Posted in Christmas

The last Christmas challenge of 2018

Stars on crackers

crackers 2.png

What do you think? How can you solve Calculating Cat’s problem?

Using the Numicon® shapes might help. Use the shapes to represent the stars.

Screenshot 2018-12-14 11.49.35.png

Or use the Cuisennaire rods to find ways to make the 19 stars.

Screenshot 2018-12-14 11.50.29.png

What if……

………..Calculating Cat wanted a differen tnumber of stars on the tree? What about 21? 22? or a larger number?

………there was a different number od stars on each cracker?

Posted in Christmas, combinations

Christmas challenge – day 16

Christmas treats – how many ways?

Eating treats.png

How many different ways could Digit Dog eat his treats?

Which one will he eat first, second, third?

How many ways do you think there could be?

How will you know when you have found all the different ways he could do it?

How are you going to record the different ways?

What about………

…….using the pictures of the treats?

…….drawing pictures of the treats?

…….writing the names or initials of the treats?

…….using a table to organise your work?

Think about how you can organise your work. How can you be systematic so that you can convince everyone that you have found all the different ways?

What if…..

……….he had a lollipop as well?

Would there then be more ways or fewer ways?

A lot more? Just a few more? Why do you think that?

Did you try the Christmas Tree Decoration Challenge on Day 11? What is the same and what is different about the two challenges? What skills and strategies did you use in both of them?

Posted in Christmas, Making totals

Christmas challenge – day 15

How many in the box?

Screenshot 2018-12-12 18.09.58.png

Digit Dog is playing a game with Calculating Cat. He has 6 tree decorations and has hidden some of them in his box. Calculating Cat has to work out how many he has hidden.

Calculating Cat is thinking about the Numicon® shape to help her work out how many are in the box.

  • She knows the whole is 6 – that’s the number of decorations Digit Dog had to start with.
  • She knows one of the parts is 3 – that’s the number of decorations not in the box.
  • Now she can work out the unknown part – that’s the number of decorations in the box – by thinking about the spaces in the Numicon® shape.

Screenshot 2018-12-12 18.18.47.png

She could have solved the problem by using number bonds. If she knows 3 + 3 = 6, she can work out the missing number.

What if………

……….Digit Dog put a different number of decorations in the box?

………..he had more decorations to start with? Fewer decorations?

Try out the game for yourself. One person hides objects in a box, their partner works out how many are hidden. Remember to explain how you work it out.

Posted in Christmas, Patterns

Christmas challenge – day 14

Snowflake patterns

Digit Dog and Calculating Cat have been using pattern blocks to make snowflake patterns.

IMG_2166.jpg

What do you notice?

How many?

Can you copy their patterns?

Are the patterns symmetrical?

Can you design your own snowflake patterns?

 

What if …………

……….we give a value to one of the shapes?

……….the green triangle is 1 what is the value of the other shapes?

……..you had to make a snowflake that is worth 20?

IMG_2169.jpg

………the blue rhombus is worth 1?

………the red trapezium is worth 1?

 

 

Posted in Christmas, Problem solving

Christmas challenge – day 13

What’s the value?

Work out the value of the tree, the snowman and Santa. What is each picture worth?

IMG_2157.jpg

What do you notice? Where would be a good place to start? Which row would help us to solve the problem?

Encourage children to use their reasoning skills and make deductions rather than use trial and improvement. Talk aloud and model your thinking.

Screenshot 2018-12-12 16.29.35.png

Is Digit Dog right? Does using Numicon® help solve the problem? What do you think about Calculating Cat’s idea?

What are you going to do next? What do we know?

Screenshot 2018-12-12 16.35.06.png

Does using pegs make it easier? What do you think about Calculating Cat’s idea? Can you work out the value of Santa? How?

Could you look at a different column instead of the middle one?

What if.……..you changed the totals?

This challenge was inspired by Bernie Westacott in his conversation with Craig Barton. Watch the podcast – it’s well worth it.

Screenshot 2018-12-11 22.37.26.png

http://www.mrbartonmaths.com/blog/bernie-westacott-teaching-maths-with-visuals-and-manipulatives/

Posted in Christmas, WODB

Christmas challenge – day 12

Which one doesn’t belong?

Digit Dog and Calculating Cat were decorating their Christmas tree when they thought they’d make up a Which one doesn’t belong? question.

IMG_2150

Screenshot 2018-12-11 21.29.07

Screenshot 2018-12-11 21.29.14

What do you think?

It doesn’t matter which you choose as long as you can give a reason for your choice.

Look at each Santa in turn and think of a reason why it doesn’t belong.

How many different reasons can you think of?

Make up your own Which one doesn’t belong?

Now ask “What is the same about all the Santas?” “What is different?

Check out this post.

 

Posted in Christmas, combinations

Christmas challenge – Day 11

Digit Dog and Calculating Cat are decorating their Christmas tree.

Screenshot 2018-12-10 08.23.05

They have three decorations to put on the tree. How many different ways can they do it?

What do you notice? What has Digit Dog done? Where has he put his decorations?

What is Calculating Cat thinking? What would her tree look like? How would hers be different from Digit Dog’s? How would it be the same?

Calculating Cat is wondering how many different ways they could put the decorations on the tree.

What do you think? Is it more than 2? Would it be as many as 10? Explain your thinking.

How shall we find out?

How are you going to record you work?

How will you know when you have found all the ways?

Look for children who:

  • can describe what they are doing.
  • can convince you that they have found all the different ways.
  • can explain using objects or drawings.
  • are starting to work systematically.

What if………

………there were more than 3 decorations?

Screenshot 2018-12-10 08.53.37

…….there were 4 decorations? Will there now be more ways to put them on the tree? How many more ways? Just a few? A lot more?

Posted in Christmas, Patterns

Christmas challenge – Day 10

Digit Dog was looking at the Christmas wrapping paper and noticed some patterns.

IMG_2140

IMG_2132

What do you notice? What is the pattern?

What will the next picture be? And the next? And the one after that? How do you know?

What will the 20th picture be? What about the 35th? How can you work it out? Challenge older children to use their knowledge of multiples to work out the answer.

What about this pattern?

IMG_2133

What is the same and what is different?

Both patterns have 4 pictures that repeat over and over and over……………

Screenshot 2018-12-06 16.46.25

They are ABCD patterns.

IMG_2136.jpg

Digit Dog has used multilink cubes to make an ABCD pattern. He has used a different colour cube for each picture. What colour will be next?

Calculating Cat has done the same.

IMG_2137.jpg

What do you notice?

 

Next Digit Dog and Calculating Cat cut their strips into smaller pieces and rearranged them to make new patterns. What is the same and what is different? Which picture would come next? Which colour multilink cube?

IMG_2139.jpg

ABCCD

IMG_2138.jpg

ABABCD

Posted in Christmas, Counting

Christmas challenge – Day 9

How many?

IMG_2131

Use a piece of Christmas wrapping paper and just ask the question “How many?”

At first, don’t specify what needs to be counted, let the question be open and the children come up with ideas and be creative.

I can count…….3 Santas, 3 elves, 3 snowmen.

You don’t need to stick to counting in ones……….I can count 32 eyes, that’s 16 groups of 2, 16 x 2 – true or false?

I can count 4 groups of 3 trees and 6 groups of 2 trees.

I can count 12 boots – I wonder how many people that is………..

What about this one? What will you count now?

IMG_2140

 

Posted in Christmas, Numicon, Problem solving

Christmas challenge – Day 8

8 roomscollecting presents

Santa has asked Digit Dog to help him collect presents from his store. Here is a map of the store. (download and print your store here) 

Digit Dog counters

Screenshot 2018-12-03 12.12.49

There are 8 rooms and the number tells you how many presents are in each room. Digit Dog has to go into the rooms and collect the presents BUT he can only go into each room ONCE.

How many presents can Digit Dog collect?

How many different ways can he go though the store?

Can you record his routes? How might you do this?

Screenshot 2018-12-04 16.45.31

Can you do it a different way, Digit Dog, and collect more presents?

What’s the most presents you can collect?

What’s the smallest number of presents?

Look for children who are planning the routes and can explain their thinking.

Simplify the task

  1. Put Numicon® shapes in each room so that Digit Dog can collect a shape when he has gone through the room. These can then be added together to find the total number of presents.

Screenshot 2018-12-04 16.58.53

I went to rooms 1, 2, 3, 7 and 8. How many presents did I collect altogether?

Screenshot 2018-12-04 17.01.28

I have put the shapes on the number line so that I can see the total without counting in ones.

Calculating Cat
Calculating Cat says that you can make 10s with the shapes and that makes it easy to find the total. 10, 20, 21

 

Screenshot 2018-12-04 16.59.30

2. Use the blank store and put just numbers 1, 2 and 3 in the rooms.

3. Put just Numicon® shapes in the rooms – no numerals.

Extend the challenge

Use the blank store and put higher numbers in each room.

Challenge children to find all possible routes and to explain how they know they have found them.

Posted in Christmas, combinations, Making totals, Money

Christmas challenge – Day 7

7p to spend – combinations of coins

Screenshot 2018-12-05 12.02.42

Digit Dog has bought a chocolate coin for 7p. He paid for it exactly, so which coins did he use?

How many different ways do you think he could do it? Convince me that you have found all the ways.

What is the least number of coins he could use? What is the most?

Which coins do you think he used? Which coins did he definitely not use? Why?

You might want to use your Numicon® purse to help you. Which coins are you going to use?

 

Screenshot 2018-12-03 17.50.40

Screenshot 2018-12-03 17.51.18
The chocolate coin cost 7p

 

What if…………..

……..Digit Dog bought something for 8p, 9p, 10p………..any amount you like?

…….he didn’t have the exact money but only had a 10p coin. How much change would he have? Which coins might he be given?

………you used larger amounts?

presentVary the amounts and the coins you can use.

Screenshot 2018-12-03 18.01.40

Posted in Calculating, Christmas, Numicon, Problem solving

Christmas challenge – Day 6

6 Christmas stars – a puzzle

Christmas tree

Download the tree

Look at the picture. What do you notice?

What are Digit Dog and Calculating Cat trying to do?

What are you going to do first?

Check that each side totals 9.

What do you think? Can you do it another way?

To simplify the task

Use Numicon® shapes instead of numerals.

IMG_2130

 

Variation

Use numbers / Numicon® shapes 1 to 6 and make each side total 9. Then try totals of 10, 11 and 12. See Number Round Up on https://nrich.maths.org/188