Having fun with the vertical algorithm
These exercises and activities are for students to use independently of the teacher to practice and develop their number properties. Some are suitable for homework, others require follow-up during teaching sessions
Number Framework domain and stage:
Addition and subtraction, stages 6-7, advanced additive to advanced multiplicative
Number, levels 2 and 3
Numeracy Project book reference:
These activities do not follow from teaching episodes described in the Numeracy Project resource books
Prior knowledge. Students should be able to:
- Mentally add and subtract 3 digit numbers
- Use the vertical algorithm for addition and subtraction
During these activities, students will meet:
- Addition and subtraction of 4 digit numbers
- Addition and subtraction of decimals and percentages involving decimals
While calculators can be expected to be used for more complicated additions and subtractions, learning the "good old vertical algorithm" still has its place - once students are able to use the place value system properly so have a chance of understanding how it works. These exercises, however, while giving some practice with this method, also show students a nice strategy for avoiding "all that borrowing", and introduces a "complementary numbers" strategy that can be very handy for decimals and percentages.
These activities are designed as an investigation that students undertake with little teacher supervision. After each stage/exercise, it is envisaged that the teacher will facilitate a discussion with and between students about what they have learned and discovered. In some cases, where students have struggled to make progress, individually or collectively, the teacher may need to 'help' students to make a discovery by showing a problem, or a range of problems. Highlighting what the students need to look at, as in the example below and asking leading questions like "what do you notice about these numbers?" is a useful approach.
When using these activities, note that the discussions around not only how to use the strategy, but when to use it, are central to the learning being undertaken by students. As this is student, and not teacher, directed the discussions also act as a reporting back process on the work students have undertaken. It may pay to highlight the expectation that all can contribute to a discussion about what they have tried and have learned before each section of the work is set to ensure the students pay attention to more than simply 'getting the answers'.
The final challenge is a good research project for a few - but some may twig immediately that the answer plus the number subtracted should give the number started with. If that number has a lot of zeros in it, adding 1 will roll all the other digits to zero. 999,999 + 1 = 1,000,000, so were are making sure that the answer and the subtracted number add to 999,999 + 1.