Grade 3 · Math · Unit

Story Problems with All Four Operations

4 lessonsabout 2 weeks

The unit ends with three more days: a review day, the unit check, and a day to act on what the check showed.

Unit 4 of 8 in the Grade 3 Math Scope and Sequence

What's included in this unit

4 lessons in teaching order, each with its objective and a teacher note
18 practice pages to print, with an easier and a harder page where available
3 classroom tools for the projector
1 activities and pages that children do on a screen
4 check-up pages to collect

The whole unit in one file

Print every page of the unit at once, with the teacher guide first. The guide has one page per lesson: the objective, what to hand out, and the teacher note.

Teacher guide only (PDF)

The unit file, the teacher guide, and saved pages are included with the Teacher plan.

Your PDF is built in your browser, so it always has the newest version of every page.

Lessons

Lesson 1

Multiplication and division word problems

Children solve word problems with equal groups, deciding whether the story asks for the total, for the size of each group, or for the number of groups.

StandardCommon Core 3.OA.A.3Operations and Algebraic Thinking

2 class days

Day 1Teach: Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Practice on screen · Check-up page

Practice on paper

Multiplication Word Problems
Core page Easier page Harder page
Division Word Problems: Sharing
Core page Easier page Harder page
Division Word Problems: Making Groups
Core page Easier page Harder page

Teacher note

Common mistakes: Children pick out the two numbers and multiply every time, or choose the operation from one word such as "each." They do not ask what the answer will be: a total, a share, or a number of groups.
Words to use: Ask three questions about every story: "Do we know how many groups? Do we know how many in each group? Do we know the total?" Then: "Which of the three is missing?" Have children finish with a sentence: "Each child gets 4 stickers."
What to watch for: Read a child's answer sentence, not only the number. A bare "4" does not show whether the child knows it is 4 stickers each or 4 bags. Each page holds one kind of story, so the page decides for the child: read one story from each page aloud, in mixed order and without the picture, and ask which of the three is missing.

Lesson 2

Two-step stories: add and subtract

Children solve two-step story problems with adding and subtracting within 1,000 and show each step as an equation.

StandardCommon Core 3.OA.D.8Operations and Algebraic Thinking

2 class days

Day 1Teach: The Exchange Machine · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open The Exchange Machine on the projector.

Practice on paper

Two-Step Story Problems Within 1,000
Core page Easier page Harder page

Check-up page

One more page of Two-Step Story Problems Within 1,000 to collect at the end of the lesson.

Teacher note

Common mistakes: Children add every number they see, or they finish the first step and write that number as the answer. With three-digit numbers, some lose track of the story while they regroup, or carry the wrong number from step a) into step b).
Words to use: Tell a story in two parts and stop in the middle: "A store has 356 pencils. A truck brings 124 more. How many pencils does the store have now?" Write 356 + 124 = 480 and circle the 480. "Then the store sells 213. Which number do we start from now?" Write 480 − 213 = 267 under it and draw an arrow from the 480 to the second line. Ask, "Does 267 make sense? The store sold more than the truck brought, so it has fewer than at the start." If the regrouping gets in the way, do one subtraction on the Exchange Machine first (it deals its own numbers).
What to watch for: On the page for everyone, the two steps are printed as a) and b) with boxes, and the dotted space is for the written work. It has three stories from four kinds: a store that gets a delivery and then sells, a market that sells and then gets a delivery, workers who pack on three days, and a truck that leaves things at two stores. The easier page has two stories with numbers that end in 0 (380 + 270). On the harder page, only the answer box is printed, and the child finds the two steps; there, in a truck story, adding the two amounts first and subtracting once is right, too.

Lesson 3

Two-step stories: multiply or divide

Children solve two-step story problems in which one step multiplies or divides within 100 and the other adds or subtracts.

StandardCommon Core 3.OA.D.8Operations and Algebraic Thinking

2 class days

Day 1Teach: The Baking Tray · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open The Baking Tray on the projector.

Practice on paper

Two-Step Story Problems: Multiply and Divide
Core page Easier page Harder page

Check-up page

One more page of Two-Step Story Problems: Multiply and Divide to collect at the end of the lesson.

Teacher note

Common mistakes: Children miss the word "each" and add: for "There are 6 baskets. Each basket holds 8 medals. 3 are taken out," they compute 6 + 8 − 3. Others multiply and stop. In the sharing stories, some divide the first number they see before they have asked what is being shared.
Words to use: On the Baking Tray, set 4 rows of 6 buns: "The baker made 4 rows with 6 buns in each row. How many buns? Which fact?" Write 4 × 6 = 24. "She sells 5." The tray cannot take buns away, so write it: "What happens to the 24?" 24 − 5 = 19. Then tell a sharing story without the tray: "There are 12 pens in a red box and 8 in a blue box. 4 children share all of them fairly. What is being shared? All the pens. What first?" Write 12 + 8 = 20, then 20 ÷ 4 = 5.
What to watch for: On the page for everyone, the steps are printed as a) and b): one story multiplies first, one divides first, and one adds the things in two boxes first and then shares. The easier page has two stories that multiply first, with factors from 2 to 5. On the harder page, only the answer box is printed; one story may be "keeps some and shares the rest," where subtracting comes first. A child who cannot say what each number counts (baskets, things in one basket, things taken out) draws the story in the dotted space first.

Lesson 4

A letter for the unknown and an estimate to check the answer

Children write one equation with a letter for the unknown for a two-step story problem, solve it, and check the answer against an estimate from rounded numbers.

StandardCommon Core 3.OA.D.8Operations and Algebraic Thinking

2 class days

Day 1Teach: The Rounding Hill · Practice on paper (Core page)
Day 2Practice and check: Practice on paper (Easier page, Harder page) · Check-up page

Warm up and teach

Open The Rounding Hill on the projector.

Practice on paper

Two-Step Stories: Equation, Estimate, Answer
Core page Easier page Harder page

Check-up page

One more page of Two-Step Stories: Equation, Estimate, Answer to collect at the end of the lesson.

Teacher note

Common mistakes: Children treat the estimate as one more exercise and never compare it with the answer. Many round the exact answer after they have computed it, which checks nothing. Some think n is the same number in every story; it is only a name for the number we do not know yet.
Words to use: Write the store story as one line: 356 + 124 − 213 = n. "n is the number of pencils the store has at the end." Estimate before computing. On the Rounding Hill, choose the ground between two hundreds, shift the hill to 300 and 400, move the boulder to 360 (the spot nearest 356), and let go: it settles into 400. "356 rounds to 400, 124 to 100, 213 to 200. 400 + 100 − 200 = 300." Compute n = 267: "Is 267 near 300? Yes." Then write n = 693: "A child got this. Near 300? No. What went wrong?" (The 213 was added.)
What to watch for: On the easier page, the equation is printed and the estimate has a frame of boxes for the rounded numbers. On the page for everyone, the child writes both on lines. The harder page has three stories; the last one prints a child's finished answer, which is right on some pages and far off on others: the child estimates, marks yes or no, and then finds n. No number on these pages ends in 45 to 55, so no one has to argue about a halfway number. A right answer is never more than 100 from the estimate, and a wrong printed answer is at least 200 away: "near" means within about 100.

Unit check: before and after

Two short paper checks made from this unit's own worksheets. Give Check A before you teach the unit and Check B after it, and you can see what changed. Each part belongs to one lesson.

Part 1: Lesson 2, Two-step stories: add and subtract (1 task)
Part 2: Lesson 3, Two-step stories: multiply or divide (1 task)
Part 3: Lesson 4, A letter for the unknown and an estimate to check the answer (1 task)

Not in the check: Lesson 1. Worksheets that cannot be split into single tasks are left out.

Check A (PDF) · 2 pages Check B (PDF) · 2 pages

Printing a check counts as a download, like any worksheet.

Answer key A Answer key B Teacher pages: points, class record, and what to do next

The answer keys and the teacher pages come with the paid Teacher plan.

This is a classroom check of this unit's lessons. It is not a standardized test, and its points are not a grade.

Unit checks

What's included in this unit

The whole unit in one file

Lessons

Practice on paper

Practice on screen

Check-up page

Make more

Warm up and teach

Practice on paper

Check-up page

Warm up and teach

Practice on paper

Check-up page

Warm up and teach

Practice on paper

Check-up page

Unit check: before and after