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# Stop Saying…

Sometimes we say things in order to help students do the math rather than understand the math. Those statements can create misconceptions and confusion when the statements no longer hold true at later grades. #### When does it fall apart?

Solve the following questions using repeated addition:

• 3 x 5
• 5 x 3
• 2 x 1.3
• 1.3 x 2
• 1.3 x 2.4
• one-half x three-fourths

Which ones could you solve using just repeated addition? Which ones couldn’t you solve using just repeated addition?

#### Why?

• a strategy that helps students bridge to multiplicative thinking

Repeated addition is one way we can solve this multiplication question # “The multiplication symbol means groups of”

#### When does it fall apart?

Solve the following questions by drawing groups of:

• 3 x 5
• 5 x 3
• 2 x 1.3
• 1.3 x 2
• 1.3 x 2.4
• one-half x three-fourths

Which ones could you solve by drawing “groups of”? Which ones couldn’t  you solve drawing “groups of”?

#### Why?

The multiplication symbol can be used to represent different phrases, including but not limited to:

• groups of: 3 groups of 5
• percent of: 30% of 5
• fraction of: 3/5 of 7

Drawing “groups of” is one way we can solve this multiplication question. # or “Move the decimal when multiplying or dividing.”

#### When does it fall apart?

Solve the following questions by adding or removing a 0.

• 3 x 10
• 10 x 3
• 10 x 1.3
• 50 ÷ 10
• 4 ÷ 10
• 4.3 ÷ 10

Which ones could you solve by adding/removing a 0? Which ones couldn’t  you solve?

#### Why?

“Multiplying by 10 is just adding a 0.”
If you “add a 0” to solve 10 x 1.3 you would end up with an answer of 1.30. Secondly, “adding a 0” actually means + 0 not appending the number by 0. 1.3+0 = 1.3.

“Dividing by 10 is just removing a 0.”
Removing a 0 to solve 4.3 ÷ 10 would be impossible as 4.3 does not have a 0. Secondly, “removing a 0” actually means – 0. 4.3 – 0 = 4.3.

“Move the decimal when multiplying or dividing.”
Students may struggle with the idea of moving the decimal when solving 4 ÷ 10 because 4 does not have a decimal “showing”. Most teachers will remind students to “stick one in” and then move it.  Visualize a place value chart. with ones, tens and tenths. Imagine moving the decimal point to the left or to the right. Did the ones, tens, tenths, etc move? No. “Moving” the decimal point actually messes up the setup of a place value chart. If you move it to the left, your decimal would be to the left of the ones.