A game for two players. Give out a 10p coin and say in order for it to be fair you should both have 10p each. When you have a 10p coin each agree that you have 20p altogether. Write: Double 10 is 20. Give out another 10p coin each. Agree that you have the same and record the total. Write: Double 20 is 40. Repeat until double 50 is 100; agree that 50p and 50p is £1.
What happened if you have 10p and 5p? How can you double this amount? What is double 10? And double 5? So double 15 is what? Write:
Explain that you can split 15 into 10 and 5, double each part, and then add it back together again to equal 30.
Repeat for double 25, 35 and 45.
How can we write this double as an addition?
If double 25 is 50, what is half of 50?
Make the number 23 out of place-value cards using the Place-value cards. Separate the cards and double 20 then double 3. Drag cards 40 and 6 underneath 20 and 3, and then put them together to form 46. Write: Double 23 is 46.
Repeat with 42.
Show 34 using the Place-value cards and double 30, then double 4. Put the new cards together to make the double, i.e. 68.
Repeat for other numbers less than 50 with 1s digits 1, 2, 3 and 4.
If double 4 is 8, what is double 40?
If double 42 is 84, what is half of 84?
Double or Halve?
A game for two players.
You will need a dice.
Decide on a target number. This is the total that both players are trying to make.
Player 1 throws the dice. S/he can choose whether to double the number shown or halve the number shown.
Player 2 throws the dice. In the same way, s/he can choose whether to double the number shown or halve the number shown. Player 2 adds his/her number onto Player 1's number to make a running total.
Play continues like this with each player rolling the dice, halving or doubling the number and adding the result onto the running total.
The winner is the player who reaches the agreed target exactly.
Here are some questions to think about:
Must each player always take a turn?
Does it matter if you go first or second?
Are there any particularly good numbers to choose as your target?
A game for two players
Use the 3×3 grid. Player 1 will write numbers in the grid on the board and Player 2 will keep up with you writing numbers in the matching spaces on their grid. Player 2 must write half of Player 1’s number each time. So if Player 1 writes four, Player 2 writes two, and so on. Keep going like this until the grid is full. Check your grids together.
Draw 24 monsters on a strip of paper (or use the Monster Fraction Strips). Ask how many monsters would be in each team if there were two teams with the same number in each. Fold the strip of monsters in half to confirm and record 1/2 of 24 is 12.
Say that the monsters are actually going to be in four equal teams, so a quarter of the monsters will be in each team. Fold the strip in half again to show quarters. Record 1/4 of 24 is 6. Emphasise that a quarter is half of a half.
Make a stick of 20 cubes/Lego, pretending that these are monsters. You need to split the monsters into four equal teams and find a quarter of twenty. Break the stick in half and in half again. Record 1/4 of 20 = 5. Read this together. Then write it as 20 ÷ 4 = 5 and explain that this is the same.
Discuss how two quarters is the same amount as one half. Write: 2/4 = 1/2. How many quarters make one whole? Discuss this and agree 4/4 = 1 whole.
Count along the quarters saying one quarter, two quarters, or one half, three quarters, four quarters, or one whole! Remind children how to write ¾.
There are 16 monsters. Half want to go swimming, a quarter want to go roller skating and a quarter want to have a mud fight. Make a strip of 16 cubes, find half, then break one half into half again to show the two quarters. Write: 1/4 of 16 = 4.
Make a strip of 16 cubes again and break into quarters. Tell children: This time, a quarter of the monsters want to go swimming and three quarters want to have a water fight as it’s such a hot day. Write: 3/4 of 16 = 12.
Which numbers can be halved twice?
Investigate which numbers from 1 to 40 can be halved twice (quartered) to give a whole number, using cubes to help.
Discuss how to record this information in a table. Encourage children to predict where a number can be split into quarters. Use the table to find 3/4 of some numbers.
Can children halve numbers twice to find a quarter (whole number answers)?
Can children make and test predictions?
Divide a piece of paper into quarters and ask children to share a number of cubes between the four parts to find a quarter of that number. Emphasise that the number in each part must be the same. Draw and cut out a cake with 12 evenly spaced cherries on the top. Say that the cake is shared fairly between two, then four children. Draw lines to cut the cake fairly to find out how many cherries each child will get on their piece of cake.
Fold the Monster Strip it into thirds. It’s not as easy to fold into thirds! How many parts will there be? How will you know that each part is equal? There will be the same number of monsters in each third.
Take feedback and write a sentence for each strip:
1/2 of 12 is 6
1/4 of 12 is 3
1/3 of 12 is 4
Work together to fold the strip of 24 monsters into 1/2s, 1/4s and 1/3s and to write the three sentences as above.
If we had twenty-four children in a class, how many would be in half of the class? How many would be in a third of the class? How many would be in the quarter of the class? Which is more, a third or a quarter?
If we fold this strip into quarters, how many parts will there be? What if we fold it into thirds?
If I fold the strip into three parts so that there are three faces on one part, four on another part, and five on the other part, have I folded into thirds? Why not?