Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Two-step problems ask students to hold a plan in their heads: find one quantity first, then use it to find the answer. A typical example is "A class has 4 boxes of 8 markers and gives away 5 markers. How many are left?" The first step is 4 × 8 = 32 and the second is 32 - 5 = 27. Any pair of the four operations can appear, with whole numbers that keep the arithmetic manageable for third grade.
Two habits make the difference. First, students represent the problem with an equation that uses a letter for the unknown, such as 4 × 8 - 5 = m, so the structure is written down before any computing begins. Second, they judge whether the answer is reasonable using mental math and rounding: if a student gets 270 markers, an estimate of about 30 should immediately flag the error. Writing the equation, solving it and checking with an estimate turns a guessing game into a reliable process.
Many students answer the first step and stop, for example giving 32 markers instead of the 27 left. Ask them to reread the question and underline what it is really asking.
Students who work left to right through the story may subtract before multiplying. Drawing the situation shows which quantity must be found first.
In m = 27, m stands for a number of markers, not the word markers itself. Talk about letters as placeholders for unknown amounts.
Answers that are far too big or small usually come from the wrong operation. A quick rounded estimate catches most of these.
A bakery makes 6 trays of 9 rolls. It sells 38 rolls. How many rolls are left? Write an equation with a letter and check with an estimate.
Answer: There are 16 rolls left.
Tape diagrams and bar models help students see the two stages of a problem. Try giving a problem with the question removed and asking students what two questions could be asked, or provide the first step and ask for the second. Sorting problems by the operations they need builds flexible thinking.
On tests, two-step problems are often multiple-choice with distractors that match a one-step answer or the wrong operation. Training students to estimate first helps them eliminate those quickly.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 17 (also accepted: 17 stickers)
Step 1: 3 × 8 = 24 stickers. Step 2: 24 - 7 = 17 stickers.
Answer: 10 (also accepted: 10 pencils)
Step 1: 45 + 15 = 60 pencils. Step 2: 60 ÷ 6 = 10 pencils per table.
Answer: B) 9 × 5 + 12 = p
First 9 × 5 = 45 pages over the five days, then add the 12 Saturday pages: 9 × 5 + 12 = p, so p = 57.
Answer: 16 (also accepted: 16 chairs)
Step 1: 8 × 7 = 56 chairs set out. Step 2: 72 - 56 = 16 chairs left.
Answer: D) 300 + 400 is about 700
Rounding to the nearest hundred, 300 + 400 = 700. The exact answer, 703, is close to 700, so 1,203 is far too large.
Answer: 36 (also accepted: $36, 36 dollars)
Each friend spends 6 + 3 = 9 dollars. 4 friends spend 4 × 9 = 36 dollars.
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
A full lesson with slides, activities and an exit ticket on two-step word problems with four operations, pitched to grade 3 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 3.OA.D.8 with an answer key, ready in about a minute.
Make a worksheet →Turn two-step word problems with four operations into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Students represent two-step problems with equations in which a letter stands for the unknown quantity, for example 6 × 9 - 38 = r.
Students are expected to check whether answers are reasonable using mental computation and estimation, including rounding (see 3.NBT.A.1).