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Skills Covered

  • Model a two-step story problem with a strip diagram
  • Write an equation with a letter for the unknown, in any position
  • Solve problems with all four operations and numbers up to 1,000,000
  • Decide whether a question needs an estimate or an exact answer
  • Refine an estimate: is it between two numbers, and closer to which?
  • Interpret a remainder and check that an answer is reasonable

How to Use This Pack

Five pages of story problems that take more than one step. Page 1 adds and subtracts: in the first three problems the strip diagram is drawn for you with a letter for the unknown, such as 2,350 + 480 − 615 = b; in the last two, about a fair and a stadium, students draw the diagram themselves. Page 2 multiplies and divides with equal groups and times as many: students write the numbers into the diagram (a mother dog that weighs 4 times as much as her puppy), write the equation and solve, then draw two diagrams of their own. Page 3 circles the one equation of three that matches a story, then writes and solves equations with the letter at the start (p − 46 + 28 = 175), inside or after the equal sign. Page 4 decides whether a question needs an estimate or an exact answer and answers it, tells whether 6 × 48 is closer to 240 or 300 before working it out, and estimates to check whether an answer someone gives is reasonable. Page 5 has three-step problems with 5th grade numbers: buses, change from $400, full egg cartons and tins, each with an estimate first and a remainder or money to think about.

In the Classroom

Read one problem from page 1 aloud and build the strip diagram on the board together: what do we know, and where does the letter go? Ask two students to write different equations for the same diagram (1,850 + 1,275 + p = 4,200 and 4,200 − 1,850 − 1,275 = p) and talk about why both are right. On page 4, have partners argue for Estimate or Exact before anyone works anything out. On page 5, compare each answer with the estimate and ask whether it makes sense.

At Home

Turn errands into two-step problems: we have $40, we buy 3 shirts for $9 each, how much is left? Ask your child to draw a strip diagram and write an equation with a letter before working it out. When you shop, ask whether an estimate is enough (do we have enough money?) or you need the exact amount (how much change?).

Tips for Success

  • Read the whole problem first, then find the question: what are you asked to find?
  • Draw a strip diagram: a bar for each amount, a brace for the total, and a letter for what you do not know
  • Write one equation for the whole problem, then solve it one step at a time
  • Estimate first, then compare your answer with the estimate
  • Think about the remainder: one more bus for the people left over, or only the full cartons?
  • Check by working backward with the inverse operation

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

  • 4.OA.A.3 Solve multi-step story problems with whole numbers and all four operations, deciding what remainders mean, writing equations with a letter, and checking by estimating.

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Multi-Step Word Problems

4th – 5th Grade

A 5-page multi-step word problems pack for 4th and 5th grade. Solve two-step story problems with strip diagrams, adding and subtracting numbers up to the hundred thousands, then multiplying and dividing with equal groups and times as many, and write an equation with a letter for the unknown. Pick the equation that matches a story, then write and solve equations with the letter at the start, in the middle or after the equal sign. Decide whether a question needs an estimate or an exact answer, tell which number a sum or product is closer to, and estimate to check whether an answer is reasonable. Finish with three-step problems with money and remainders to interpret. Every page comes in color and in black and white. Answer keys included.

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What’s Included

  • 5 worksheets in color and in black and white, with answer keys (15 pages)
  • Two-step problems with strip diagrams: given, filled in and drawn, with an equation for each
  • Matching, writing and solving equations with a letter for the unknown in any position
  • Estimate or exact, closer to and between, checking answers, and three-step problems with money and remainders
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