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Posted in Additive relationships, Calculating, Fluency

Bone Splat!

Digit Dog and Calculating Cat are playing a game of Bone Splat!

Screenshot 2020-07-01 08.57.08

You need:

A “splat” and some bones (download here).

To play:

First decide on the total number of bones – in this game they are exploring pairs of numbers that total 10. Count out that number of bones and put a digit card in the empty box on the “splat”.

Player One: close your eyes.

Player Two: hide some of the bones under the “splat”.

Player One: open your eyes and work out how many bones have been hidden under the splat.

Explain how you worked it out. Convince your partner that you are right.

Encourage learners to explain how they worked out the number of bones that are hidden. They might:

  • Use a 10 frame and objects (or visualise them like Calculating Cat);
  • Use a Numicon shape and toy bones or pegs;
  • Use a number line to count on;
  • Draw a picture;
  • Just know the number bond.

Record some number sentences to show how many different ways the bones can be hidden. For Digit Dog’s problem we could write: 6 + 4 = 10, 4 + 6 = 10, 10 – 4 = 6, 10 – 6 = 4.

 

Posted in Additive relationships, Calculating, Conceptual understanding, Strategic competence

What’s the question?

Digit Dog’s answer is 6 bones. What could the question be? Calculating Cat has thought of one question. How many questions can you think of?

6 bones

Encouraging learners to ask their own questions:

  • helps deepen their conceptual understanding.
  • encourages creativity and flexibility in thinking.
  • develops their strategic competence because they need to understand the structure of mathematical problems in order to make up their own. Creating your own questions is a challenging task.
  • develops their use of mathematical language and communication skills.
  • encourages use of logical reasoning as they explain their thinking and work systematically with the numbers in the questions they create.

Start with making up some subtraction questions like Calculating Cat’s question:

Digit Dog had 8 bones for his dinner. He ate 2. How many are left?  8 – 2 = 6

What if Digit Dog had a different number of bones to start with? Explore some different numbers. Which numbers can you use? Which can’t you use? What happens to the number of bones he eats if you change the number of bones he starts with?

Digit Dog had 9 bones for his dinner. He ate 3. How many are left?  9 – 3 = 6

Digit Dog had 10 bones for his dinner. He ate 4. How many are left?  10 – 4 = 6

Look for patterns. Work systematically.

What else could happen to the bones? Calculating Cat says he eats some. He could hide some, give some away, lose some……………be creative. Make up some funny problems. Remember his answer is 6 bones.

What if………..

………you made up some problems using addition? For example, Digit Dog had 4 bones, Calculating Cat gave him 2 more. How many does he have now? 4 + 2 = 6

 

 

Posted in Calculating, Fluency, Games

Go Fish 10

You play Go Fish 10 in the same way as Go Fish but the aim of the game is to make pairs that add up to 10.

Print Digit Dog’s cards here. You need 4 sets for 2 -3 players.

To play:

Deal each player 7 cards and spread out the remaining cards face down on the table. The aim of the game is to find pairs of cards that add up to 10.

Each player takes a turn. During a turn the player:

  1. Looks at the cards in their hand, if they have any pairs that add up to 10, they put them in front of them, face up.
  2. They then ask another player if they have a particular card so that they can make another pair. For example, player 1 might have a 4 in their hand and so ask aplayer 2 “do you have a 6?” – the card they need to make a pair that adds to 10. If player 2 has a 6 card, then they must give it to player 1. If they don’t have a 6 card, they say “go fish” and player 1 takes a card from the pool of cards on the table.
  3. If the player gets the card they asked for, either from the pool or from the other player, then they put their pair of cards in front of them, face up.

The game ends when one player runs out of cards or there are no more cards in the pool. The winner is the player with most pairs in front of them.

What if………

………….you played the game by making pairs of cards with a difference of 1?

Posted in Counting, Games

Play Go Fish

How to play Go Fish

For 2 – 3 players you need to print 4 sets of Digit Dog’s cards, onto card. The cards have numerals along with ten-frames.Screenshot 2020-06-29 08.58.52

The game can also be played with digit cards 0 – 10 or 0 – 20, or  a pack of playing cards.

To play:

Deal each player 7 cards and spread out the remaining cards face down on the table. The aim of the game is to find pairs of cards.

Each player takes a turn. During a turn the player:

  1. Looks at the cards in their hand, if they have any pairs, they put them in front of them, face up.
  2. They then ask another player if they have a particular card so that they can make another pair. For example, player 1 might ask player 2 “do you have a 5?” If player 2 has a 5 card, then they must give it to player 1. If they don’t have a 5 card, they say “go fish” and player 1 takes a card from the pool of cards on the table.
  3. If the player gets the card they asked for, either from the pool or from the other player, then they put their pair of cards in front of them, face up.

The game ends when one player runs out of cards or there are no more cards in the pool. The winner is the player with most pairs in front of them.

Posted in Counting, Number sense, Subitising, Ten frames

Ten frame games

1. Make the number

Screenshot 2020-06-24 11.27.44

You need:

For 3 – 5 players

Two sets of Digit Dog ten frames – large or small

Small objects such as pennies, buttons or counters.

To play:

One player is the leader and has the ten frame cards in a pile, face down.

Other players have a blank ten frame and ten small objects each.

The leader turns over the top card for a few seconds and then turns it back again.

Other players make the pattern they saw with objects on their ten frame.

The leader turns over the card again to check the patterns. Players who were correct score one point.

Play until all cards have been turned over, or one player reaches 10 points.

The winner is the player with most points.

Variations

  • Make the number on your ten frame one more than the number on the card.
  • Make the number on your ten frame two more than the number on the card.
  • Make the number on your ten frame one less than the number on the card.
  • Make the number on your ten frame two less than the number on the card.

 

2. Who has more?

 

Screenshot 2020-06-24 11.59.59

You need:

For 2 players

A set of Digit Dog ten frames for each player, in a pile face down.

To play:

On the count of 3, players turn over their top card. The player with more dogs wins the two cards and says “I have …….dogs. I have more dogs than you”. The other player says “I have ……. dogs. I have fewer dogs than you”.

The game ends when all cards have been turned over. The winner is the player with more cards.

Variation

  • The player with the fewer dogs wins the cards.
  • Say how many more and how many fewer dogs there are.Screenshot 2020-06-24 12.10.41
Posted in Counting, Number sense, Subitising, Ten frames

Ten frame flash

This game practises subitising (see June 24th Post)

Screenshot 2020-06-24 09.51.27

To play Ten Frame Flash you need:

A few sets of Digit Dog ten frame flash cards – large or small

To play:

Place the cards in a pile face down.

One player shows the top card and then turns it back again, the other players have to say how many dogs were on the card. The length of time that the card is revealed can get shorter as learners get better at recognising the patterns.

Encourage learners to recognise patterns and to work out the number without counting each dog.

How did you know how many there are? Explain your thinking.

Variations

  • For learners still practising counting accurately, turn over the cards and count each dog. Place an object on each dog and count the objects.
  • Use the five frame flash cards.
  • For a challenge: turn over the card, show the dogs and then hide them again. This time say one more than the number of dogs or one less than the number, e.g. if there were 4 dogs on the card, you would say “one more is 5” or “one less is 3”.

Try these on-line ten frame games:

https://gregtangmath.com/tenframemania

https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Ten-Frame/

Posted in Counting, Number sense, Subitising, Ten frames

Using ten frames

Show these slides for a couple of seconds to practise saying how many objects there are without counting in ones.

To play:

Open slideshow.

Click once to reveal an image, click again for it to disappear.

Ask: “How many Digit Dogs can you see?”

At first learners will want to count each dog and you will need to leave the image on the screen. Practise recognising the groups of dogs and saying how many there are without having to count each one. How quickly can you do this?

Being able to look at a small set of objects (up to 5) and say how many there are without counting in ones is called subitising. Once children can count objects accurately we want them to move onto subitising, this is an important step in the development of number sense.

It is easier to subitise if objects are arranged in recognisable patterns, such as the dice dot patterns or on ten-frames. The frames are used so that learners can relate numbers to 5 and 10, an important understanding for calculation.

DD4
I know there are 5 spaces in each row, so I can see this 4 in relation to 5. 4 is one less than 5.

 

Perceptual subitising – instantly recognising a small group of objects, usually up to 5 or 6.

DD3.jpgDD4.jpg

 

How many Digit Dogs can you see?

 

Conceptual subitising – seeing smaller groups of objects within a larger group to say how many there are without counting in ones. We do this when there are more than 5 or 6 objects.

 

I know there are 7 because I see 5 and 2 more.

Screenshot 2018-03-15 17.01.54.pngScreenshot 2018-03-15 17.02.01.png

I know there are 7 because I can see 4 and 3 more.

 

Posted in Logical reasoning, Patterns

Patterns in names

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 09.51.40Screenshot 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

What has changed?

What about a smaller grid? What patterns can you see then?

Screenshot 2020-06-23 09.53.31

Try some different sized grids with your name.

Download grids

Grids 2 to 8,

Grids 9 and 10.

For more pattern activities go to Digit Dog’s home page, go to Categories and select Patterns

Posted in Logical reasoning, Problem solving

100 square jigsaw

Digit Dog and Calculating Cat are doing a 100 square jigsaw. They are looking at each piece and deciding where it goes on the grid.

Screenshot 2020-06-18 12.37.30

Have a go at completing the puzzle.

Download the blank grid here. Download this 100 square and cut along the thicker lines to create the jigsaw pieces.

Think about which piece you are going to put in first. Why have you chosen that one? Which piece has the lowest number on it? Where does that go? How do you know?

Where does the highest number go?

Whenever you place a piece on the board, explain why you are placing it there.

Can you see patterns to help you?

Challenge yourself

  • Turn all the pieces face down. Turn over one piece at a time and work out where it goes on the grid. Explain your thinking.
  • If you want to try an interactive version of this puzzle, go to https://nrich.maths.org/5572
  • Print this 100 square and cut out your own puzzle pieces for a friend to solve.

 

 

 

Posted in Calculating, Fluency, Games

Double your number

Play Double your number

You need:

A game board.

A set of counters for each player. One colour for each player. You can download Digit Dog counters here – print on card and cut out or print on paper and stick them on milk bottle tops.

A dice.

Screenshot 2020-06-16 11.35.19

To play:

Take turns to throw a dice.

Double the number you throw, find the answer on the board and put your counter on it.

The winner is the first player to get three counters in a row.

Variation

Use a set of digit cards 1 – 19 and this board. Take turns to turn over a card, double the number and cover the answer on the board.

 

 

 

 

Posted in Calculating, Fluency, Games

Pass the Peas, Please

Digit Dog and Calculating Cat are playing Pass the Peas Please, a game they found on www.nrich.org

Screenshot 2020-06-16 10.20.55

A game for 2 or more players

You need:

A game board

2 dried peas (or beans or counters or sweets).

A plastic cup.

A piece of paper and pencil for each player.

To play:

Each player begins by writing 50 on their piece of paper.

Player 1 places two dried peas into the plastic cup and tosses them onto the game board.

They add the two numbers the peas land on and then take the total away from 50 and write the answer on their score sheet.

The next player takes a turn.

In the following turns, the players take the sum of the numbers away from the new remaining number.

The first player to reach zero wins.

Variations

Start with 0 on your score card and keep a running total of scores. The winner is the first to reach 50.

Use one pea instead of 2 and either subtract the number the pea lands on from 50 or keep a running total.

Use 3 peas to play the game.

Change the number you start with on your score card – make it higher or lower.

Each player takes a turn to throw two peas and add the numbers. The player with the highest total wins that round. Play 10 rounds.

Each player takes a turn to throw two peas and add the numbers. The player with the lowest total wins that round. Play 10 rounds.

Each player takes a turn to throw two peas and finds the difference between the numbers. The player with the highest difference wins that round. Play 10 rounds.

Use this board and start with 10 or 20 on your score cards.

Make your own boards. Choose the numbers you put on the board.