In this unit students, are encouraged to extend their use of part/whole methods from working with small numbers to working with multi-digit numbers. This work follows naturally from the Smart Doubling and Make a Ten units.
In this unit students, are encouraged to extend their use of part/whole methods from working with small numbers to working with multi-digit numbers.
Students need to be able to understand a range of simpler part/whole strategies before working on this unit. These strategies are described in the units Smart Doubling and Make a Ten, and include:
The students work out 8 + 5 by removing 2 from the 5 to leave 3, add this 2 to the 8 to make 10 then add the 3 to the 10 to give 13.
The students work out 38 + 8 by removing 2 from the 8 to leave 6, add the 2 to the 38 to give 40, then add 6 to the 40 to give 46.
Tens frames (Material Master 4-6)
To start with, students solve addition and subtraction problems involving one single-digit number and one multi-digit number. Once they can confidently solve these, progress to problems that involve two multi-digit numbers.
Over the next 3-4 days pose addition and subtraction problems for the students to work on, individually, in pairs or in a small teaching group. Encourage the progression from using pre-printed tens frames to imagining the tens frames and then to completing the problem mentally.
Pose the problem:
Kiri has 37 Jaffas and 26 wine gums. How many lollies does Kiri have altogether?
Discuss the students’ ideas for solving the problem.
- take away 20 from the 45 to leave 25. Another 9 needs to be removed. Remove the 5 to leave 20 then remove 4 more to give an answer of 16.
- take away 20 from the 45 to leave 25. Another 9 needs to be removed. Remove 9 from a 10 frame to leave 1. There is another 10 and a 5 to add to 1 to give 16.
- take away 30 from the 45 to leave 15. But taking away 30 is 1 too many. So add 1 to 15 to give 16.
In these problems the students are encouraged to add and subtract more than 2 numbers in which there are smart ways to do them. Begin by discussing the following problem:
Harry adds up the number of lunches his class orders in the week. By pairing up some of the numbers Harry quickly noticed the total lunches sold for the week was 60. How did Harry work this answer out so quickly?
(Pairing the 28 with the 2 gives 30. Pairing the 17 with the 3 gives 20: 30 + 20 + 10 = 50.)
Discuss the students’ ideas:
- 56 - 26 = 30, 30 - 28 = 2
- 28 + 26 = 54 (from 27 + 27) and 56-54 =2
At the end of each session gather the students together to share strategies.
Dear family and whānau
At school this week we have explored strategies for working out the answers to addition and subtraction problems.
Ngaire knows a number of ways to work out 19 + 38
Her first way is 20 + 40 = 60. Now 20 is one more than 19 and 40 is 2 more than 38 so take away 3 from 60 to leave 57.
Her second way is to remove add 10 and 30 to give 40, then add 9 and 8 to give 17 then add 40 and 17 to give 57.
Her third way is to remove 2 from the 19 to leave 17, then add this 2 to the 38 to give 40 then add and 7 to give 14 then add 17 and 40 to give 57
Write stories to show two different ways to work out the following problems. Make sure that both stories produce the same answer.
58 + 27
Story One:
Story Two:
81 - 19
Story One:
Story Two: