(1) A Learning and Teaching Resource for Mental Computation Strategies 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The folder cards pictured above were created from the following materials; A3 sized cardboard, scissors, glue, black and red markers, coloured pencils and purchased craft materials.

Firstly the cardboard was measured using a ruler and lined using the appropriate colour as I had to ensure that there was space for the selected images; use-10, doubling, and build up/down needed extra card glued on to accommodate for more numbers. Once I was certain they would fit, I went over the outer lines with permanent marker and then cut the cardboard to the required shape and size.

 

Use-10: 50.5cm x 29.5cm

Count on/back: 21.5cm x 21cm

Doubling/halving: 29.5cm x 35cm

Build up/down: 33cm x 33.5cm

Real world: 42cm x 16cm

Use doubles: 13.5cm x 72cm

Use counting: 42cm x 29.5cm

 

The chosen images were then glued into their selected squares. Although, Use-10 was made using a stencil I had made out of remainder cardboard. The reason I changed my mind was the stencils would be impractical for a classroom teacher.

The purchased craft materials are not only appealing to students, but also to classroom teachers as it does not require cutting out. The craft materials also give a 3d-effect providing a multi-sensory learning experience for students, allowing them to learn through sight and touch. The reasoning for having large sized cards is to ensure that they are appropriate for a whole class to use and see, allowing the folder cards to be used with a class of thirty students or in smaller groups.

 

(2) The Purpose of the Mental Computation Folder Cards 

The Mental Computation Folder Cards act are a visual aid used to practice and reinforce strategies. This assists children in understanding the inverse relationship between addition/subtraction and multiplication/division.

 

The count-on 3 card is used for counting-on or back 3 from any number, for example 6 ducks add 3 more ducks becomes 6,7,8,9 ducks.

The doubling/halving card shows how a number can be doubled for example double 6 is 6 zebras add 6 more zebras. Then later reversing the strategy to reinforce halving. Smaller numbers can also be counted on.

The use-10 strategy is used for the addition and subtraction of numbers 8 and 9, in which you round the numbers to 10. For example 9 cats add 5 cats becomes 10 cats add 4 cats.

The use doubles card shows how the number facts 2, 4 and 8 can be repeatedly doubled. For example double 4 is 8, double 8 is 16, double 16 is 32.

The think real world card is to demonstrate the concept of multiplying by 0 and 1.

The use counting card is used for multiplying by numbers 5 or 10. For example, 3 rows of 10 frogs becomes 10, 20, 30 frogs.

The build up/down card uses multiples of 3, 6 or 9. Children build up their previous knowledge of double (by 2) and add a row making it by 3, and also using multiply by 5 and adding a row to make by 6. Children build down by using multiply by 10 and remove one row to make by 9.

 

In connection with ACARA (2014), the following reference is for set one: Year 1, number and algebra, number and place value. Content Description- Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015). Elaboration – developing a range of mental strategies for addition and subtraction problems (ACARA, 2014).

The ACARA Reference for set two is: Year 4, number and algebra, number and place value. Content description- develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076). The Elaboration is using known facts and strategies, such as commutativity, doubling and halving for multiplication, and connecting division to multiplication when there is no remainder (ACARA, 2014).

The folder cards would be introduced in the materials language stage. The students learn the concept in children’s language and the strategies are later introduced in the materials language stage. 

 

(3) Using a Folder Card to demonstrate the Inverse Relationship between Multiplication and Division (text only)

Demonstrating the inverse relationship between multiplication and division to year 4 students:

 

(Holding the Counting card horizontally for class to see)

So here we have a counting card for multiplying and dividing by 5. This is how we can use the card to multiply 5 by 3. We can see that there are 3 rows of 5 sunflowers. How many flowers are there all together?

 

 

 

 

 

Lets count in 5s, (fold and point to each row) 5, 10, 15! There are 15 sunflowers all together, so 5 multiply by 3 is 15.

 

 

 

Now, we can use this card to divide (turn card vertically for class to see). What is 15 divided by 5? How can we work this out? Lets think. How many groups of 5 can 15 be divided into?

(Point at counting card) 15 can be divided into 3 groups of 5.

So, 15 is 3 groups of 5. 15 divided by 5 is 3.

 

 

 

 

(Folding card to create 5 groups of 3) When we fold the card we can see how 15 can be divided into groups of 3, 5 times.

1 group of 3, 2 groups of 3, 3 groups of 3, 4 groups of 3, 5 groups of 3!

 

 

15 divided by 5 is 3. 

 

 

 

 

 

(4) References. 

Mental Maths Cartoon [Image] Retrieved from https://www.oxfordpanama.com/oxford/common/news.jsp?id=652

 

Sports images, felt people and felt hearts purchased from - Riot Mt Ommaney 

Butterflys purchased from - Overflow Jindalee Homebase

Flowers furchased from - STACKS Discounts Indooroopilly

 

 

Australian Curriculum Assessment and Reporting Authority (2014) Mathematics. Retrieved from: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1