Teaching multiplication using Arrays
This approach to multiplication instruction gives the structured support for students who still no not
trust the count, and/or need to count all. However it builds a deep understanding of the size and reason
for the answer.
It gives meaning to the algorithm for multiplication.
Growth Point: develop the multiplication concept
VELS Level:
Number:
2.75: representation of multiplication as a rectangular array and as the area of a rectangle
Working mathematically
2.75 use of materials and models to illustrate and test generalisations
2.75 selection of multiplication and division as more efficient processes than repeated addition and
subtraction
Equipment: MAB ones, or similar blocks)
Dice (2 per pair of students)
1cm grid paper
Introduction.
All students have 12 MAB ones, ask the students to arrange them into 3 groups of 4.
Observe the way students do this.
Encourage them to manipulate the blocks to show different ways of showing the question.
When you observe a student forming rows and columns, ask:
What makes this easy to see?
Can you show me how to calculate the total?
If they use repeated addition ask:
Is there another way to find the total?
You are looking for students to arrange the blocks into rows and columns
Introduce the terminology of rows and columns, and array to the class.
In pairs, ask students to form all arrays for 24, and draw these into their books.
The students should then make and record different arrays for a range of numbers.
Try 24, 12, 15.
The drawing of arrays for prime numbers can be useful here.
Conclusion of Lesson:
Ask students for the different multiplication equations that they have formed for the numbers
that you have posed.
Leonie Anstey
anstey.leonie.m@edumail.vic.gov.au
Department of Education
Victoria, Australia
Extension: Students set their own problems and draw all the arrays for that number
Students use decimals and fractional amounts.
Assessment: record the strategies that students are using to calculate the array.
Leonie Anstey
anstey.leonie.m@edumail.vic.gov.au
Department of Education
Victoria, Australia
ARRAY PADDOCKS:
VELS levels:
Number
2.75: representation of multiplication as a rectangular array and as the area of a rectangle
2.75: use of fact families (5 × 7 = 35, 35 ÷ 7 = 5) to solve division problems
Working mathematically
2.75 use of materials and models to illustrate and test generalisations
2.75 selection of multiplication and division as more efficient processes than repeated addition and
subtraction
Growth Points: develop the multiplication concept
To solve the multiplicative problem where not all objects are modelled or perceived
Equipment: Dice (2 per pair of students)
1cm grid paper
Introduce the game by modelling with two students, either use a whiteboard, or overhead
projector.
Ask the student to roll two dice and draw an array on graph paper to match.
For example: 4 and 6
4 rows and 6 columns
6
4
The student writes 4 x 6 = 24 in the array square.
The student determines which die is the multiplier (that is the row leader)
Students use different color pencils to draw arrays on the same paper.
It also uses cumulative addition to keep track of their total after each roll of the dice. The student who
captures the greatest area after a given amount of time wins the round.
Variations:
If you are focusing only on one table, you could use that multiplier and only roll one die.
You can use 10 sided die, or other multi sided dice.
Assessment: As the students are completing the game, recording of the method that students are using
to find the total should be recorded. That is: count all, additive or multiplicative thinking strategies.
Leonie Anstey
anstey.leonie.m@edumail.vic.gov.au
Department of Education
Victoria, Australia