Posted in Calculating, Making totals, Numicon

Total 6

An extension of Investigating totals

Put the shapes on the grid but this time each row, column and diagonal has to have the same total.

6 grid

You might want to make the task simpler:

  1. Make each row total 6
  2. Make each column total 6
  3. Make the rows and columns total 6
  4. Include the diagonals.

Which shapes are you using in each row / column? Why?

Is there more than one way of completing the grid?

Look at your partner’s grid. What is the same and what is different?

Make the task more challenging:

  1. Use digit cards instead of the shapes.
  2. Don’t give the total – Can you put the Numicon shapes on the grid so that each row, column and diagonal add to the same total?

What do you think the total might be? Why?

How are you going to start? What are you going to try first?

What if.……..you used three different consecutive shapes?

3 twos, 3 threes and 3 fours                                 3 threes, 3 fours and 3 fives

Screenshot 2018-09-26 14.28.32or   Screenshot 2018-09-26 14.28.43

What will the totals of each row be now?

Screenshot 2018-09-26 15.51.01

Posted in Calculating, Making totals, Numicon

Investigating totals

Digit Dog has got a 3 x 3 grid and 9 Numicon shapes – 3 one shapes, 3 two shapes and 3 three shapes. He is going to put the shapes on the grid and investigate the totals he can make.

Screenshot 2018-09-23 15.50.21

This is what he does first:

Screenshot 2018-09-23 15.50.32

Copy what Digit Dog has done.

Digit Dog says that the sum of the shapes in the first row is 6. Do you agree with Digit Dog? Why or why not? Are you sure?

Expecting learners to explain their thinking helps develop their reasoning skills.

If you agree, convince me that Digit Dog is correct. If you don’t agree, explain why you think he is wrong.

Encourage learners to explain why the total of the first row is 6. Use the Numicon shapes to show that the 3 shapes in the first row are equivalent to a six-shape. Explanations are much easier when you use concrete apparatus.

Screenshot 2018-09-23 18.01.53     Screenshot 2018-09-23 18.01.40

Screenshot 2018-09-23 18.07.13

Use the pan balance to explain.

Calculating Cat says that the total of the shapes in the third column is 6 too. Is she right? How do you know?

What is the same and what is different about Digit Dog’s row and Calculating Cat’s column?

Can you find any other rows or columns that total 6? Are there any that total more than 6? What about less than 6?

Can you find a row or column that totals 1 more than 6? What about 1 less than 6?

What else do you notice?

How are you going to record the totals you have found?

Now arrange the shapes on the grid in any way you want and investigate the totals that you make. What do you notice? What is the largest total you can make? The smallest total?

Look at a grid your friend has done. What is the same? What is different?

What if you used other shapes?

Posted in Problem solving

Ladybird Box

Digit Dog saw the Ladybird Box problem on www.nrich.maths.org/144 and thought he’d try it out.

The Challenge

The box has 9 little square compartments. Can you put the 6 ladybirds in the box so that there are just 2 ladybirds in every column and every row?

Ladybird box

I wonder how many ways there are to do the puzzle?

Does it matter which compartment you put the first ladybird in?

What do you need to keep checking? Remember that each row and each column can only have 2 ladybirds in them.

How many empty compartments will there be?

Record your work on this grid

Look at your friend’s solution. What is the same? What is different?

 

Posted in WODB

Digit Dog is making his own “Which one doesn’t belong?”

dice

What do you notice?

Do you agree with Calculating Cat? What does she mean by “a double”?

Can you think of reasons why each of the pairs of dice could not belong?

Choose each pair of dice in turn and think of reasons why it doesn’t belong. Can you think of more than one reason?

Put this picture on your challenge board and come back to it during the day. How many answers can you think of by the end of the day?

Can you make up a “which one doesn’t belong?” of your own?

Posted in Books, Shape, WODB

which one doesn’t belong? A Shapes Book by Christopher Danielson

Really enjoying this book:

IMG_0669

A great way to focus on the properties of shape and to start conversations and thinking. Each page has four shapes and the challenge is to find which one doesn’t belong. Any answer is acceptable as long as it is true. The important thing is to have a reason for your answer.

Can you find a reason why each of the shapes on the cover don’t belong?

How is the shape you have chosen different from the others?

What do you notice?

By doing this activity you are encouraging learners to notice similarities and differences, to use correct mathematical language, to reason and to explain their thinking.

The question on each page of the book “Which one doesn’t belong?” is the same but some pages are more challenging than others. They really make you think.

Find more ideas from this author at www.talkingmathwithyourkids.com