulatives, number stories, skip-counting arrays, area of a rectangle, or repeated addition.

Apply basic multiplication facts through 9 x 9 using manipulatives, solving problems, and writing number stories.

Solve addition problems with multiple addends.

Represent addition using manipulatives.

Distinguish between rows and columns.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number. Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.

Mathematics MA2019 (2019) Grade: 4

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Unpacked Content

Evidence Of Student Attainment:

Students:

When given word problems involving multiplicative comparison, will solve using concrete, pictorial representations, and write related equations involving a single unknown.

Example: There are 12 children and 3 adults at the playground. How many times as many children are at the playground than adults? Represent the situation with the equation 12 = n × 3 and a tape diagram with a total of 12 and groups of 3, repeating each group 4 times to solve.

Teacher Vocabulary:

Multiplicative comparison

Times as many

Product

Factor

Multiplication

Equation

Symbol

Additive comparison

Tape diagram

Unknown

Knowledge:

Students know:

how to find products and quotients.

Recognize situations represented by multiplicative comparison.

Distinguish between multiplicative comparison and additive comparison.

Skills:

Students are able to:

Solve word problems involving multiplicative comparison.

Write equations using a symbol for the unknown to represent word problems involving multiplicative comparison.

Use drawings to represent the word situation involving multiplicative comparison.

Understanding:

Students understand that:

additive comparison focuses on the difference between two quantities and multiplicative comparison focuses on one quantity being some number times larger than another.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.2.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
M.4.2.2: Recognize key terms to solve word problems.
Examples: in all, how much, how many, in each.
M.4.2.3: Apply properties of operations as strategies to add.
M.4.2.4: Recall basic multiplication facts.
M.4.2.5: Demonstrate computational fluency, including quick recall of addition and subtraction facts.

Prior Knowledge Skills:

Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.

Identify key vocabulary words to solve multiplication and division word problems.
Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Recall basic multiplication facts.

Add and subtract within 20.

Represent repeated addition, subtraction, and equal groups using manipulatives.

Distinguish between rows and columns.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number.
Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.

Mathematics MA2019 (2019) Grade: 4

3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

Unpacked Content

Evidence Of Student Attainment:

Students: When given multi step word problems,

Solve a variety of multistep word problems involving all four operations on whole numbers including problems where remainders must be interpreted.

Explain and justify solutions using connections between the problem and related equations involving a single (letter) unknown.

Evaluate the reasonableness of solutions using estimation strategies.

Note: Multi step problems must have at least 3 steps.

Teacher Vocabulary:

Operation

Multi Step problem

Remainder

Unknown quantity

Equation

Rounding

Mental strategy

Partition

Estimation

Reasonableness

Knowledge:

Students know:

Context situations represented by the four operations.

How to calculate sums, differences, products, and quotients.

Estimation strategies to justify solutions as reasonable.

Skills:

Students are able to:

Solve multi-step word situations using the four operations.

Represent quantities and operations physically, pictorially, or symbolically.

Write equations to represent the word problem and use symbols to represent unknown quantities.

Use context and reasoning to interpret remainders.

Use estimation strategies to assess reasonableness of answers by comparing actual answers to estimates.

Understanding:

Students understand that:

Using problem solving strategies will help them determine which operation to use to solve a problem.

Remainders must be interpreted based on the context, and remainders are sometimes ignored, rounded up, or partitioned.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.3.1: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
M.4.3.2: Solve single-step word problems.
M.4.3.3: Recognize key terms to solve word problems. Examples: in all, how much, how many, in each.
M.4.3.4: Solve division problems without remainders.
M.4.3.5: Recall basic addition, subtraction, and multiplication facts.

Prior Knowledge Skills:

Demonstrate computational understanding of multiplication and division by solving authentic problems with multiple representations using drawings, words, and/or numbers.

Identify key vocabulary words to solve multiplication and division word problems. Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Recall basic multiplication facts.

Add and subtract within 20.

Represent repeated addition, subtraction, and equal groups using manipulatives.

Distinguish between rows and columns.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number. Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.

Mathematics MA2019 (2019) Grade: 4

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use strategies based on place value, properties of operations, rectangular arrays, area models, and equations to illustrate and explain the product of two factors (up to four digits by a one-digit number and two two-digit numbers).

Note: Standard algorithm is not an expectation for grade 4.

Teacher Vocabulary:

Product

Factor

Compose

Decompose

Digit

Strategy

Place value

Properties of operations

Equation

Rectangular array

Area model

Partial product

Multiple of 10

Knowledge:

Students know:

How to compose and decompose numbers in a variety of ways using place value and the properties of operations.

How to represent the product of two factors using an area model.

Use strategies based on place value (partial products), the properties of operations, arrays and area models to represent a two digit factor times a two digit factor.

Skills:

Students are able to:

Use strategies based on place value and the properties of operations to find products.

Illustrate the product of two factors using rectangular arrays and area models.

Explain the product of two factors using equations.

Make connections between models and equations.

Understanding:

Students understand that:

arrays, area models, place value strategies, and the properties of operations can be used to find products of a single digit factor by a multi-digit factor and products of two two-digit factors.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.4.11.1: Divide within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.2: Divide within 100, using strategies such as properties of operations.
M.4.11.3: Multiply within 100, using strategies such as properties of operations.
M.4.11.4: Multiply within 100, using strategies such as the relationship between multiplication and division (e.g. knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).
M.4.11.5: Recall products of two one-digit numbers.
M.4.11.6: Name the first 10 multiples of each one-digit natural number. Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.
M.4.11.7: Recall basic addition, subtraction, and multiplication facts.

Prior Knowledge Skills:

Apply divisibility rules for 2, 5, and 10.
Example: Recognizing that 32 is divisible by 2 because the digit in the ones place is even.

Apply basic multiplication facts.

Understand subtraction as an unknown

addend problem.

Recognize division as repeated subtraction, parts of a set, parts of a whole, or the inverse of multiplication.

Name the first 10 multiples of each one-digit natural number.
Example: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Recognize multiplication as repeated addition, and division as repeated subtraction.

Apply properties of operations as strategies to add and subtract.

Recall basic addition and subtraction facts.

Use repeated addition to solve problems with multiple addends.

Count forward in multiples from a given number.
Examples: 3, 6, 9, 12; 4, 8, 12, 16.

Recall doubles addition facts.

Model written method for composing equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.4.11 Add and subtract one and two-digit numbers up to 49 with regrouping using concrete manipulatives and visual models.

Tags:

array, divide, equation, multiplicative comparison, multiply, operations, place value, word problems