Two-Step Equations
Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity
What a learner can do afterwards
- Solve a two-step problem that combines addition/subtraction with multiplication/division
- Write an equation using a letter for the unknown (e.g. 3 × n + 5 = 26)
- Assess the reasonableness of the answer using estimation and mental computation
1 · Read
You already solve two-step word problems. Now you will write them as equations. A letter, like n, stands for the number you don't know yet. One step can be multiplication or division, and the other can be addition or subtraction.
Some problems tell you the ending number and ask where you started. Ravi had some trading cards. His friend gave him 25 more, and now he has 60 cards. The equation is n + 25 = 60. To find n, subtract: 60 - 25 = 35. So Ravi started with 35 cards.
Estimate before you solve. Round the numbers and do the math in your head first. If your estimate is about 30 and your exact answer comes out as 300, you likely made a mistake somewhere.
Turn the story into an equation with a letter, solve it step by step, then check that the answer makes sense.
More to read
8.EEI.C.7 Unpacked
A letter can stand for a mystery number. In 3 x n + 5 = 26, the letter n hides the number you must find.
Undo the story backwards. The last thing done to n was adding 5, so subtract 5 first: 3 x n = 21. Then undo the triple: n = 7.
2.2 Linear Equations in One Variable
Equations with two steps mix operations. Doubling then subtracting, or tripling then adding, are classic pairs.
For 2 x n - 3 = 11, add 3 to both sides to get 2 x n = 14. Then halve: n = 7. Each undo peels one layer.
Add and subtract within 20: FAQ
Estimation tests whether an answer is sensible. For 4 x n + 3 = 19, try n = 4: 4 x 4 = 16, plus 3 is 19.
The estimate lands exactly on target, so 4 is reasonable. An answer like 40 would give 163, far too big.
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2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 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.