Estimating sweets
 Give the students the problem of estimating 225 ÷ 6 to identify whether they already know how to use nice numbers and factors.
 Discuss students' methods. Use the language of estimation in the Computational estimation concept map for each different method.

Introduce the nice numbers and factors method in division, i.e., change at least one of the numbers so that one number is a factor of the other. This should be based on basic multiplication facts. You may wish to write this example down as you discuss it.
Example: Estimate 225 ÷ 6
Change 225 to 240
because 24 ÷ 6 = 4, so 240 ÷ 6 = 40 or
because 6 × 40 = 240
Discuss why this is closer to the exact answer than changing 225 to 180 because there is a smaller change to go to 240. Also, 30 is an underestimate of the number of bags so he will not have enough.  Students complete the sentence with the word "nice numbers and factors", and then answer parts b) to d) to assess if they can apply it. Emphasise they are to use the nice numbers and factors method only.
This resource can help to identify students' ability to apply multiplicative strategies flexibly to whole numbers when estimating quotitive division problems.
This resource involves recording the strategies students use to estimate in quotitive division problems. This relates to the Key Competency: Using language, symbols and text.
a) 
Makes a reasonable estimate close to 40 and gives a reasonable explanation of their method of estimating it. The nice numbers method would be: 
b) 
30 because 210 ÷ 7 = 30 (or because 7 × 30 = 210) 
c) 
50 because 1 500 ÷ 30 = 50 (or because 30 × 50 = 1 500) 
d) 
Any 1 of:

NOTE:
 Other strategies are possible. If they don't use the nice numbers and factors methods, conference them to see if they can, even if they prefer other strategies.
 Students may use a combination of estimation and computation (i.e., computations that they cannot easily do in their heads and may need to write down, e.g., 230 ÷ 6).
Common error  Likely calculation  Likely misconception  
a) b) c) d) 
37.5 28.28 47.76 48.82 
225 ÷ 6 198 ÷ 7 1 433 ÷ 30 3 271 ÷ 67 
Performs exact calculation rather than estimation. 
a) b) c) d) 
30 20 40 40 
180 ÷ 6 140 ÷ 7 1 200 ÷ 30 2 800 ÷ 70 
Rounds down to a nice number and therefore underestimates the number of bags. Indicates they have the idea of nice numbers, but they need to choose a factor that gives an answer closer to the exact one. 
a) b) c) d) 
38.33 28.57 46.67 47.14 
230 ÷ 6 200 ÷ 7 1 400 ÷ 30 3 300 ÷ 70 
Rounds to the nearest 10, 100, etc., then does an exact calculation. 
a) b) c) d) 
37 or 38 28 or 29 47 or 48 48 or 49 
225 ÷ 6 (or 38 × 6 = 228) 198 ÷ 7 (or 29 × 7 = 203) 1 433 ÷ 30 (or 48 × 30 = 1 440) 3 271 ÷ 67 (or 49 × 67 = 3 283) 
Does an exact calculation but either rounds up or down to get an answer (or works out an exact multiple of one number rather than using basic facts ones). 
Information on using nice numbers and factors in estimation
 Nice numbers is often known as compatible numbers. It involves making the numbers compatible with respect to the operation being undertaken. In division, this means making one of the two numbers a factor of the other. The relationship should be based on basic multiplication facts.
 Changing the value of at least some numbers is referred to in the literature as reformulation.
 Nice numbers division gives a reasonably accurate estimate only if the amount of rounding of one number is proportionally about the same as the amount of rounding of the other number. Both numbers need to be rounded in the same direction, i.e., both rounded up, or both rounded down. Recognising that one number being rounded roughly balances the other one being rounded in the same direction is referred to as intermediate compensation.
 Final compensation (i.e., updating an initial estimate to a more accurate one) can be done with nice numbers division.
Prior knowledge needed
 A firm base of multiplicative basic facts.
 Good place value concepts.
 Understanding that estimation is a quick mental way of getting an answer close to the exact one.
 Ability to evaluate the order of magnitude of answers in division.
Using nice numbers and factors as an estimation method involves at least advanced multiplicative partwhole (Stage 7) knowledge and strategies (see The Number Framework, Book 1 (2004, p. 11 & 15). Wellington: Ministry of Education).
For similar ARB resources about nice numbers and factors as an estimation method refer to Estimating scores and crowds.
For further information about estimation, refer to Computational estimation concept map.