Logical reasoning – Digit Dog Challenges

Chinese New Year, Logical reasoning, Numicon, Problem solving

Chinese Year of the Tiger

Posted on January 16, 2022 by Digit Dog

February 1st 2022 is the beginning of the Year of the Tiger

It’s the Chinese year of the tiger and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the tiger.

You will need the tiger picture (download here – make sure you print at 100% so that it is the right size for the shapes) and a set of Numicon® shapes. If you don’t have the plastic shapes you can download a set of printable Numicon® shapes here.

Use the Numicon® shapes to cover the tiger in any way you can. You could copy Digit Dog and Calculating cat.

What do you notice about the ways they have covered the tiger? Which shapes did they use? How many shapes? What is the same and what is different?

How many different ways can you cover the tiger? Describe what you’ve done.

Compare your tiger with your friend’s. What’s the same and what’s different? How did you check that your way was different from your friend’s?

Questions to ask:

How did you cover the tiger? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?

Can you cover the tiger again, using different shapes?

How many different ways can you do it?

What is the fewest number of shapes you can use? The most?

Can you just use odd shapes? Even shapes?

What if you weren’t allowed to use the same shape more than once? How many ways can you do it? Is this more difficult? What are you thinking?

Play What’s missing? with Digit Dog.

Digit Dog and Calculating Cat have removed one shape from their tiger. Which shape do you think it is? Why do you think that?

Could you fill that space with more than one shape? Which ones?

Play the game with a friend. Cover your tigers with shapes. Player 1 close your eyes, player 2 take away one shape. Player 1 say which shape is missing and explain how you know.

Feely bag challenge

Put some shapes in a feely bag, take them out one at a time and place on the tiger. Can you find the shapes you want by touch alone? This helps with visualising the shapes.

Challenge learners to:

describe and explain what they are doing, to reason why they have chosen certain shapes.
have a strategy for choosing shapes rather than do it randomly.
swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.
put all their completed tigers together and ask “what is the same?” “what is different?”

Try the same activities with the other animals (download here).

Christmas, Logical reasoning, Numicon, Problem solving, Strategic competence

Cover Rudolph’s head

Posted on December 8, 2021 by Digit Dog

This is the latest addition to the popular Cover with Numicon® series.

You can explore the other activities here: Santa’s Sleigh, Christmas Tree, Baubles and Presents.

For this activity you will need a Rudolph (download and print) and Numicon® shapes.

How many shapes do you think Calculating Cat needs to finish covering Rudolph’s head? Is there more than one way she can do it?

Get some Numicon® shapes and see if you can cover Rudolph’s head.

Can you explain how you did it? Which shapes did you choose first and why? What did you notice? Are some shapes more useful than others?

How many different ways can you find to cover Rudolph’s head? Compare your Rudolph with your friend’s. What’s the same and what’s different about the two Rudolphs?

How many shapes have you used? Who has used most shapes? Who has used fewest?

What is the total of all the shapes you have used?

Can you cover Rudolph using only odd shapes? Why or why not? What about even shapes?

Can you use one shape repeatedly to cover Rudolph? Which shapes will work? Which won’t? Why?

Look for learners who:

Show strategic competence by understanding and tackling the task; by trying different ways of doing it and seeing which ways work.

Use logical reasoning to try different shapes and explain their thinking; are becoming systematic in their choices of shapes; can reason about which shapes will/will not fit; substitute shapes so that they have more or fewer, rather than starting from scratch each time; talk about similarities and differences.

Communicate mathematically about what they are doing; can describe the shapes and say which are bigger/smaller, too big/too small.

Can confidently and fluently choose shapes to fit the spaces on the board; can recognise the spatial patterns and find the shapes that fit.

Calculating, Fluency, Logical reasoning, Making totals, Strategic competence

Making ten with the Bottle Top Bugs

Posted on September 16, 2021September 8, 2021 by Digit Dog

You need a set of Bottle Top Bugs 0 – 10 with spots or numerals

Take turns to choose two bugs so that the numbers on their backs add up to 10.

bottletop bugs add to 10

What do you think?

How many pairs of numbers can you find to make 10?

How do you know you have found all the pairs?

Write a number sentence to go with each of your pairs.

Make up word problems using your pairs of numbers.

What if.…………

…….you looked for 3 numbers which, added together, make 10?

……you weren’t making 10?

…….you looked for numbers with a difference of 1? What do you notice?

…….you made up some of your own questions?

If you don’t have Bottle Top Bugs you can do the same activity with:

digit cards (download here)

Numicon shapes

numbers on pieces of paper

number pebbles like these.

number pebbles 2

Additive relationships, Calculating, Conceptual understanding, Fluency, Logical reasoning, Mathematical language, Number sense, Problem solving

Exploring inverse relationships with the Bottle Top Bugs

Posted on September 14, 2021September 8, 2021 by Digit Dog

Play Under the Leaf

How many spots are under the leaf?

Digit Dog is using the bottle top bugs and leaves to create some number problems.

This type of problem encourages learners to think and talk mathematically and use the link between addition and subtraction.

Ask children to:

Explain what the problem is about in their own words.
Explain what information they know and what they are trying to find out. How many spots are there altogether? How many spots are on the bug you can see? What number of spots cannot be under the leaf?
Find a way to work out how many spots are on the bug under the leaf.
Describe the strategy they have used. They might:
- use concrete representations to work out how many more they need to make 10, for example,Put counters on a ten frame to represent the total amount and the number of spots you can see. Use Numicon shapes to represent the total and spots. Either use the pegs or shapes. Make sure that learners can explain what the resources represent. The pink shape represents the number of spots Calculating Cat can see. Using concrete resources helps learners to explain their thinking.
- draw pictures of the bugs and spots.
- find the numbers on a number line and count on or find the difference.
- use number bonds – the numbers that add together to make 10.
  - I know that 7 + 3 = 10 so there must be a 3-spot bug under the leaf.
  - I know that 10 – 7 = 3 so there must be a 3-spot bug under the leaf.
Convince everyone that their answer is correct. Use sentence starters such as:
- I know the answer is 3 because ….
- First of all I…………then I………
- I know that …….. so…………
Write a number sentence
Change the bugs – choose two different bugs, work out the total number of spots and then hide one under a leaf.

What if you tried a more difficult problem?

Use 3 bugs. Work out the total and then hide one bug under a leaf. What strategies will you use now?
Use two bugs but try multiplying the numbers. Hide one bug under a leaf but this time say “the product of my numbers is…..”

Additive relationships, Calculating, Games, Logical reasoning

Reasoning with the Bottle Top Bugs

Posted on September 12, 2021September 7, 2021 by Digit Dog

Collect the bugs

You need:

A set of bottle top bugs (0 – 12)

A set of leaves to put the bugs on (optional)

2 dice

Set out the leaves with one bug on each leaf. Take turns to roll both dice and use either addition or subtraction to capture a bug. For example, if you throw a 5 and a 3 you can either add the numbers together, 5 + 3 = 8, and capture the 8 bug, or you can subtract the numbers, 5 – 3 = 2, and capture the 2 bug.

collect the bugs

Explain your reasoning like Digit Dog.

When all the bugs have been captured, the player who has most bugs is the winner.

Which bugs are easiest to capture? Why do you think that?

Which bugs are more difficult to capture?

Chinese New Year, Logical reasoning, Numicon

Chinese Year of the Ox

Posted on February 10, 2021 by Digit Dog

2021 is the Year of the Ox

It’s the Chinese year of the ox and Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the ox.

screenshot-2021-02-10-at-09.02.21

You will need the ox picture (download here – make sure you print at 100% so that it is the right size for the shapes) and a set of Numicon® shapes. If you don’t have the plastic shapes you can download a set of printable Numicon® shapes here.

Use the Numicon® shapes to cover the ox in any way you can.

How many different ways can you do it? Describe what you’ve done.

Compare your ox with your friend’s. What’s the same and what’s different? How did you check that your way was different from your friend’s?

Ask:

How did you cover the ox? How many shapes did you use? Talk about how you chose the shapes. Which shapes were most useful?

Can you cover the ox again, using different shapes?

How many different ways can you do it?

What is the fewest number of shapes you can use? The most?

Can you just use odd shapes? Even shapes?

What if you weren’t allowed to use the same shape more than once? How many ways can you do it? Is this more difficult? What are you thinking?

What’s missing?

When the ox is covered, player 1 closes their eyes, player 2 takes away one shape. Player 1 says which shape is missing and explains how they know.

Feely bag challenge

Put some shapes in a feely bag, take them out one at a time and place on the ox. Can you find the shapes you want by touch alone? This helps with visualising the shapes.

Challenge learners to:

describe and explain what they are doing.
have a strategy for choosing shapes rather than do it randomly.
swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.
put all their completed rats together and ask “what is the same?” “what is different?”

Try the same activities with the other animals (download here).

Logical reasoning, Patterns, Shape

Patterns with tiles

Posted on January 21, 2021January 21, 2021 by Digit Dog

Use 4 of the pattern tiles (download here) to make as many different designs as you can.

Digit Dog and Calculating Cat have arranged the tiles into a square.

What do you notice about the patterns they have made? Can you think of a way of describing the patterns?

What is the same? What is different?

How many different patterns do you think you could make by arranging the tiles in a square?

Try it. Take some pictures of your designs.

How will you know you have found all the ways?

Is there a way of being systematic? Explain your thinking.

What if……..

…….. you only made symmetrical designs?

…….. you arranged the tiles in a straight line?

…….. you used more than 4 tiles?

…….. you designed your own tile?

Calculating, Christmas, Logical reasoning

5 Christmaths baubles

Posted on December 9, 2020December 9, 2020 by Digit Dog

An activity to explore numbers that total 5.

Screenshot 2020-12-09 at 08.51.42

Digit Dog and Calculating Cat have some red and blue baubles to put on their tree. They can only put 5 baubles on the tree and have to decide how many of each colour they use. How many different ways can they do it?

Download tree and baubles

Ask:

Look at the picture. What do you notice? Describe what you see.

What has Digit Dog done? What is Calculating Cat thinking?

How many different ways do you think they can put the baubles on the tree? Why do you think that?

Try it yourself. How are you going to record your different ways? How will you remember what you have done?

How do you know you have found all the different ways? Convince me.

Have you found any patterns?

Look for children who are starting to organise their work and systematically look for all the combinations. The activity is about exploring the combinations and reasoning about choices and patterns.

Ways to record

Provide enough baubles and trees so that each combination can be kept and checked. Children can then look at all the trees and say what is the same and what is different. Ask them to put the trees in order and look for a pattern.

Have number sentences on card and ask children to match the number sentence to the trees.

Screenshot 2020-12-08 at 17.39.58

What does the 5 represent? It is the 5 blue baubles. The 0? There are no red baubles.

Write number sentences for each tree on separate post-it notes. These can then be sorted and put in order.

Use Numicon shapes to represent the number pairs.

What if…………

There was a different number of baubles on the tree? Explore other numbers.

There were more than two colours of bauble?

Communication using symbols, Conceptual understanding, Fluency, Logical reasoning, Mathematical language, Strategic competence

Have you seen Digit Dog’s challenge card packs?

Posted on November 24, 2020November 24, 2020 by Digit Dog

The challenge cards are extended versions of Digit Dog’s popular posts and are now available in packs of 5 with links to Curriculum for Wales 2022.

Each pack has 5 challenge cards, linked to a theme, concept or resource. There is also an overview of how Digit Dog Challenges address the five proficiencies, and links to the relevant Descriptions of Learning in the Mathematics and Numeracy Area of Learning and Experience.

There are currently two packs available.

The first pack has activities using my favourite resource – the Two-sided Beans

Packs can be purchased from Collective Learning

The second pack has activities that focus on solving non-routine problems that involve additive relationships. They are aimed at Progression Step 2 level descriptions:

Statement of What Matters 1

I have explored additive relationships, using a range of representations. I can add and subtract whole numbers, using a variety of written and mental methods.

Statement of What Matters 2

I can find missing numbers when number bonds are not complete.

Packs are available to purchase at Collective Learning

Logical reasoning, Mathematical language, What do you notice?

Bottle Top Bugs – What do you notice?

Posted on September 26, 2020September 24, 2020 by Digit Dog

Digit Dog and Calculating Cat have arranged their bugs in 4 rows of 4.

What do you notice?

How many ways can you finish the sentence?

I notice that……….

Screenshot 2018-06-06 12.20.39

Is Calculating Cat correct? Or has she made a mistake? Convince me. Explain your thinking.

What can you say about:

the rows?
the columns?
the number of bugs?
patterns in the numbers on the bugs’ backs?
diagonal patterns?
odd ones out?
totals of spots?
their eyes?
anything else?

Digit Dog is also asking What do you wonder?

Look at the bugs and finish the sentence – I wonder…………..

How many ways can you finish the sentence? You might say things like:

I wonder what the total of each row is……

I wonder which row has the lowest total……..

I wonder if I can arrnage the bugs in order………

Collect the I wonder statements to use as challenges and activities.

Logical reasoning, Patterns

Patterns in names

Posted on June 23, 2020 by Digit Dog

What patterns can you see on the grids? Describe the patterns on each grid. What do you notice?

Screenshot 2020-06-23 09.31.57

Screenshot 2020-06-23 09.51.40 Screenshot 2020-06-23 09.50.21

If we added another row, can you predict which square you would colour in? Why do you say that? Explain your thinking.

Try your own name and look for patterns.

Print the 6 x 6 grid here. Write your name in the grid, one letter in each square, repeating it until all the squares are filled. Now colour in the squares which have the first letter of your name in them. What patterns have you made? Can you think of a way to describe the patterns?

Ask people you know to try it. What is the same and what is different about the patterns different names make?

What if you tried a larger grid?

Screenshot 2020-06-23 09.53.25