Expressions and structure
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
Evaluate 2³ + 3 × 4.
Check 2
Which expression is equivalent to 2(a + 5) + 3a?
Challenge 1
A museum charges $6 per child and $9 per adult. Write an expression for c children and a adults; evaluate it for c = 8 and a = 3.
Show a hint
Multiply each group count by its own ticket price, then add.
Show the worked solution
6c + 9a; $75.
For eight children and three adults, 6 × 8 + 9 × 3 = 48 + 27 = 75. The two variables represent different counts.
Challenge 2
A learner says 4(x + 2) = 4x + 2 because it works when x = 0. Evaluate both sides at zero, then correct and justify the identity.
Show a hint
Check the claimed evidence before using distribution.
Show the worked solution
At x = 0 the sides are 8 and 2, so the claim is false. The correct identity is 4(x + 2) = 4x + 8.
Distribution multiplies both x and 2 by four. A claimed matching input must actually be checked; even a genuine match at one input would not prove an identity.
Decide what to revisit
If a method was difficult to explain, return to that lesson and schedule a recall check. Unit-review answers are not saved as a score.
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