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LESSON PLAN

Order of Operations with Whole Numbers

A
Apothem Team
Grade 6 · Number
LESSON AT A GLANCE
Warm-up
5 min
Explore
15 min
Consolidate
10 min
Practice
12 min
Exit ticket
3 min

Warm-up

What is 3 + 4 x 2? Show two different evaluations: left to right (7x2=14) and multiplication first (3+8=11). Which is correct by convention? (11: multiplication before addition.) Now: what brackets would change the answer to 14? ((3+4)x2=14.) This demonstrates both the convention and how brackets override it.

Explore

Error hunt: each pair receives 8 worked expressions, 4 of which contain errors. They must identify correct and incorrect evaluations, find the error in each incorrect one, and correct it. Present their most interesting find to the class.

Consolidate

Practice

Students evaluate 8 expressions using BEDMAS, correct 4 student errors from worked examples, and write 2 real-world problems that produce specific expression structures. Exit ticket: evaluate 4 + (10 - 6) x 3 / 2.

Exit ticket

Students evaluate 8 expressions using BEDMAS, correct 4 student errors from worked examples, and write 2 real-world problems that produce specific expression structures. Exit ticket: evaluate 4 + (10 - 6) x 3 / 2.

TIP  Error analysis is more effective than additional practice. Showing a worked example with a deliberate error and asking students to find and fix it produces deeper understanding than a page of correct problems.
WORKED EXAMPLES
Evaluate: 20 - 3 x (2 + 4) + 8 / 4.

Brackets: 2+4=6. Then: 20 - 3x6 + 8/4. Multiplication/division: 3x6=18, 8/4=2. Then left to right: 20 - 18 + 2 = 4.

A student evaluates 15 - 9 / 3 as (15-9)/3 = 6/3 = 2. Is this correct?

No. Without brackets, division comes before subtraction: 15 - (9/3) = 15 - 3 = 12. The student incorrectly subtracted first. To get 2, brackets are needed: (15-9)/3=2.

MATERIALS
Order of operations error-analysis cards
Expression evaluation recording sheets
Calculator for checking complex evaluations
WATCH FOR
!Students may apply division and multiplication in the wrong order (right to left instead of left to right): 12/4x3 = 12/12 = 1 instead of 3x3=9. Emphasize left to right for same-priority operations.
!Students may treat subtraction as lower priority than addition. They have the same priority: work left to right.