connect with maths webinar "beyond the tip of the iceberg mathematics"

Exploring mathematical problems

beyond the tip of the iceberg

Exploring mathematical problems

beyond the tip of the iceberg

Pick problems...

Pick problems...

maths300.esa.edu.au

maths300.esa.edu.au

Attributes of aMaths 300 lesson

maths300.esa.edu.au

Challenges in my classroom...

Arithmagons

Strategy Board

Learning outcomes and related concepts•basic addition•difference between•algebraic representation•problem posing and solving•the Working Mathematically process

Arithmagons

Pen Pen thicknessthickness

Pen colourPen colour

t1 = a + bt2 = b + ct3 = a + c

t1 = a + bt2 = b + ct3 = a + c

The number on the edge is The number on the edge is the sum of the two the sum of the two

numbers on the vertices.numbers on the vertices.

t1 = a + bt2 = b + ct3 = a + c

t1 - t2 = (a + b) - (b - c)

this becomest1 - t2 = a - c

t1 = a + bt2 = b + ct3 = a + c

t1 - t2 = (a + b) - (b - c)

this becomest1 - t2 = a - c

Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)

Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.

Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)

Put your finger near the top circle to highlight the difference between 13 and 8, which is 5.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Zero is not being used. The only pairs of numbers which sum to 9 are: (8, 1), (7, 2), (6, 3), (5, 4)

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Another approach...

Pick any numberPick any number

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Pick any numberPick any number

Complete the other Complete the other other two verticesother two vertices

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Pick any numberPick any number

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

Complete the other Complete the other other two verticesother two vertices

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Pick any numberPick any number

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

Complete the other Complete the other other two verticesother two vertices

6 needs to be shared 6 needs to be shared between two verticesbetween two vertices

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

6 needs to be shared 6 needs to be shared between two verticesbetween two vertices

Add 3Add 3

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

6 needs to be shared 6 needs to be shared between two verticesbetween two vertices

Add 3Add 3

Take 3Take 3

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

6 needs to be shared 6 needs to be shared between two verticesbetween two vertices

Add 3Add 3

Take 3Take 3

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Total needs to be 9, but Total needs to be 9, but 10 + 5 = 15...over by 6.10 + 5 = 15...over by 6.

6 needs to be shared 6 needs to be shared between two verticesbetween two vertices

Add 3Add 3

Take 3Take 3

Extensions...

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Extensions...

Challenge older kids to program a SS

So, the opposite circle numbers must have a difference of 5 AND sum to 9.

Challenge older kids to program a SS