1. Each student can choose to either have the easier card or the harder card.
2. The easier card follows a sequence from the top left hand corner to the bottom right hand corner. The harder card follows a sequence on a row and starts a new one on the next row.
3. All numbers need to be covered and also all the blank spaces so, for example, 1.5 may be called but only 1.4 is showing so they should put the counter on the right side of 1.4 .
4. As you call the numbers the students cover their spaces.
5. They should finish up with 15 counters covering 15 spaces

1. Write a decimal number on the board (to two decimal places). 
2. Brainstorm different ways to represent it.
   For example 3.81 could be expressed as;

• Three point eight one
• 3 + 0.8 + 0.01
• (3 x 1) + (8 x 0.1) + (1 x 0.01)
• 381 / 100
• 4 – 0.19
• Three and eighty one hundredths
• 7.62 / 2

3. Give each student a decimal number and ask them to represent in as many ways as they can.  Depending on the level of individual students they could be to one, two, or three decimal places.  Less confident students could work in pairs.
4. Students could present their work on a sheet of A3 paper to be displayed on the wall.
5. As the students work encourage them to use a variety of approaches (not just a whole list of addition sums).

1. Players take turns to throw the two dice
2. After each throw they find the common multiples of these numbers.
3. They cover these numbers with counters.
4. Each player has five turns and the winner is the person who has the most numbers covered on their game board.

Extension

You may like to get the students to make up their own game board, deciding which numbers would need to be on it for them to win. If you wanted to extend the game you could use 10 sided dice and construct a game board for that.

At this stage, offering students a regular daily dose of mental calculation is strongly recommended. It is a good idea to record only one problem on the board or in the modelling book at a time and not allow the students to use pencil and paper. Make sure they all have time to solve each problem. Don’t allow early finishers to call out the answer.

For example, take the problem 73 – 29 = ?.
Prompt the students to look carefully at the numbers before deciding how they might solve this. The following are possible strategies:

• Equal adjustments: solved by adding 1 to both numbers, so 74 – 30 = 44.
• Rounding and compensating: 73 – 29 becomes 73 – 30 = 43, then 43 + 1 = 44.
• Reversibility: adding up from 29 to 73, so 1+ 40 + 3 = 44.
• Place value: partitioning the 29, so 73 – 20 = 53 →53 – 3 = 50 →50 – 6 = 44.

When recording the strategies the students selected to use, ask: “What is it about the numbers that made you choose the strategy you used?” and “Which of these strategies is the most efficient? Why?” If the students have used place-value strategies to solve the problem, they may need to revise equal adjustments and rounding and compensating.

As well as presenting problems for the students to solve as equations, it is also important to present them as word problems – for example: “The children had to blow up 182 balloons to decorate the school hall. By playtime, they had blown up 26. How many more did they still need to blow up?”

Some Problem Sets

Record the problems on the board or modelling book in the horizontal form.

Set 1
45 + 58     
67 + □ = 121    
8 001 – 7 998    
26 + □ = 52    
81 – 67     
456 + 144   
789 – 85         
□ + 58 = 189     
33 + 809 + 67 + 91
 

Set 2
28 + 72       
191 + □ = 210       
7 001 – 21      
39 + □ = 77        
234 – 99         
6091 + 109  
2 782 – 15            
□ + 123 = 149       
616 + 407 – 16 + 93
 

Set 3
999 + 702        
287 + □ = 400        
2 067 – 999       
45 + □ = 91     
771 – 37 316 + 684        
709 – 70                
□ + 88 = 200        
7 898 – 6 000 – 98 – 100
 

Set 4
38 + 128          
14 + □ = 101          
9 000 – 8 985         
102 – □ = 34   
800 – 33 78 + 124       
4 444 – 145                
□ + 8 = 1 003          
4 700 – 498 + 200 –2
 

Set 5
405 + 58         
880 + □ = 921        
8789 – 7 678        
80 – □ = 41    
701 – 96  8 888 + 122     
781 – 45                 
□ + 48 = 789         
6 000 – 979 – 11 – 10

1. Each student needs a gameboard and 10 transparent counters.
2. The target number needs to be up on the board (15.287).
3. The aim is be on target or as close as possible by adding all the numbers that have a counter on them at the end of 10 rolls of the dice.
4. The teacher rolls the die 10 times. Not all at once, as the students need time to keep a running total.
5. Every time the dice is rolled the students choose which number to cover. For example, if you call 5 the students elect to cover 5 or 0.5 or 0.05 or 0.005.
6. They must participate in every roll of the die.
7. Counters cannot be moved once they have been placed.
8. They cannot put counters on top of each other.
9. If 0 is thrown then everyone misses a turn and the counter is put above the card so the students can keep track of how many rolls are left.
10. When finished the closest totals are put up on the board and compared.
11. Depending on the ability of the students you may need to stop after 5 rolls and let them check their totals.

This game can be played simultaneously with Target 15 287, allowing for students of a range of abilities to participate.

Acknowledgement

This game of Target has been adapted from one originally made up by a group of South Auckland teachers.

Activity

1. One sheet for each student
2. Roll the die and name the fraction
3. They record the fraction in one of the cells of the table trying to match the description in that row.
4. The students write the answer when they have completed the description. For example, if they have completed ‘adds to more than 1’ they may have 1/2 and 5/8 so they should write in the third column 1 1/8
5. They are awarded one point when both fractions in a row match the description.
6. No points if only one fraction matches the description.
7. The player with the most points wins.

The Problem

There is a special number in each of these envelopes.
When you get your envelope, open it and find out what your number is.
This number is the solution to a maths problem that YOU make up.
What is your problem?

Teaching sequence

There are many ways to have your students create their own problems for others to solve.
This is just one possible way to consider.

1. Tell the students that their challenge is to create some mathematics problems. 
2. Ask the students to give you a number. Have them to make up a problem using that number as the answer.
3. Read and explain the task. Check that it is understood.
4. Have them work singly or in groups to create problems of their own. If they produce a sum, product, difference or quotient rather than a problem, have them to find other ways to make up that number or help them to craft a word problem.
5. As students write their problems have them put them into an envelope for later use.
6. Those students who finish quickly might like to try to write another problem or solve someone else’s problem.
7. Pose some of the students’ problems from the sealed envelopes for the whole class to solve.
8. You might like to keep some of these problems to use with the class over the next few weeks. You might have students identify the best problem, the funniest problem, and so on. 

Solution

The solutions will depend on your class.