Grade 4 Number and Algebra
Blast activity D9: Section D – Operations
Multiply two digits by one digit
Preparation: Use this activity AFTER Journal problem 9 and Blast activity D8. You will need grid paper and possibly calculators for this activity. Use your discretion as to your students’ capabilities. You will need to read through both sheets to make sure that you are familiar with the thinking before beginning. The second sheet especially is a little different to the traditional way of teaching this skill. Teaching Tips: 1. Students are to use grid paper to draw the shape mentioned and then using this to work out
how to multiply the numbers. The intention of this activity sheet is to prompt the students to come up with their own models for multiplication. You may wish to stop after the first page and challenge students to represent this in written format rather than moving straight on to the second sheet. If you have time to spare this would be ideal. 2. Discuss students' findings as a class. Share findings and models of multiplication. Discuss the
usefulness of each model and the problems associated with it. 3. Tell students that we are going to use their models to teach them how multiplication has
traditionally been written. The traditional method is not the only acceptable or even best possible algorithm. It is just the most commonly used. 4. Start on the second activity page using their previous grid drawings.
5. Discuss the example as a class and try to work out where the numbers came from. Working
backwards is often a better way of teaching than simply telling students where to put the
numbers. Try to challenge students to find the pattern for themselves rather than relying on
you to tell them.
Follow up and application: Everyone in your class pays $7 for an excursion. How much money is it? (as long as your class has more than 10 students) © Kennedy Press
For use by 2016 licence holders only
Grade 4 Number and Algebra
D9.
Section D – Operations
Multiply two digits by one digit
‡ Often when we are multiplying two digits by one digit we can use a
mental strategy to help. Sometimes it is more efficient to use another strategy.
In this activity you will learn how to use written methods to multiply in these
situations.
Use grid paper to draw 7 rows by 35 columns (7 x 35)
1. How many squares have you included altogether?
2. Find the part that is 7 x 30. How many squares are there here?
3. How is this number related to 7 x 3?
4. Find the part that is 7 x 5. How many squares are there here?
5. Add up the answers to 7 x 30 and 7 x 5. What do you get? How is this related to
7 x 35?
Use grid paper to draw 9 rows by 24 columns (9 x 24)
1. How many squares have you included altogether?
2. Find the part that is 9 x 20. How many squares are there here?
3. How is this number related to 9 x 2?
4. Find the part that is 9 x 4. How many squares are there here?
5. Add up the answers to 9 x 20 and 9 x 4. What do you get? How is this related to
9 x 24?
What patterns have I found? How might this be useful for solving multiplication problems?
If you tip your grid drawings sideways you will see that 7 rows x 35 columns is the same as
35 rows x 7 columns. This is true for all multiplication problems. It doesn’t matter what
order the numbers are in when you are multiplying them.
The equation below represents the first equation that you drew (7 x 35). Look at it and try
to find the 7 x 5 part and the 7 x 30 part.
Which part is this number?
Which part is this number?
How did we get this number from 35 and 210?
© Kennedy Press
For use by 2016 licence holders only
Grade 4 Number and Algebra
Section D – Operations
Try these:
5 6
x
5
2 7
x
6
8 3
x
4
4 9
x
2
6 8
x
7
9 2
x
5
This way is easy to see which parts are already multiplied, but it takes quite a long time to
write. A quicker way is shown below.
Look at it and try to find the 7 x 5 part first and the 7 x 30 part second. The part that
represents 7 x 30 already has the tens from 7 x 5 added to it. This is why it isn’t just 210.
See below:
What part is this?
3 5
x
7
3
2 4 5
What part is this? What has happened to the 3 tens from the 35?
Try these:
5 6
x
5
2 7
x
6
8 3
x
4
4 9
x
2
What patterns have I found? How can I use these?
How do I multiply two-digit by one-digit numbers?
How could I check my answers to make sure that I’m right?
Backwards Question:
How could you work out the following question?
Explain how you did it:
6
x
7
4 7 6
© Kennedy Press
For use by 2016 licence holders only
6 8
x
7
9 2
x
5