Category: Logical reasoning

Posted in Logical reasoning, What's the same / different?

Buttons

Posted on by Digit Dog

Helping children to notice similarities and differences helps them to spot patterns and to use their reasoning skills. Spotting patterns and logical reasoning are key when learning mathematics.

Ask children “What is the same?” “What is different?”

Then ask them to explain what they notice, this improves their language and thinking.

two sets of buttons 3

two sets of buttons 2

Look at the two sets of buttons. Find things that are the same about the two sets, for example, both sets have different coloured buttons in them. How many similarities can you find?

Now look for differences. Find things that are different about the two sets, for example, there are a different number of buttons in each set. How many differences can you find?

Make your own sets of objects and look for similarities and differences.

Posted in Calculating, Logical reasoning, Money

How much money?

Posted on by Digit Dog

Calculating Cat has set Digit Dog a challenge. She has put five coins in her purse and is asking Digit Dog to work out how much money she might have.

5 coins

Use coins to investigate which coins could be in the purse.

Write down the different ways you have found.

Digit Dog thinks there could be 6p in the purse. Which 5 coins would you need to make 6p?

Can you work systematically so that you know you have found all the different combinations?

What if……..

………there was a different number of coins in the purse? What amounts could you make then?

 

 

Posted in Games, Logical reasoning

Strategy game

Posted on by Digit Dog

Have a go at Digit Dog’s strategy game.

strategy game

You need:

A game board (download here)

A pile of counters / buttons/ pebbles

To play:

Take turns to place counters on the any of the hexagons.

A counter cannot be put on a hexagon which touches another hexagon already holding a counter.

The last player who is able to put a counter on the board wins.

Play a few times and see if you can find a winning strategy.

Is there a good place on the board to start?

Does it matter who starts? Does the player who goes first always win?

 

Posted in Calculating, Conceptual understanding, Easter, Logical reasoning, Problem solving

Two eggs left

Posted on by Digit Dog

Digit Dog has been eating his Easter mini eggs.

He has 2 eggs left.

Calculating Cat is wondering how many eggs he could have had to start with and how many he could have eaten to be left with 2.

two eggs left

How many eggs could he have had at the start? What if it was 6? How many would he have eaten to be left with 2?

What other numbers could he have started with?

What number do you know he couldn’t have had at the start?

How many different solutions can you find?

How did you work it out? Explain your reasoning.

Can you record your solutions?

Can you put your solutions in order?

What if………..

……………he had a different number of eggs left?

………….he was eating bones not eggs?

………..you made up a problem like this about your Easter eggs?

Posted in Easter, Logical reasoning, What's the same / different?

Compare the Easter eggs

Posted on by Digit Dog

Helping children to notice similarities and differences in everyday life helps them to spot patterns and to use their reasoning skills. Spotting patterns and logical reasoning are key when learning mathematics.

Ask children “What is the same?” “What is different?”

Then ask them to explain what they notice, this improves their language and thinking.

Digit Dog and Calculating Cat are playing “what’s the same and what’s different?” with their Easter eggs.

same different eggs

same different eggs W

Look at the two eggs and find similarities and differences. Any answer is acceptable. Encourage children to keep looking for more. Make a list that can be added to.

What can you say about the two eggs? What do you notice?

Can you think of anything that is the same?

I can see that both eggs have Peter Rabbit on them.

Encourage and model the use of full sentences.

Anything else?

Both eggs are made of chocolate.

Both eggs are in a box.

Can you think of more things that are the same?

What about the differences? What is different about the two eggs?

I can see that one egg has creme eggs in it and the other has mini eggs.

Any other differences?

The boxes are different colours.

Use your own Easter eggs to play this game.

Posted in Calculating, Logical reasoning, Making totals

Making totals

Posted on by Digit Dog

Digit Dog and Calculating Cat are using 4 bottletop bugs (or you can use digit cards) to make different totals.

make totals with bugs.png

They have got the 2, 3, 4 and 8 bugs.  They have made two totals already and are wondering how many more they can make.

What totals can you make? Which bugs are you using?

How are you going to record what you have done? With a drawing? With a number sentence?

Can you make these totals:

9

10

11

13

14

15

How will you know when you have found all the possible totals?

Can you record your work in a systematic way?

What if…………

…………you choose a different 4 bugs / numbers and do the same thing?

 

 

Posted in Games, Logical reasoning

Two or More

Posted on by Digit Dog

The Two or More Game

You need:

A Two or More board (download here)

Cards numbered 1 – 9 (download here) or be like Digit Dog and use stones from the garden with numbers written on them.

Rules:

Put the numbers on the squares so that the difference between each pair of numbers is 2 or more.

two or more

Digit Dog and Calculating Cat are playing Two or More.

Is Calculating Cat right? How do you know?

Which number couldn’t she put next? Can you explain your reasoning?

Is there more than one way of doing it? How do you know?

How could you record what you have done?

How did you decide where to put the numbers? What were you thinking about?

What if……..

…….the difference was 3 or more?

…….you made up a game of your own using the board and numbers?

Posted in Calculating, Games, Logical reasoning, Making totals

Which Square?

Posted on by Digit Dog

How to play Which Square?

A game for 2 players.

You need:

A game board (download here), two dice and 12 counters for each player.

Rules:

  • Each player puts their counters on the board. They can put them on any number and more than one counter on a number if they wish.
  • Players take turns to throw 2 dice and to add the two numbers. If they have a counter on the total they have thrown, they can take it off. If they have more than one counter on the total, they just remove one.
  • The winner is the first to remove all 12 counters.

Digit Dog and Calculating Cat are playing the game. They both think that they will win. What do you think?

Which square

Look at where they have placed their counters. Who do you think will win? Why do you think that?

When you are playing the game do you notice that you get some totals more than others?

Which numbers are the best to put your counters on? Are there any numbers you don’t want to put your counters on? Can you explain why you think that?

Play the game a few times to see if your ideas work.

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

Calculating Chicks

Posted on by Digit Dog

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

Cover the Chick

Posted on by Digit Dog

Easter animals

For those of you who enjoyed the Chinese New Year activity Cover the animals, here’s an Easter version.

Digit Dog and Calculating Cat are using the Numicon® shapes to cover the picture of the Easter Chick .

You will need the Chick picture (download and print on yellow paper) and a set of Numicon® shapes. Ask learners to use the Numicon® shapes to cover the chick in any way they can.

Screenshot 2019-04-03 13.39.12

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

Compare your chick 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?

Play What’s missing?

  1. When the chick is covered with shapes, one child closes their eyes, another takes away one shape. Which one is missing? How do you know?
  2. Put some shapes in a feely bag, take them out one at a time and place on the chick. Can you find the shapes you want by touch alone?  This helps with visualising the shapes.

Ask:

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

Can you cover the chick again but 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?

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

Encourage learners to describe and explain what they are doing.

Look for those learners who have a strategy for choosing shapes and those who use trial and improvement.

Look for learners who swap shapes for other equivalent shapes each time they look for a new arrangement rather than starting from the beginning.

Encourage learners to put all their completed chicks together and ask “what is the same?” “what is different?”

 

Try the same activities with the Easter Bunny  (download here).

 

IMG_1332

Posted in Easter, Estimation, Logical reasoning

Easter Estimation

Posted on by Digit Dog

Digit Dog and Calculating Cat have been inspired by Steve Wyborney www.stevewyborney.com to create this estimation activity. Screenshot 2020-03-16 12.18.57

Screenshot 2020-03-16 12.20.08

Download the powerpoint here

Show the first slide and ask:

How many eggs are in the pot?

Take estimations and then reveal the answer.

Show picture 2 and ask the same question. Compare the pots – are there more eggs or fewer eggs? Take some estimates and then reveal the answer.

Show picture 3 but this time ask learners to write down their estimation and then to tell their partner why they chose that number. This generates mathematical talk and explanations.

I chose _____ because___________

I looked at pot __ and thought__________

I think __________ because_____________

Repeat for picture 4.