The idea in brief. Name the quantity being found, decide how the known quantities relate to it, and reverse changes in reverse order when the start is unknown. Name the quantity you are finding first: the word "more" can lead to an addition or a subtraction. In the lesson. In Primary 2, you learnt that subtracting undoes adding, and adding undoes subtracting. Today, we work backwards to find how many there were at first. To find how many there were at first, work backwards and undo the last change first.
Lesson video, with the working
Finding the start
4 min 43 s
The film teaches 3 questions in turn. Each question shows first; its working is written as the film explains it.
A science centre had some brochures. It gave out 125 brochures, then received 48 more. It had 376 brochures at the end. How many brochures did it have at first?
376 − 48 = 328
328 + 125 = 453 brochures
Ans: 453 brochures
Example 1 of 2
A science centre had some brochures. It gave out 215 brochures, then received 64 more. It had 1286 brochures at the end. How many brochures did it have at first?
1286 − 64 = 1222
1222 + 215 = 1437 brochures
Ans: 1437 brochures
Example 2 of 2
A science centre had some activity cards. It received 134 activity cards, then gave out 87. It had 562 activity cards at the end. How many activity cards did it have at first?
562 + 87 = 649
649 − 134 = 515 activity cards
Ans: 515 activity cards
How to solve it
Find what the question asks for: how many there were at first.
You know the amount at the end, so work backwards from the last change.
Undo the last change. If it received some, subtract them. If it gave some out, add them back.
Then undo the first change in the same way.
The number you reach is how many there were at first.
To find how many there were at first, work backwards and undo the last change first.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its solution film.
Question 1 of 6 · Basic · free to tryTwo community centres collected used batteries for recycling. The first…Two community centres collected…
Two community centres collected used batteries for recycling. The first collected 1238 batteries and the second collected 864 batteries. How many batteries did they collect altogether?
How do you solve P3 how many at first word problems?
This page teaches 1-step and 2-step word problems with numbers up to 10 000: finding a total, finding a difference, and working backwards to find how many there were at first.
What your child learns here
This page teaches 1-step and 2-step word problems with numbers up to 10 000: finding a total, finding a difference, and working backwards to find how many there were at first. It applies the MOE Primary 3 addition and subtraction outcomes to word problems.
Name the quantity to find before choosing an operation.
Use a part-whole or comparison bar model to decide whether to add or subtract.
Know that the words more or fewer in a question do not decide the operation by themselves.
Work backwards from a final amount, undoing the last change first: something gained is undone by subtracting, something given away by adding.
Check an answer by running the story forwards from it.
Does the answer make sense?
A total of two amounts must be bigger than each of them, and a 'how many more' answer must be smaller than the bigger amount. For an 'at first' answer, your child can replay the story forwards from it and should land exactly on the final number given.
How to practise these questions
The Basic question practises finding a total or a difference from a short story. The Intermediate questions add stories with a change part way through, so two steps are needed. The Challenge question asks your child to find the starting amount by working back from the end of the story. If a word problem stalls, watch its solution film and attempt it again later from Revision.
Questions parents ask
Does my child need to draw a bar model for these word problems? A bar model shows which amount is the whole and which are the parts, and it helps decide whether to add or subtract. For working backwards, a short list of the changes in order can be just as clear. Either is fine if each step is written.
Are word problems part of the P3 addition and subtraction syllabus? The syllabus lists addition and subtraction algorithms up to 4 digits, and these word problems apply them. They use the same column methods taught on the other pages of this chapter.
What is the easiest way to teach working backwards to a P3 child? Start with a short story and real objects, then reverse it one step at a time, undoing the last change first. Something gained is undone by subtracting and something given away by adding, and running the story forwards checks the answer.
