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MathBait™ Multiplication

What's That Called?

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Take the difficulty out of terminology! In this activity we help students understand multiplication words by building connections to what they already know.


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In this activity, we will provide students with the terminology for the × symbol. This is an investigation to allow students to feel like they have discovered the name on their own and to help make sense of the new terminology.

Draw out the large X on the board and ask students to share what this means. Drawing on the Warm Up, students should recall this is the symbol we use for skip counting. A statement such as 4×5 tells us to find the 5th number when skip counting by 4's.

In the Warm Up, we called this symbol "ex", because it looks like an X! But, later we will see there are many symbols we can use. Some people use a dot. Write out 4·5. Explain that in middle school, we no longer use the × and instead use a dot. Some people use parentheses like 4(5). While we don't care much about the different ways to write ×, we shouldn't call it "ex" because it doesn't always make an ex!

Provide students with their skip counting chart. Have each student write out a statement like they did in the warm up (such as 3×4). Remind students of the activity in MathBait™ Multiplication Part 2 where they made squares on their chart. This time, we will make rectangles.

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With a colored pencil or crayon, ask students to draw out the rectangle that matches their statement. It can be helpful to model for students. For example, if we picked 3×4, I'll go down to row 3 and trace out 4 over. Next, complete the rectangle starting in the top left corner.

Fact 3×4 shown as a 3by4 square on a skip counting table

Ask students to count the number of small 1-by-1 squares in their rectangle. What do they notice? Here are a few key points to highlight:

  • There are 12 squares in a 3×4 rectangle and 12 is the 4th number said when skip counting by 3's.

  • The rectangle is 4 tall and 3 wide, which are the numbers we used.

Explain to students that we often describe a rectangle by how big it is. We would call this rectangle 3-by-4 because it is 3 wide and 4 tall. For this reason, we often call the × symbol "by". Allow students to each say the statement they selected using the word "by".

Another word we can use for the × symbol is "times". If possible, place students in small groups and allow them 5-7 minutes to come up with an idea why we might call this symbol times. After their discussion, ask students what something like 5×6 means. Students should recall this meant the 6th number we say when counting by 5's. It's like we count 5 how many times? "6!".

Conclude by explaining we can say 5×6 as "5 times 6" because it is telling us to count by fives six times. We call this multiplication. Allow students to guess at why we might call this multiplication. Explain or bounce off student comments to note that when we multiply we are finding multiples. Five times six is asking us to find the 6th multiple of 5, so we are multiplying.

If time permits, allow students to practice with a partner. Each student writes a multiplication statement such as 3×6 and they practice saying 3×6 in multiple ways: "3 times 6", "the 6th number counting by 3's", "counting by 3, 6 times", "3 by 6 (like a rectangle)". Explain it is not necessary that students remember all the different ways to say the same thing, our goal is to recognize these words and understand the meaning behind the words. They can pick the way they like best to communicate.

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