Mathematical language – Digit Dog Challenges

Christmas, Counting, Mathematical language

How many?

Posted on December 9, 2021December 8, 2021 by Digit Dog

Design by Cordelia Hutchinson Ling Design produced for National Trust www.nationaltrust.org.uk

Look at the card and see what you can count.

How many cats are smiling? How many are not?

How many cats are not wearing hats?

How many cats have stripes?

How many more cats have hats than have scarves?

How many fewer scarves are there than hats?

How many legs? How did you count them? Did you count in 2s or 4s?

How many eyes? Ears? Whiskers?

How many holly leaves?

How many more hats do they need so that all the cats are wearing one?

Make up some word problems

Ten cats are coming to the party, how many haven’t arrived yet?

At the beginning of the day there were 8 cats, how many have gone home?

Some cats were playing in the snow, 4 cats ran away and now only 6 are left. How many were there to start with?

Write some number sentences to go with the picture.

6 = 4 + 2 There are six cats altogether. Four cats standing plus 2 that are not.

6 = 1 + 5 There are 6 cats altogether. 1 cat holding holly and 5 not or 1 cat sleeping and 5 awake.

What if……..?

What if Calculating Cat joined in? How many cats would there be then?

What if 3 cats ran away? How many would be left?

What if two more cats fell asleep? How many would then be sleeping?

What if two more cats put on a scarf?

Christmas, Mathematical language

Christmas card questions

Posted on November 25, 2021November 25, 2021 by Digit Dog

Choose a Christmas card and see how many mathematical questions you can ask about it.

Card by Louise Cole for DementiaUK (2020) http://www.dementiauk.org

How many sheep are wearing headphones? How many are not wearing them?

How many sheep are upside down? How many are the right way up?

Use concrete resources and number sentences to explain your answers.

One sheep is holding a present, 9 sheep are not. There are 10 sheep altogether. 1 + 9 = 10, 10 – 1 = 9.

Use the words more than, fewer than, less than in your questions.

How many fewer sheep are upside down than are the right way up?

How many more presents do they need so that all the sheep have one?

What’s the difference between the number of sheep with scarves and the number without?

How many legs are there? How do you know? How did you count them?

How many eyes?

Ask some what if questions:

What if one more sheep came along? How many would there be?

What if 3 sheep ran away?

What if 2 more sheep put a hat on?

How many more sheep would you need to make a larger triangle? Explain your thinking. What do you notice?

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…..”

Conceptual understanding, Counting, Mathematical language, Number sense, Subitising

Counting and comparing with Bottle Top Bugs

Posted on September 9, 2021September 7, 2021 by Digit Dog

Count, order and compare with Bottle Top Bugs.

Digit Dog and Calculating Cat are playing **Who has more?**

To play the game you need:

A set of Bottle Top Bugs

A feely bag, box or cloth

Put your bottle top bugs in a feely bag or a box or under a cloth. Each player takes one bug out, puts it in front of them and says how many spots there are. The player with more spots captures both bugs.

Keep playing until all the bugs have been used. The winner is the player who has captured most bugs.

Ensure learners are using correct mathematical language.

Ask:

Who has more spots? Who has fewer spots?

Who has more? Who has less?

Say:

I have more spots. I have fewer spots.

I have more. I have less.

Make sure that learners practise using fewer/less as well as more.

Practise subitising (saying how many spots there are without counting in ones). Seeing patterns and arrangements of objects is an important skill that helps with rearranging, combining, breaking up and putting together amounts in number.

When you turn over a bug, say how many spots there are without counting in ones. How do you know how many spots there are? Calculating Cat knows she has 7 spots because she saw 5 plus 2 more.

Match the numeral

Say how many spots you have and find that number on a number line.

Say how many spots you have and find a digit card to match that amount.

Extend the game

Ask Who has more spots? How many more?

Who has fewer spots? How many fewer?

I have …..spots. I have ……. more spots than my friend.

I have …….. spots. I have …….. fewer spots than my friend.

Vary the game

Change the rules so that the player with fewer spots wins.

Players take two bugs and add the number of spots together. They then compare their totals. The player with the greater total captures all four bugs.

Players take two bugs and find the difference. They then compare their differences. The player with the greater difference captures the four bugs.

Counting, Mathematical language, Subitising

Exploring number with Bottle Top Bugs

Posted on September 7, 2021 by Digit Dog

How to make a set of Bottle Top Bugs.

Use the tops from plastic milk bottles.

Draw eyes and spots. Think about the patterns of spots – this arrangement focuses on the pattern of 5. The numbers above 6 are arranged as “5 and some more”.

The spots on these bugs are arranged to match the Numicon shape patterns.

These bugs have “goggly eyes” and the spots are divided into two so that number bonds can be explored.

Explore your bugs.

Ask:

What do you notice?

Find bugs with the same number of spots.

Count the spots and put the bugs in order.

Start to recognise patterns. Say how many spots there are without counting in ones.

Find the bug with 5 spots. Now find the one with one more than 5, one less than 5, two more/less than 5.

Find two bugs that have 8 spots altogether. Can you find another two with 8 spots? How many different pairs can you find? How do you know you have found them all?

Christmas, Counting, Mathematical language

Christmas wrapping counting

Posted on December 10, 2020December 9, 2020 by Digit Dog

How many?

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?

How many stars can you see? How many holly leaves? How did you count them?

Describe what you can see.

I can see more…….than…………

I can see fewer …………than ……………..

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.

Counting, Mathematical language, Subitising

Bottle Top Bugs

Posted on September 24, 2020 by Digit Dog

Wondering what to do with the tops of plastic milk bottles?

Make a set of Bottle Top Bugs.

Look at your bugs.

Count the spots and put the bugs in order.

Try to say how many spots there are without counting in ones. Start to recognise patterns.

Find the Bug

Find the bug with 5 spots. Now find the one with one more than 5, one less than 5, two more/less than 5.

Find two bugs that have 8 spots altogether. Can you find another two with 8 spots? How many different pairs can you find? How do you know you have found them all?

COMING NEXT

More activities with Bottle Top Bugs.

Counting, Fluency, Mathematical language

Counting leaves

Posted on May 15, 2020 by Digit Dog

Digit Dog is out in the garden again. This time he is counting leaves.

counting in threes

See if you can find some leaves that are arranged in threes.

Put the leaves in front of you, counting in threes as you go. Now take them away and count back in threes. Write the numbers you are saying. Find the numbers on digit cards or on a number line.

Digit Dog has 4 groups of 3 leaves. He has 12 leaves altogether.

What if he had 6 groups of 3 leaves? How many leaves would he have then?

What if he had 15 leaves altogether? How many groups of 3 would he have?

Make up some questions like this to ask someone about your set of leaves.

What about finding leaves that are arranged in different numbers?

leaves in nines