# Developing Understanding of Multiplication

Last week in 302, we began exploring multiplicative situations. We started by looking at some photos of equal groups that we might encounter in life, such as egg cartons, boxes of markers, or multiple bags of marbles.

It’s important for multiplication to be a part of real life, not just numbers and equations on the page. Pictures are a natural way to introduce students to a foundational big idea in multiplication: equal groups. To really think multiplicatively, children have to think of the group as a unit. Students build upon what they know in addition: 6 + 6 + 6 + 6 can also be thought of as 4 groups of 6.

Many students are already aware of the **commutative property of multiplication**– that 4×6=6×4. Both of these equations total 24, however, each equation can represent very different situations. Here is an example:

The crayons image is an example of 6 x 4, 6 boxes of crayons with 4 crayons in each, or “6 groups of 4”. The rolls image depicts the equation 4 x 6, 4 groups of rolls, with 6 rolls in each, or “4 groups of 6”. This is a common convention of multiplication, that the first factor tells you *how many groups*, while the second factor tells you *how many in the group. *We have begun to use mathematical notation to describe the groups. Many students are even using the **distributive property** (though we haven’t named it yet).

An example of the **distributive property connected to the crayon image** would be noticing that there are 3 groups of 4 on the left and 3 groups of 4 on the right. Therefore, (3×4) + (3 x 4) = 6 x 4

The purpose of making groups, and groups of groups, is to find the total in an efficient way. If you’re looking at your children’s math homework with them, you can support us in this by saying “groups of” rather than “times” as you talk about multiplication.

Ms Marcy 🙂

**Upcoming Dates**

**Family Friday: December 1- **Families are welcome in the classroom following the PTO meeting. We will be hosting families from 9:25- 10:10.

**World Map Assessment- **Children may re-take the assessment on **December 5th.** Students will be assessed using the same criteria- identification of all 7 continents, 5 oceans, the Mediterranean Sea, the Equator, and the North and South Poles.

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