Mixed Review and Exam Prep
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Learning Objectives
- 1Recall one key formula or rule from each major Grade 6 math unit
- 2Solve mixed review problems on integers, ratios, percent, geometry, statistics, and probability
- 3Apply test-taking strategies such as estimating first and checking units
- 4Identify which unit a problem belongs to before choosing a method
Mini Lesson
You have studied a lot of math this year: integers and the number line, ratios and proportions, percent, expressions and equations, geometry, statistics, and probability. An exam will mix all of these together on the same page. The trick is not to learn new content - it is to recognize which unit a question belongs to, then pull the right formula from memory.
A formula from each unit
- Integers: opposites cancel. -a + a = 0. On a number line, going left subtracts, going right adds.
- Ratios and rates: a : b = (a x k) : (b x k). To find a unit rate, divide both numbers by b. Example: 60 km in 2 h = 30 km / 1 h.
- Percent: percent of a number = (percent / 100) x number. 25% of 80 = 0.25 x 80 = 20.
- Expressions and equations: keep both sides equal. To solve x + 7 = 12, subtract 7 from both sides.
- Geometry: area of a parallelogram = b x h. Area of a triangle = (b x h) / 2. Volume of a rectangular prism = l x w x h.
- Statistics: mean = sum / n. Median = middle value when ordered. Mode = most frequent value.
- Probability: P(event) = favorable outcomes / total outcomes. Always between 0 and 1.
How to attack a mixed-review question
- Read the question twice and underline the question word: how many, what percent, find the area, etc.
- Decide which unit it belongs to. A "%" sign means percent. A picture of a shape means geometry. Numbers in a list usually means statistics.
- Write the matching formula in the margin BEFORE you start plugging numbers in.
- Estimate the answer with rounded numbers. If your final answer is far from the estimate, you made an error.
- Check units: cm, kg, %, $, m squared. A wrong unit is a wrong answer.
A bag has 3 red marbles and 7 blue marbles. What is the probability of drawing a red marble?
Total marbles = 3 + 7 = 10. Favorable = 3 red. P(red) = 3 / 10. As a percent that is 30%. Both answers are correct.
Common exam traps
- Reading "increase by 20%" as "= 20%". An increase by 20% on $50 is $50 + $10 = $60, not $10.
- Forgetting the divide-by-2 in the triangle area formula.
- Mixing up median and mean. Mean uses every value; median uses only the middle.
- Writing area in cm instead of cm squared, or volume in m squared instead of m cubed.
- Skipping a step under time pressure - then losing the part marks for showing work.
Tip: when you finish, do not put the pen down. Use leftover time to redo the two questions you felt least sure about. A quick second pass catches more marks than staring at the ceiling.
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