Diagnostic questions
- Tennis balls come in cans of four balls. How many tennis balls will I have if I buy:
a. 2 cans? b. 5 cans? c. 10 cans? d. 8 cans? - Ask the student the questions below, telling them to say the number that comes into their head:
a. 2 x 6 e. 7 x 7
b. 5 x 8 f. 9 x 2
c. 10 x 3 g. 6 x 2
d. 8 x 4
What to notice in the student’s response
Does the student use their knowledge of basic facts to solve the tennis ball problems?
Do they use basic fact knowledge for some of the tennis ball questions but use another strategy for others?
Can a student who knows their two times table solve 6 x 2 as easily as 2 x 6?
Note: If the student has not mastered the two, five, and ten times tables, use the ALiM resource to develop the basic facts required for stage 5.
Deliberate acts of teaching
Materials
- Long strips of paper
- Materials for contextual problems to demonstrate doubling sets
- Blank Grids (Number and Algebra, level 3)
- Four in a Row Multiplication (Material master 6-6a) (PDF, 92KB)
The best way for a student to learn new information is to link it to something that they already know.
Start by showing the student the 10 x 10 times tables grid and make sure that they are familiar with the concept of commutativity. Highlight on the grid the times table facts that the student has already mastered and use these to show them related times table facts. For example, if the student knows that 2 x 8 = 16, point out that they also know 8 x 2.
Seeing Double
Review the 2 times table as “doubles”. For example, 2 x 6 is the same as double 6.
Introduce the 4 times table as doubles of the 2 times table. Use materials to demonstrate that two groups of seven and four groups of seven are halves or doubles of each other.
Create four number line strips (A–D), marking 10 equally spaced points on each one.
Ask the student to write out the 1 times table on line A, using the numbers 1–10, and to write out the 2 times table on line B, using the numbers 2–20.
Position line B under line A and discuss why the numbers on line B are the double of the corresponding numbers on line A.
Ask the student to write out the 4 times table on line C, using the numbers 4–40, and to write out the 8 times table on line D, using the numbers 8–80.
Position line C under line B and show the student that the numbers on line C can be found by doubling each number on line B.
Give the student flashcards with the 4 times table on them and provide time for practice.
Position line D under line C and show that the numbers on line D can be found by doubling each number on line C. Emphasise that if the student knows their 4 times table, they can use it to find the 8 times table. Give the student flashcards with the 8 times table on them and provide time for practice.
Extend the activity by working on the 3 times table. Use number strips to demonstrate that numbers on the 6 times table are doubles of the corresponding numbers on the 3 times table.
What to do next if the student is stuck
Keep the pace slow. Continue to emphasise links to the student’s prior knowledge. Use arrays in place of number lines.
Initiating home-based activities
Give the student doubling tasks by giving them a list of objects and their prices and asking them to find the cost of two, four, and eight of each item.
Next teaching steps back in the classroom
Use problem-solving activities that require doubling. Target independent learning based on the multiplication set that the student is working on.