MathaMagic Stages of Progression

Profiling a student’s knowledge forms a basis for instruction that is targeted at the student’s point of need (Bobis et al., 2005) and the sequence of colour and levels aim to enable the student to structure and invent their own “context bound strategies” (Ellemor-Collins & Wright, 2009) to progress from inefficient backup strategies, such as count by ones, to more formal, efficient ones, such as doubles and tens facts (Ellemor-Collins & Wright, 2008).

MathaMagic Structure Levels

YellowNumber Combinations to 5

Children’s facility to make and read finger patterns is important as using fingers is the common starting place to keep track of counting. Children need to be familiar with basic patterns for numbers in the range 1 to 5 on each hand, and with practice learn to trust the amount they raise on their fingers. This knowledge can be extended to all of the 25 combinations involving two numbers in the range 1 to 5.

Pink

Small Doubles

Typically the first five doubles are among the first additions that a child comes to know. This knowledge can be used to advance to the more complex and powerful strategy of doubles +/-1, making counting from 1 or counting by 1’s redundant.

Blue

Five Plus

An important goal of the activities in this colour is for children to develop more sophisticated ways of reasoning. Activities create situations in which children are encouraged to count on from 5 and reflect on the mathematical activity. Reflection of this kind can lead to more sophisticated ways of reasoning.

Green

Combinations to 10

Partitions of 10 are one of the most important stages of MathaMagic. Understanding that 10 can be split in a different ways can make the operations of addition, subtraction, multiplication and division easier.

Red

Sums less than or equal to 10

Sums less than or equal to 5 builds upon the previous levels as students use these foundational stages to build more complex procedures and skills. In order to add through 5, without counting by ones, children need to use and connect previous knowledge such as small doubles, numbers that make 5 and number that make 10. A number fact such as 4+3 can be calculated by using doubles plus or minus 1 (4+4-1, 3+3+1) or knowledge of 5 (4+1 +2).

Orange

Numbers 11 to 20

Orange extends students knowledge of the structure of numbers in the range 11 to 20, continuing to develop the use of non counting strategies and providing a crucial basis for the development of mental strategies for addition and subtraction involving 2 digit numbers.

Purple

Subtraction

This level is the culmination of all counting and number knowledge up to this point. To be competent within the range 1 to 1000 all skills covered within levels yellow to orange need to be applied. It introduces each of the hundreds and focuses on bridging over a hundreds number, the value of each digit in a 3 digit number and counting by 10’s within the hundreds.

MathaMagic Numbers and Numerals Levels

Yellow

Where all number knowledge begins! Yellow is the most important level and should be given the most time. A strong knowledge of numbers 1 to 10 will be the stepping stones for all other Number based knowledge.

Pink

Teen numbers can be tricky, especially 11 and 12 whose names seem to have no link the rest of the counting pattern. This level introduces just five more numbers but a whole lot of knowledge is needed to master them. Pink bridges from the ones into the teens, it introduces the concept of ten and ones and the skill of being able to decode the language of eleven, twelve and the beginning of teens.

Blue

Blue builds on the knowledge of pink and introduces the next four ‘teen numbers’ and another bridge of the tens. It reinforces tens and ones and gives time to consolidate all teen numbers.

Green

A leap into the 20’s. Green level introduces the 20’s which establishes the base for counting from here on. Once the twenties are mastered, the knowledge can be transferred to all other 10’s. It establishes the pattern of tens and ones, what happens when you bridge and the fact that the tens numbers increase in the same pattern as ones ie. one more 10 than 20 is 3 tens.

Red

99 …… 100. The introduction of the next base 10 place value and a level for consolidation of all numbers up to. Red is an opportunity to reinforce the bridging of tens and the value of each digit in a two digit number ie 34 is 3 tens and 4 ones.

Orange

Orange level enters into the hundred. Numbers are up to 130 to ensure the knowledge of a three digit number and bridging over the hundred are given due diligence. If we rush through this important counting milestone a misconception may form, such as one hundred and thirteen is recorded as 10013.

Counting by 10’s forwards and backwards is also introduced as a strong understanding of counting by tens becomes the foundation for adding and subtracting 2 digit numbers.

Purple

White

White level focuses on a very common misconception. A common mistake that is made when counting within the range 1 to 10 000 is when bridging a hundred number I say the next thousand ie 7098, 7099, 8000.