Mental Computation Strategies

A Learning and Teaching Resource for Mental Computation Strategies

The purpose of the Mental Computation folder cards

Using a folder card to demonstrate the inverse relationship between multiplication and division (text only)

Reference

Australian Curriculum Assessment and Reporting Authority (2014) Mathematics: Foundation Year. Retrieved September 13, 2014 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10#level=F

Classroom Clipart (2013). Teacher & Student image. Retrieved July 30 2014 from http://classroomclipart.com/clipart-view/Clipart/Mathematicsjpg.htm

Jamieson-Proctor, R. (2014). Language Model. Week 1 Lecture - Addition, Foundations of Numeracy EDX1280. USQ, Springfield.

Jamieson-Proctor, R. (2014). Numeration. Week 6 Lecture - Numeration, Foundations of Numeracy EDX1280. USQ, Springfield.

Count On/Back

The counting on and counting back can be used for the addition and subtraction of 0,1,2,3 from any number.

Doubling/ Halving

The use of doubles can be used for e/g 4+4, 5+5, 6+6 and where a number is added by itself. Halving is used when we have a number that can be doubled, e/g 4,6,8,10 then this is the doubling strategy reversed.

Use – 10

The strategy of use-10, is used for the addition and subtraction of numbers in the 8 and 9 fact cluster.

Think Real World

Think Real World is used for the multiplication and Division of 1x and 0x numbers.

Doubling

Doubling is used for the 2x,4x and 8x fact clusters. This can be furthered to double, double double, double double double.

Counting

The counting strategy is used for the multiplication and division of numbers in the 5x fact clusters.

Build Up/ Down

Building up using 3x and 6x is used to demonstrate multiplication and division. Building down is used for 9x fact clusters.

These folder cards were constructed using the Caldwell pattern. The images used on the folder cards are realistic and life related images. The images are also simple yet effective for students to recognise easily and see the clear outlines of each image to show that this one picture represents one. Two A3 sized coloured pieces of cardboard were cut in half to be used at the folder cards. The use of coloured crayons constructed the colourful shapes on the each card. Black was used to outline each image to ensure they stood out. As there are many different images that could be included rather than hand drawn images, it was more ethical to colour the self-made stencilled outlines of each image. Each card has contrasting colours and shapes that illustrate the type of folder cards they are. Each card is large enough to facilitate the learning to a class of approximately 30 students. The sizes of each folder card are:

Count On/ Back -

Doubling/ Halving - L 23cm x W 16 cm

Use – 10 - L 25 cm x W 16 cm

Counting - L 26 cm x W 19 cm

Doubling - L 28 cm x W 23 cm

Think Real World - L 32 cm x W 8.5 cm

Build Up x3 - L 24cm x W 10.5 cm

Down - L 25.5 cm x W 14 cm

The mental computation folder cards are introduced to students in year 1 and 3. Each card was created to practice and reinforce strategies for mental computation of addition and subtraction and multiplication and division.

In connection with ACARA (2014), the following reference is most relevant to the mental computation teaching resources; (ACMNA057)

Sub-strand: Number and Place Value

Content Descriptor: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

Elaboration: writing simple word problems in numerical form and vice versa

At this stage on the language model, the strategies are introduced during the materials stage. The numbers have been substituted with concrete/visual images of shapes on the cardboard folder cards. At the materials stage of the language model, students are still answering questions verbally as multiplication and division is still being introduced to them. The folder cards allow the young students to physically see the substituted numbers and how they are visually multiplied and divided.

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Using the Build up and down folder card strategy to visually show the inverse relationship between multiplication and division. For students to understand the inverse relationship between the multiplication and division, both a types of equations will need to be demonstrated. For the concept of multiplication, we know that this means we are adding multiple equal amounts together. Here we are going to use the Build Up to show how to work out an equation from the 9 number fact family. Lets look at the build up card with the green circles. How would I work out how many green circles there are in 4 groups of 9? Which strategy can I use for the equation of 4 groups of 9? Build up to 10! (Open card) Lets see, if I already know that 4 groups of 10 is 40 green circles. If I take away 4 green circles (close card), this will be equivalent or equal to 4 groups of 9. So what is 40 take away 4? 36! Therefore, 4 groups of 9 green circles, or 4 groups multiplied by 9 is 36 green circles.

Using the build down strategy to assist in the mental computation of division is more difficult. The concept of division is to work out how many groups a number with be group equally. So how would I work out how many green circles would be placed into 4 equal groups? We have worked out that there are 36 green circles (with the card closed). You would easily be able to work out how many equal groups of 40 green circles there are (open card). You can see there are equal amounts of green circles placed in their rows. How many are there? That’s correct! There are 4 equal groups of 10 green circles (close card). How many equal groups are there now? That’s right! There is still 4 equal groups of but now there are only 9. So 36 green circles grouped equally, or divided 9 into 4 groups.