Primary Standards:
MAFS.4.OA.1.1: Interpret a multiplication equation as a comparison e.g. interpret 35=5 x 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.
MAFS.4.OA.1.2: 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.
Connecting Standards:
MAFS.4.OA.1.3: Solve multistep word problems posed with whole numbers and having whole number answers using the 4 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.
Content Knowledge:
Students have explored multiplication as repeated addition, e.g. thinking of 3 groups of 4 as 4 + 4 + 4 etc. This type of thinking is additive thinking, but multiplication is more than repeated addition. It can also represent comparisons in which one set or quantity is described in terms of another using multiplicative thinking. For example, if a tree is 4 feet tall and a building is 3 times as tall, the two factors and their product represent a comparison (3 times as tall as 4 feet is 12 feet tall; 3 x 4 = 12).
The three types of multiplicative comparison problems include: when the number being compared is unknown, when the number being compared to is the unknown, and when the multiplier is the unknown. In this Unit, students are challenged to understand the problem situation, model it, identify or write equations to show what is happening in the problem, and solve problems.
Students extend their understanding of multiplication and division as inverses as they explore multiplicative comparison problems and notice that many can be solved with either multiplication or division. Bar models may help students to visualize the types of problems and connect to the relationship between multiplication and division.
GCG 1 – Learning Goal: As a mathematician, I can Represent multiplicative comparison situations with models, drawings, and equations MAFS.4.OA.1.1, MAFS.4.OA.1.2
- Step 1: Relate a multiplicative comparison situation to multiplication and division
- Step 2: Use concrete materials to model a multiplicative comparison situation
- Step 3: Use a drawing to model a multiplicative comparison situation
GCG 2 – Learning Goal: As a mathematician, I can Solve for unknown factors in multiplicative comparison problems MAFS.4.OA.1.1, MAFS.4.OA.1.2