Learn · Illustrative Mathematics · Grade 6 · Unit 4
Short lessons you can play with. Count groups of a fraction with pattern blocks and tape diagrams, find how much is in one group, see why dividing by a fraction means multiplying by its reciprocal, and use it for lengths, areas, and volumes, then check yourself. When you’re ready, practice in Fraction Workshop.
Eight chapters follow the unit’s lessons in order. Each step shows one idea with something to change, then a quick check. A wrong answer names the likely mistake and gives one more try. Fraction answers can be typed as 14/3, 4 2/3, or a close decimal.
Pattern blocks (a hexagon is 1 whole), tape diagrams cut into equal parts with the groups bracketed, double number lines when there are two amounts to track, rectangles tiled in small squares, and boxes filled with small cubes. Every division comes with the multiplication that checks it.
“How many groups?” (how many ¾-cup scoops are in 6 cups) and “How much in each group?” (5 cups fill ⅔ of a pitcher, so how much fills the whole pitcher). Most mistakes come from mixing up the two, so the steps keep asking what the groups are and what is known.
Besides the tape diagrams from class: hops along a ruler, rewriting both fractions with the same denominator (6 eighths ÷ 1 eighth is 6), estimating first (is the answer more or less than 1?), and multiplying back to check. “Flip and multiply” is built up from the pictures (multiply by the denominator, then divide by the numerator) rather than handed over as a rule.
Each chapter ends with a link to the matching station in Fraction Workshop, the practice game for this unit. Progress is saved on this device.
Lesson 17 (Fitting Boxes into Boxes) is a hands-on project, and Lesson 12’s info gap is a partner activity, so both work better in class.