Two-step word problems
Solve one- and two-step word problems within 100 using addition and subtraction, with unknowns in all positions
What a learner can do afterwards
- Solve two-step problems within 100 by tracking changes, finding totals or finding what is still needed
- Represent a word problem with an equation using a symbol for the unknown
- Solve more/fewer comparisons within 100, including a missing group size or the amount needed to match another group
1 · Read
You have used drawings and equations for one-step stories. A two-step problem needs two calculations. Find what the question asks, then put the events in order. If you know the start, work forward. Getting more adds to the group; giving some away subtracts from it. Use the first result for the next calculation. Check each action against your equation.
Mia had 26 crayons. She got 13 more, then gave 7 away. First add: 26 + 13 = 39. This is the middle number, before she gave any away. Then subtract: 39 - 7 = 32. Mia has 32 crayons now. If the question asked how many she had before giving 7 away, you would answer 39.
A question mark stands for the number you need. Some blocks get 14 more and become 43: ? + 14 = 43. Find the start with 43 - 14 = 29. If 43 blocks lose some and 29 remain, write 43 - ? = 29. Find the amount lost with 43 - 29 = 14.
In 29 + ? = 43, the question mark is the amount added. Find it with 43 - 29 = 14. In ? - 9 = 24, the question mark is the start. Put the 9 back: 24 + 9 = 33. Put each answer into its equation to check that both sides match.
To find how many more or fewer, subtract the smaller count from the larger count. Eli has 48 shells; Noor has 31. The difference is 48 - 31 = 17. Noor needs 17 to match Eli. If you know only Noor's 31 and Eli has 17 more, add: 31 + 17 = 48. If you know only Eli's 48, subtract 17 to find Noor's 31.
For a missing start in a two-step story, undo the last change first. A box gets 8 blocks, then loses 5, and ends with 23. Put back the 5 lost blocks: 23 + 5 = 28. Then remove the 8 added blocks: 28 - 8 = 20. Check forward: 20 + 8 = 28, then 28 - 5 = 23.
To reach a target, first add what you have. Then subtract that total from the target. You collect 18 tokens and 26 tokens toward a target of 60: 18 + 26 = 44. You still need 60 - 44 = 16 tokens. Check: 44 + 16 = 60.
To find empty seats, add the people and subtract that total from all the seats. A room has 42 seats, 17 children and 8 adults. Each person uses one seat, with nobody else there. There are 17 + 8 = 25 people. The number of empty seats is 42 - 25 = 17.
Two steps can use the same operation. For three groups of 21, 16 and 9, add twice: 21 + 16 = 37, then 37 + 9 = 46. If a shop starts with 55 rolls and sells 13, then 11 more, subtract twice: 55 - 13 = 42, then 42 - 11 = 31.
Find what the story asks. Use two calculations when needed, match each change to its sign, and check your answer in the story.
This lesson, practice bank and flashcards were written for the LightMySky dataset.
The readings, extra questions and flashcards were written for the LightMySky dataset. The linked video, "Multi step addition word problem", is by Khan Academy.
More to read
Keep track of the middle number
A cupboard holds 28 cups. Seventeen cups are added, then 9 are taken to a table. After the cups arrive, the cupboard holds 28 + 17 = 45. That is the middle number. Next, 45 - 9 = 36. The cupboard ends with 36 cups. Keep the middle number because the second change starts there.
Put the unknown in its place
Some cards are in a box. Add 11 cards and the box holds 38. Write ? + 11 = 38 because the starting count is missing. Find it with 38 - 11 = 27. Check: 27 + 11 = 38. If instead some of 38 cards are taken away and 27 remain, write 38 - ? = 27. Then the missing count is 11.
Use the difference between groups
A red box holds 57 blocks and a blue box holds 39. Subtract to find the difference: 57 - 39 = 18. The red box has 18 more blocks. The blue box has 18 fewer. Adding 18 blocks to the blue box would make the counts equal. If you know the red box has 57 and the blue box has 18 fewer, use 57 - 18 = 39.
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2 · Watch
En anglaisTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.