Discover Mathematics P5: Term 1, Unit 1, Lessons 10–13
GoalSolve two-step stories that use both adding and subtracting decimals.
New words
two-step problem · a problem that needs two calculations to solvechange · the money you get back when you pay more than the price
Explanation
A story problem has a plan. First read it and say what is asked. Then find the numbers you need and decide which operation each step needs: putting together means adding, taking away or finding what is left means subtracting, and comparing two amounts means subtracting the smaller from the greater. Estimate the answer. Do the steps one at a time, writing what each answer means. Finally check that the answer fits the story. For example: 10 m of cloth, 3.5 m used for curtains and 2.75 m for cushions. Step 1: used together 3.5 + 2.75 = 6.25 m. Step 2: left 10 − 6.25 = 3.75 m.
Read→Plan→Estimate→Solve→Check
Worked examples
Farida has a roll of 10 m of cloth. She uses 3.5 m for curtains and 2.75 m for cushions. Together she uses 3.5 + 2.75 = 6.25 m. What is left is 10 − 6.25 = 3.75 m. Estimate: 10 − 6 = 4, which is close.
Day
Time (s)
Monday
28.45
Tuesday
26.75
Wednesday
27.1
Karim swims 25 m in 28.45 seconds on Monday. On Tuesday he is 1.7 seconds faster: 28.45 − 1.7 = 26.75 s. On Wednesday he is 0.35 seconds slower than on Tuesday: 26.75 + 0.35 = 27.1 s. His Wednesday time is 27.1 seconds.
Mina has 50 LE. She buys a notebook for 12.75 LE and pens for 8.5 LE. Spent: 12.75 + 8.5 = 21.25 LE. Change: 50 − 21.25 = 28.75 LE. Check: 21.25 + 28.75 = 50.
Class activity
Shopping story. Look at three prices on a shop shelf or in a leaflet (for example 14.5, 9.25 and 3.75 LE). Make up a two-step story: you pay with a 50 LE note. How much do two items cost together, and how much change do you get? Write the story and its solution, and let someone else solve it.
Practice
1
A bag has 5 kg of rice. 1.75 kg is used on Monday and 2.4 kg on Tuesday. How much rice is left?
Used: 1.75 + 2.4 = 4.15 kg. Left: 5 − 4.15 = 0.85 kg.
2
A new pencil is 17.5 cm long. After sharpening it loses 0.85 cm. How long is it now?
17.50 − 0.85 = 16.65 cm.
3
The shallow end of a pool is 1.2 m deep and the deep end is 2.05 m deep. How much deeper is the deep end?
2.05 − 1.20 = 0.85 m.
4
Tamer walks 1.35 km to the library and then 0.9 km to the park. His planned walk is 3.5 km. How much of the walk is still left?
Walked: 1.35 + 0.9 = 2.25 km. Left: 3.5 − 2.25 = 1.25 km.
5
Make up a story for 8.5 − 2.75 and solve it.
For example: a ribbon is 8.5 m and 2.75 m is cut off. 8.50 − 2.75 = 5.75 m is left.
