Twos, Fives, and Tens

Using Materials

Tell the students that they already know a lot of their multiplication (times) tables.This may surprise them but indicate that you are going to prove it. Move two strings of seven across on the bead frame. Ask, How many beads have I moved? How do you know?” Students will reply that the answer is fourteen since double seven beads have been moved. Tell them that fourteen is also the answer to “two multiplied by (times) seven.” Record the operations as addition and multiplication expressions:
 

7 + 7 is the same as 2 x 7 (two rows of seven)

Provide similar examples connecting doubles with the two times tables and recording the related expressions using symbols. Do this in sequence and ask students to predict missing members of the pattern.

5 + 5 is the same as 2 × 5 = 10
What is 2 × 6?
7 + 7 is the same as 2 × 7 = 14
8 + 8 is the same as 2 × 8 = 16
What is 2 × 9?

Similarly link the ten times tables with students’ knowledge of the “-ty” words.

4 × 10 is the same as forty

Provide several examples of the “-ty” word link so that students generalise the idea.Joke that ten really should be called, “one-ty.”Develop the idea that 10 × 2 has the same answer as 2 × 10 by separating the beads as shown below:

Give other examples, like 10 × 5 has the same answer as 5 × 10, to generalise the idea.Connect the five times tables to the ten times tables in the following way.

Ask: “Here are three tens. How many fives is that?” (six fives). Record this as: 3 × 10 = 30 so 6 × 5 = 30.Pose similar related problems, such as:2 × 10 = 20 so 4 × 5 = 20 and 4 × 10 = 30 so 8 × 5 = 30

Organise the equations in a pattern and ask students to derive examples within the pattern:

1 × 10 = 10 so 2 × 5 = 10
What will 3 x 5 be?
2 × 10 = 30 so 4 × 5 = 20
3 × 10 = 30 so 6 × 5 = 30
What will 7 x 5 be?
4 × 10 = 30 so 8 × 5 = 30
What will 9 x 5 be?

Demonstrate that 4 × 5 has the same answer as 5 × 4. 

Provide other examples to generalise the idea. For example:7 × 5 has the same answer as 5 × 7

Using Imaging

Role playing: Send a student behind a screen with a bead frame. Ask them to move over beads that match the operation you give. For example: “Tipene, make two times eight for me, please.”

What will 3 × 5 be?What will 9 × 5 be?

Ask the other students to explain what Tipene has done and tell you how many beads have been moved. Record the operations using equations, like 2 × 8 = 16. Tipene can be asked to confirm the students’ ideas.

Provide many examples to illustrate the connections between the twos, fives and tenstimes tables. Examples might be:
Make double nine. What is two times nine?
Make five times ten. What “-ty” number is that?
Make ten times seven. What “-ty” number has the same answer?
Make four times ten. How many fives is that?

Using Number Properties

Provide written examples that are outside the number range of the bead frame problems the students have encountered. For example:

2 × 11, 2 × 50, 2 × 20, 2 × 19, 2 × 300, 2 × 25, 10 × 10, 10 × 20, 10 × 100,
10 × 12, 19 × 10, 25 × 10, 5 × 20, 5 × 40, 5 × 12, 5 × 14, 13 × 5, 18 × 5

Students may realise that the five times problems can be solved by doubling and halving:

12 × 5: double five to make 10, and halve 12 to get 6 × 10 = 60.

Figure It Out activities to reinforce students’ knowledge of the 2, 5, and 10 times tables include Number: Book Two, Level 2, page 18 (Double Trouble) and Number Sense: Book One, Years 7–8, page 9 (Flying Feet).