Chapter 7, Lesson 3 Multiplying Ones, Tens, and Hundreds with Regrouping

What types of problems have we solved so far? 9 x 8 90 x 8 80 x 9 900 x 8 Strategies we have worked on . . . Making ten and subtract a group If I know 4’s I can double to make 8’s Multiplying by ten . . . Multiplying by one hundred . . .

What types of problems have we solved so far? 23 x 4 Distributive Property Compose and decompose into place values Partial Products – begin in either ones or greatest place value on the left Use doubling and halving

Multiply Ones, Tens, and Hundreds with Regrouping What is regrouping? Can you give me an example with addition?

15 x 5 4 x 31 What do we know about the problem? How can we write it? Can we do it mentally? When we write it vertically, how do you want to write it? Can you show me what we are doing in this problem? Make the tape diagrams. Work out the first one. Model working it from both left to right or right to left – writing the products underneath and then adding for the total product. Let students try to model the second problem on their own a little.

Compare to the book Breaking or decomposing into place values Work with the place value – 3 x 30 is not the same as 3 x 3. We call the 30 – 3 tens or thirty. We can write the whole value of the multiplication problem and then add up all the products. Shortcut can be writing the digits in the right place value showing the regrouping above the place value.

Grade 3 Chapter 9 – Lesson 1 – Real-World Problems: Multiplication Use bar models to solve one-step multiplication word problems

Bar models What are unit bars? What do they represent? How many units are in this diagram? How many dots are there in each unit? How many dots are there in all? How did you figure that out?

What do we do when we solve word problems? Read the problem What do I have to answer? Re-read each sentence and draw the bar models, label the units. Adjust the bars as necessary. Place your question mark. Check your diagram. Write the equations to solve the problems, solve the problem Check your answer. (Plug value back into the diagram. Check the arithmetic.)

There are 5 boxes of pencils. Each box contains 12 pencils There are 5 boxes of pencils. Each box contains 12 pencils. How many pencils are there in all? Model the process – read – what do we have to answer? Re-read each sentence and create the diagram. Each box represents a unit – that is why it is called a unit bar! Each unit is equal, so need to try and draw the unit bar equal size. Label each 12 pencils. Model one unit is 12 pencils Then 5 units are 12 x 5. Break up and show how we can multiply this in our head, not writing up and down.

Compare to our book What do you see as the same? What do you see as different? What does “twice” mean? Can you tell your partner a problem that uses the word twice? Partners do you agree with how they used the word twice.

Zach has 342 stamps. Ron has twice as many stamps as Zach Zach has 342 stamps. Ron has twice as many stamps as Zach. How many stamps does Ron have? Let students draw this first. Make sure to label each as you model it. Students can use the tape diagram strips. Show the multiplication writing across and decomposing into place values. Can be written vertically to help also. Show going left to right or right to left. Always show the checking with this.