NC.4.OA.1

Interpret a multiplication equation as a comparison. Multiply or divide to solve word problems involving multiplicative comparisons using models and equations with a symbol for the unknown number. Distinguish multiplicative comparison from additive comparison.

Step 1: Lesson Standards & Learning Goals

Unpacking Clarification

Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

Students should be able to translate comparative situations into equations with a variable (e.g., “21 is n times as much as 7”) and then find the value of the variable. Students should have several opportunities to solve contextual problems as well as write and identify equations and statements for multiplicative comparisons. When given an equation, students should be able to create a model and a word problem that matches the equation.

Students are expected to distinguish between additive and multiplicative comparisons.

Additive comparisons focus on the difference between two quantities.
Multiplicative comparisons focus on one quantity being some number times larger than another (e.g., “a is n times as much as b”).
- The referent, which is the number of times a quantity is larger than or smaller than another quantity, should be limited to 10 or less.
- Multiplicative comparison situations are limited to only whole numbers in Grade 4.

Sample Essential Questions

How can unknown division facts be found by thinking about a related multiplication fact?
What models can be used to show problems using multiplicative comparisons?
How can the inverse relationships between multiplication and division be helpful in solving problems?
How can multiplication and division situations be represented in equations using a symbol for the unknown?
What are ways to represent problems using equations with letters standing for the unknown in any place?

Vocabulary

Additive comparison
Comparative
Equation
Factor
Multiplication
Multiplicative comparison
Multiply
Number sentence
Product
Variable

Students will be able to...

Interpret a multiplication equation as a comparison.
- (i.e. Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.
Distinguish between addition and multiplicative comparisons.
Write and identify equations for multiplicative comparisons.
Multiply or divide to solve word problems involving multiplicative comparison.
Solve multi-step word problems using equations with whole numbers and a variable.

Students will know...

Multiplication is the repeated addition of equal groups.
Statements of comparison (“times as many”) are other ways to think about multiplication or division.
Mathematical situations can be represented with equations using variables (letters) for the unknown quantity.

Step 2: Assessment