Mixing the methods - mental exercises for the day

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