Week 4 · Subtraction with regrouping and story problems · 3 lessons
2
Bar models and missing numbers
Discover Mathematics P4: Term 1, Unit 2, Lessons 5–7
GoalDraw a bar model for a story and use a letter for the unknown number.
New words
bar model · a drawing of bars that shows the parts and the whole of a storyvariable · a letter that stands for an unknown numberequation · a number sentence with an equals sign
Explanation
A bar model helps us see a story. One long bar is the whole. It is split into parts. If we know the whole and one part, we subtract to find the other part. If we know both parts, we add to find the whole. When a number is not known, we write a letter for it, like n or a. This letter is a variable. Then we write an equation. Salma had a LE, spent 380 LE and has 620 LE left: a − 380 = 620. The whole is a, so a = 620 + 380 = 1,000. A missing part is found by subtracting: n + 1,250 = 3,000 gives n = 3,000 − 1,250 = 1,750. A missing whole is found by adding. After you find the unknown, put it back in the equation to check.
Worked examples
Salma had a LE. She spent 380 LE and has 620 LE left. The whole bar is a, the parts are 380 and 620. So a = 380 + 620 = 1,000. Check: 1,000 − 380 = 620.
Solve n + 1,250 = 3,000. The whole is 3,000 and one part is 1,250. The missing part is n = 3,000 − 1,250 = 1,750. Check: 1,750 + 1,250 = 3,000.
Library A has 9,500 books. Library B has 3,750 fewer books than A. The bar for B is shorter by 3,750. So B has 9,500 − 3,750 = 5,750 books. Together they have 9,500 + 5,750 = 15,250 books.
Class activity
Draw the story. A grown-up tells a short story with a missing number, such as: I had some stickers, gave away 45 and now have 120. The child draws a bar model, writes an equation with a letter and finds the number. Then the child makes up a story for the grown-up.
Practice
1
Find n: n + 475 = 900.
n = 900 − 475 = 425.
2
Find a: a − 2,300 = 5,800.
a = 5,800 + 2,300 = 8,100.
3
Youssef had some marbles and found 128 more. Now he has 450. Write an equation and find how many he had at first.
n + 128 = 450, so n = 450 − 128 = 322 marbles.
4
Rahma has 7,200 LE and Karim has 2,950 LE less. How much does Karim have?
7,200 − 2,950 = 4,250 LE.
5
Is n = 600 the answer to n + 360 = 940? Check.
No. 600 + 360 = 960, not 940. The answer is n = 940 − 360 = 580.
