Building the multiplication concept using arrays
![Picture](/uploads/1/9/8/3/19834597/1400699495.png)
Spinning
Multiplication
As the multiplication concept is not readily shown with stories it is important to instead use arrays (Booker, 2011). In this activity, a spinner is used to generate arrays and build up the language and direction of operating that will be used. This activity will also assist students who confuse multiplication with addition or rely on repeated addition without extending their thinking to multiplication (Booker, 2011).
How to Play:
A student spins the spinner and makes the array indicated using unifix cubes or counters. This can be done individually or perhaps competing against the teacher or peers in small groups to see who is first to put the counters out one row at a time to build the array.
The arrays should then be rotated to build an understanding of the two linked multiplications that are evident.
Extension:
The 100 grid game board can be introduced to enable further practice in making multiplication arrays whilst strengthening the learners understanding that multiplication facts can be expressed in two ways (Booker, 2011)
How to Play:
The first player spins the spinner and makes the array on the grid using counters in one colour
The second player then spins the spinner and makes their array on their grid using a different colour to the first player.
During the game the learning manager should discuss what is shown in terms of 4 fives, 6 threes, to ensure conceptual language is consolidated.
Students keep playing until the whole grid is filled. The first to fill their grid is the winner.
Further extension can be achieved be asking students to then write symbols to match each array.
As the multiplication concept is not readily shown with stories it is important to instead use arrays (Booker, 2011). In this activity, a spinner is used to generate arrays and build up the language and direction of operating that will be used. This activity will also assist students who confuse multiplication with addition or rely on repeated addition without extending their thinking to multiplication (Booker, 2011).
How to Play:
A student spins the spinner and makes the array indicated using unifix cubes or counters. This can be done individually or perhaps competing against the teacher or peers in small groups to see who is first to put the counters out one row at a time to build the array.
The arrays should then be rotated to build an understanding of the two linked multiplications that are evident.
Extension:
The 100 grid game board can be introduced to enable further practice in making multiplication arrays whilst strengthening the learners understanding that multiplication facts can be expressed in two ways (Booker, 2011)
How to Play:
The first player spins the spinner and makes the array on the grid using counters in one colour
The second player then spins the spinner and makes their array on their grid using a different colour to the first player.
During the game the learning manager should discuss what is shown in terms of 4 fives, 6 threes, to ensure conceptual language is consolidated.
Students keep playing until the whole grid is filled. The first to fill their grid is the winner.
Further extension can be achieved be asking students to then write symbols to match each array.
Developing 1 by 2 didget multiplication Algorithm
![Picture](/uploads/1/9/8/3/19834597/1400837690.png)
Once the learner has a strong understanding of the
multiplication concept and basic facts are known, multiplying larger numbers
needs to be linked these understandings to place value, renaming and the
concept of zero in a similar manner to addition.
The learning manager should model several examples before scaffolding the learners using place value charts and base 10 materials.
Example 35 x 3
1. Ask the learners to show 35 on a place value chart. Then place two more 35’s on the chart. Read as ‘3 thirty-fives’
2. Have the learner bundle ten ones and place into the tens column. Leaving the 5 ones in place. The way the materials are introduced can be used to emphasise the idea of ‘crossing places’ and this meaning can be applied to the multiplication symbol ‘X’.
When ready, recording should be introduced alongside the use of the materials as shown on the example provided.
The learning manager should model several examples before scaffolding the learners using place value charts and base 10 materials.
Example 35 x 3
1. Ask the learners to show 35 on a place value chart. Then place two more 35’s on the chart. Read as ‘3 thirty-fives’
2. Have the learner bundle ten ones and place into the tens column. Leaving the 5 ones in place. The way the materials are introduced can be used to emphasise the idea of ‘crossing places’ and this meaning can be applied to the multiplication symbol ‘X’.
When ready, recording should be introduced alongside the use of the materials as shown on the example provided.
Consolidating Learning and Catering For Diverse needs
![Picture](/uploads/1/9/8/3/19834597/1400839536.png)
Once students have access to meaningful, efficient strategies for the multiplication facts, consolidation of multiplicative thinking can be achieved through a wide range of digital and hands on games and activities (Siemon, Beswick, Brady, Clark, Faragher, Warren, 2011).
Learners should be encouraged to work in group situations and share their strategies with each other (Siemon, Beswick, Brady, Clark, Faragher, Warren, 2011).
To ensure all learners’ needs are catered for, the Tool Kit include a range of hands on and digital resources. Modification and extension opportunities are provided for with three levels of abilities offered for:
Maths Power towers - easy, med, hard
Math Go around game - easy, med, hard
Top Trumps Math - easy, med, hard
Sticky Multiplication sticks - easy, med, hard
Problem Solving Cards - easy, med, hard
Maths Bullseye - easy, med, hard.
It is importants that learning managers create challenging learning environments that encourage the active involvement of all students. (International Academy of Education, 2001).
Learners should be encouraged to work in group situations and share their strategies with each other (Siemon, Beswick, Brady, Clark, Faragher, Warren, 2011).
To ensure all learners’ needs are catered for, the Tool Kit include a range of hands on and digital resources. Modification and extension opportunities are provided for with three levels of abilities offered for:
Maths Power towers - easy, med, hard
Math Go around game - easy, med, hard
Top Trumps Math - easy, med, hard
Sticky Multiplication sticks - easy, med, hard
Problem Solving Cards - easy, med, hard
Maths Bullseye - easy, med, hard.
It is importants that learning managers create challenging learning environments that encourage the active involvement of all students. (International Academy of Education, 2001).