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

Have you seen Digit Dog’s challenge card packs?

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

Posted in Additive relationships, Calculating, Communication using symbols, Conceptual understanding, Easter, Fluency, Logical reasoning, Strategic competence

Calculating Chicks

How many chicks are hiding?

Screenshot 2018-03-22 23.20.51

Digit Dog is using a hollow plastic egg and some fluffy chicks to create some number problems. This type of word problem requires more thinking than the problems such as “There are 4 chicks in my egg and 4 chicks on the floor.  How many chicks are there altogether?”, where the end result is unknown.

The aim is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships and the link between addition and subtraction.

Ask learners 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 chicks are not in the egg? What number of chicks cannot be in the egg?
  • FInd a way to work out how many chicks are in the egg.
  • Describe the strategy they have used. They might:
    • act it out – using children themselves (with chick masks)
    • act it out – using toy chicks
    • use counters to represent the chicks
    • draw pictures of the chicks
    • use an eight Numicon shape to lace the chicks on
    • use number bonds
  • Convince everyone that their answer is correct. Use sentence starters such as:
    • I know the answer is 4 because ….
    • First of all I…………then I………
    • I know that …….. so…………
  • Write a number sentence
  • Change the number of chicks in the egg.
  • Think about a What if………?

What if there were more than 8 chicks altogether?

What if the story wasn’t about chicks?

Can learners transfer their thinking to a new problem?

Make up some of your own problems like this one for your friend.

The five proficiences

Learners will use:

  • strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.
  • logical reasoning to explain their thinking, to make sense of the problem and to use what they know to work it out.
  • conceptual understanding of, and fluency with, number bonds for 8 in order to use them to solve the problem and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to write number sentences and explain their thinking .

Learners will need to be competent in all five proficiencies in order to create their own problems.

Posted in Additive relationships, Calculating, Communication using symbols, Conceptual understanding, Fluency, Logical reasoning, Number sense, Strategic competence

How many bones?

Screenshot 2020-03-16 11.08.55

The aim of the activity is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships. This structure of problem is more difficult than the usual “I had 2 bones and then ate 2 more, how many did I eat altogether?”

Ask:

What has Digit Dog been doing? Can you tell me in your own words? What is Calculating Cat wondering?

How many bones could Digit Dog have had in the beginning? How many could he not have had? Explain your thinking.

Take suggestions for numbers of bones.

Is there just one answer?

Use one number as an example.

If Digit Dog started with 3 bones, how many bones did he eat?

Explain how you can find out. You might want to use bones, drawings, Numicon shapes, cubes to help.

Can you write a number sentence?    3 – ? = 2

Try some other numbers of bones.  Record your answers. Can you put your answers in order? What do you notice?

Use this speaking frame to explain your work:

Digit Dog started with ______ bones, he ate _____ bones, now he has 2 bones left.

What if……….

He had a different number of bones left?

Make up your own problem like this about Calculating Cat and some fish.

The five proficiences

Learners will use:

  • strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.
  • logical reasoning to explain their thinking and work systematically to find possible numbers.
  • conceptual understanding of, and fluency with, number bonds to recognise that they need numbers with a difference of 2 or to see this pattern as they try out numbers, to see that 1 or 2 are not possible numbers to start with and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to show and explain their thinking .

Learners will need to be competent in all five proficiencies to make up their own problems.

Posted in Additive relationships, Calculating, Communication using symbols, Conceptual understanding, Easter, Fluency, Logical reasoning, Strategic competence

Calculating Chicks

How many chicks are hiding?

Screenshot 2018-03-22 23.20.51

Digit Dog is using a hollow plastic egg and some fluffy chicks to create some number problems. This type of word problem requires more thinking than the problems such as “There are 4 chicks in my egg and 4 chicks on the floor.  How many chicks are there altogether?”, where the end result is unknown.

The aim is to encourage learners to think and talk mathematically – to have a mathematical conversation and use their knowledge of additive relationships and the link between addition and subtraction.

Ask learners 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 chicks are not in the egg? What number of chicks cannot be in the egg?
  • FInd a way to work out how many chicks are in the egg.
  • Describe the strategy they have used. They might:
    • act it out – using children themselves (with chick masks)
    • act it out – using toy chicks
    • use counters to represent the chicks
    • draw pictures of the chicks
    • use an eight Numicon shape to lace the chicks on
    • use number bonds
  • Convince everyone that their answer is correct. Use sentence starters such as:
    • I know the answer is 4 because ….
    • First of all I…………then I………
    • I know that …….. so…………
  • Write a number sentence
  • Change the number of chicks in the egg.
  • Think about a What if………?

What if there were more than 8 chicks altogether?

What if the story wasn’t about chicks?

Can learners transfer their thinking to a new problem?

Make up some of your own problems like this one for your friend.

The five proficiences

Learners will use:

  • strategic competence to make sense of the problem, work out what is known and what needs to be found out and to decide on a way of solving it.
  • logical reasoning to explain their thinking, to make sense of the problem and to use what they know to work it out.
  • conceptual understanding of, and fluency with, number bonds for 8 in order to use them to solve the problem and to be efficient and accurate with the basic calculations.
  • communication using symbols and correct mathematical vocabulary to write number sentences and explain their thinking .

Learners will need to be competent in all five proficiencies in order to create their own problems.