Multiplying and dividing by up to 1000

1. Support students to anticipate the result of multiplying or dividing a whole number by ten or one hundred. Give students a calculator and pose questions like those shown below. If possible, use materials (e.g. place value people, place value blocks) to model these problems, with the aim of moving students towards relying on number properties.
   What number is 56 times 10? …times 100?
   What number is one tenth of 4900? ...one hundredth of 4900?
   Record equations for each calculation, such as 10 x 56 = 560 and 100 x 56 = 5600, 4900 ÷ 10 = 490 and 4900 ÷ 100 = 49.
   Continue until students fluently and accurately predict the answers.
    
2. Extend the examples to include decimals. Ask students to predict the answer then confirm it with a calculator. Such as:
   What number is 4.1 times 10? …times 100?
   What number is one tenth of 63? ...one hundredth of 63?
   Record equations for each calculation, such as 10 x 4.1 = 41 and 100 x 4.1 = 410, 63 ÷ 10 = 6.3 and 63 ÷ 100 = 0.63. Discuss why the calculator shows zero?
   Continue until students fluently and accurately predict the answers.
    
3. Use pattern to encourage prediction for multiplying and dividing by 1000. Encourage students to predict the answers, before confirming them with a calculator.
   • 10 x 38 = [ ]                                          
   • 100 x 38 = [ ]                                         
   • 1000 x 38 = [ ]                                      
   • 9300 ÷ 10 = [ ]
   • 9300 ÷ 100 = [ ]
   • 9300 ÷ 1000 = [ ]
      
4. Discuss the patterns that occur as the same number is multiplied by increasing powers of ten. Consider multiplying 2.9: When 2.9 is multiplied by ten, the digits shift one place to the left because the units are worth ten times what they were. This shifting pattern occurs repeatedly. 1000 x 2.9 is the same operations as 10 x 10 x 10 x 2.9= 2 900. Therefore the digits shift three places to the left.
   
    
    
5. Discuss the patterns that occur as the same number is divided by increasing powers of ten. Consider multiplying 720: When 720 is divided by ten, the digits shift one place to the right because the units are worth one tenth what they were. This shifting pattern occurs repeatedly. 720 ÷ 1000 is the same operation as 720 ÷ 10 ÷ 10 ÷ 10 = 0.72. Therefore the digits shift three places to the right.
   
    
    
6. Provide other examples of multiplying and dividing a number by 1000. Ensure students express the relevant equations, using a suitable means of expression (e.g. written, verbal), as they work. Use calculators to connect equations to the word problems. Also consider allowing students to work in groupings that will encourage peer scaffolding and extension. Some students might benefit from working independently, whilst others might need further support from the teacher. Examples might include:
   What number is 1000 times 56.1?
   What number is one thousandth of 4315?

Next steps 

1. Use toy money as a place value model. Students can be asked to justify the results of multiplying or dividing by 1000. For example:
   Show why $4,600 ÷ 1000 = $4.60.
    
2. Connect multiplication and division as inverse operations that undo one another. 
   For example:
   10 x 63 = 630 then 630 ÷ 10 = 63
   100 x 57 = 5 700 then 5 700 ÷ 100 = 57
   490 ÷ 1000 = 0.49 then 1000 x 4.9 = 490
   What do you notice is happening in all three equations?
   Why does that happen?
   Ask students to create division and multiplication equation pairs (e.g. 10 x 63 = 630 and 630 ÷ 10 = 63).
    
3. Provide problems framed in real-life, meaningful contexts that involve multiplying and dividing a number by 1000. Examples might be:

• A baker makes 54 loaves of bread per day. How many loaves would 1000 bakers make?
• How many $1000 notes make $83,000?
• A giant mural of an ant is 7 metres long. The real ant is one thousandth of the mural. How long is the ant?