Brianna had $12. She spent $4 on dinner and $3 on dessert. How much did Brianna have left?
Elvin had $12 for dinner. He spent $4 on a sandwich and then his friend gave him $3. How much did Elvin have left?
Same 3 numbers, same operations, same sequence: 12 – 4 + 3. Yet the solution to the two problems are different. Pairs of identical computations like these make it clear why we need an order of operations: without the context, either solution is correct. The order of operations take the place of the story – without those rules, every problem would have to become a story problem.
These are 10 pages with a variety of problems. All the sequences of operations like the one above are paired with the identical sequence, but with parentheses included. Students need to insert the parentheses according to the rules to arrive at the correct two solutions.
A second format gives the students multistep story problems. The students need to first solve the problem, then identify the single expression that combines the operations correctly. A third format requires students to read sequences of operations in English, and then either write or identify the single expression that represents those operations. These problems are seen on SBAC and PARCC assessments.
Common Core Standards:
3.OA.8: “Solve two-step word problems using the four operations…” 3
This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
5.OA.1: “Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.”
Subject: Math, Computation,
Level: Grade 4-5
Length/Duration: 24 pages of student work beginning with 1 by 2-digit problems
A Smart Notebook 14 file is also included.