A Learning and Teaching Resource for Mental Computation Strategies
The folder cards have been made using a think cardboard which I chose as a darker colour for the other images to stand out of the background. The images on each of the cards are bright coloured stickers with a variety of themes. I used scissors, a ruler and a pencil to make these folder card as well as stickers and cardboard.
I believe that the folder cards are durable but also pliable, I was originally going to laminate however I thought that this might also limit the ability to easily fold over the section of the cards when using them. |
The dimensions of the folder cards are as follows
Count on/back - L 10.5 cm x W 15 cm (4 cards measuring the same) Use doubles/halves - L 20 cm x W 15 cm Use 10 - L 16 cm x W 27 cm Use counting - L 15 cm x W 21 cm Use doubles - L 52.5 cm x W 15 cm Think real world - L 4 cm x W 27 cm Build up/build down- L 15 cm x W 20 cm |
The Purpose of the Mental Computation Folder Cards
Folder cards are used with the intended purpose of assisting students to visually see how these strategies work, and by practicing and reinforcing these strategies students will be able to effectively learn and use mental computation strategies without using visual aids.
Set one:
Use-10 is used to help students add to the numbers eight or nine. The number fact cluster is eight and nine. For example 9 add 5 is like 10 add 4, so we move this one from the 5 and add it to the 10 then we have 10 add 4 with equals 14. Doubling/halving is the strategy of doubling or halving any number when students are given opportunities to practice and reinforce these strategies they become effective at these mental computation strategies. The folder cards can also be used for doubling a number and counting on one or two. Doubling/halving can be used with any number. The doubling/halving strategy has 44 number facts. For example six ducks plus six more could be double six is twelve plus two is fourteen. Count-on/back is used to practice and reinforce the strategy of counting-on or back from any number. Counting-on/back can be used for adding or subtracting zero, one, two or three from any number. The number fact cluster is zero, one, two and three. For example there are 3 octopus pictures and we add 3 more we can count on 3 more so 3, 4, 5, 6 there are 6 octopus pictures altogether. |
Set two:
Build up/down is used to demonstrate to the students the relationship between the numbers three, six and nine. The build up/down strategy provides students the ability to use their multiplication skills and subtraction skills to find the correct answer. The number fact cluster is three, six and nine. For example, we have 2 groups of 5 planes here and we wanted to have 3 groups of planes on the runway, we could build up 5 more planes and have 3 groups of 5 planes. Counting is used to help students in their counting skills. The number fact cluster is five and ten. For example we have 5 footballs and there are 5 more over there, how many are there altogether? Doubling is used to help students use their previous knowledge of multiplication to assist them in working out more complex multiplication sums. The number fact cluster is two, four and eight. Real world is used to demonstrate the use of multiplying numbers by zero and one. The number fact cluster is therefore zero and one. |
Implementing folder cards and their strategies within the Australian Curriculum
Addition and Subtraction (Set one of the folder cards)
Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015) Strand: Number and Algebra Sub – Strand: Number and Place Value Content Description: Represent and solves simple addition and Subtraction problems using a range of strategies including counting on, partitioning and rearranging parts. Elaboration: Developing a range of mental strategies for addition and subtraction problems. ( ACARA, 2014) |
Multiplication and Division (Set two of the folder cards)
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Strand: Number and Algebra Sub – Strand: Number and Place Value Content Description: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies. Elaboration: Writing simple word problems in numerical form and vice versa ( ACARA, 2014) |
The language ModelWhen using the folder cards the language that we will be using will be the mathematics language, when giving students the questions the teacher will use words such as add, subtract, multiply by, divide and equals.
Students will use the folder cards to visualize concrete materials which are the folder cards however there are also images on these cards that are known to students such as trucks, ducks and pirate ships. Students will be using substitutes objects, photographs and graphics. |
Using a folder card to demonstrate the Inverse Relationship between Multiplication and Division
References
Australian Curriculum Assessment and Reporting Authority, (2013). V 5.1, Yr 1 Mathematics. Retrieved January 1, 2015 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10#level=1 )
Australian Curriculum Assessment and Reporting Authority, (2013). V 5.1, Yr 3 Mathematics. Retrieved January 1, 2015 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10#level=3)
Mental Math [Image] (n.d). Retrieved December 30, 2014 from http://www.communication4all.co.uk/Screen%20Shot%20Images/Maths%20Strategies.png
Boy with math signs [Image] (n.d). Retrieved from http://www.londonderry.org/assets/twps/images/math_icon.gif
Children with question marks [Image] (n.d). Retrieved from http://science.phillipmartin.info/science_questioning.gif
Jamison-Proctor, R. (2014). EDX1280 Foundations of Numeracy: Lecture notes week 1. Fraser Coast. University of Southern Queensland
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 2. Fraser Coast. University of Southern Queensland.
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 3. Fraser Coast. University of Southern Queensland.
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 4. Fraser Coast. University of Southern Queensland.
Australian Curriculum Assessment and Reporting Authority, (2013). V 5.1, Yr 3 Mathematics. Retrieved January 1, 2015 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10#level=3)
Mental Math [Image] (n.d). Retrieved December 30, 2014 from http://www.communication4all.co.uk/Screen%20Shot%20Images/Maths%20Strategies.png
Boy with math signs [Image] (n.d). Retrieved from http://www.londonderry.org/assets/twps/images/math_icon.gif
Children with question marks [Image] (n.d). Retrieved from http://science.phillipmartin.info/science_questioning.gif
Jamison-Proctor, R. (2014). EDX1280 Foundations of Numeracy: Lecture notes week 1. Fraser Coast. University of Southern Queensland
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 2. Fraser Coast. University of Southern Queensland.
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 3. Fraser Coast. University of Southern Queensland.
Jamieson-Proctor,R.(2013). EDX1280 Foundations of Numeracy: Lecture Notes Week 4. Fraser Coast. University of Southern Queensland.