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Fraction Classroom · 2.6.0 · Student pages

Translate a story into a grouped numerical expression

Write numerical expressions from short supply stories and explain how parentheses distinguish repeating a whole group from adding an amount once.

Anonymous group code: __________   Date: __________

Both stories have six kits and four pencils per kit. In the first, three markers are included in every kit. In the second, three markers are added once to the class total. Parentheses and operation placement record that difference.StoryRepeated unitExpressionObjects3 in each kit4 + 36 × (4 + 3)423 added once4(6 × 4) + 327
Both stories have six kits and four pencils per kit. In the first, three markers are included in every kit. In the second, three markers are added once to the class total. Parentheses and operation placement record that difference.

Start with a diagnostic

diagnostic. Two bags each contain 3 green beads and 1 yellow bead. Write one numerical expression for all the beads, then enter its value. Underline the part that describes one bag.

Build the idea

model. Six table kits each contain 4 pencils and 3 markers. Write a numerical expression for the total number of objects. How does it differ from a second story with 6 kits of 4 pencils and only 3 extra markers shared by the whole class?

  1. Read the first story and identify the repeated unit: one complete kit contains 4 pencils plus 3 markers. Write (4 + 3) and label it 'objects in one kit.' Ask learners to explain the parentheses before performing any arithmetic.
  2. Repeat the whole kit six times, writing 6 × (4 + 3). Connect the expression to six identical groups of seven objects. Its value is 42; multiplication applies to both kinds of objects in every kit.
  3. Read the second story and write (6 × 4) + 3. Circle six groups of four pencils, then a separate group of three markers added once. Its value is 27. Ask partners to point to the words that determine whether the three markers are inside or outside the repeated group.
  4. Check each operation against its verbal action, including its order. 'Subtract 3 from 12' means 12 - 3, not 3 - 12; 'share 12 among 3 equal groups' means 12 ÷ 3, not 3 ÷ 12. Reversing subtraction or division asks a different question. In a multi-action story, use parentheses to identify the quantity formed first and explain what the resulting group means.

Worked example: The first story is 6 × (4 + 3), which has value 42 objects. The second is (6 × 4) + 3, which has value 27 objects. In the first, every kit includes all seven objects; in the second, the three markers are added once after counting the 24 pencils. Explain that grouping difference before evaluating.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. Support: three kits each contain 2 pencils and 1 marker. Write a numerical expression for all the objects, then enter its value. Explain what belongs inside the repeated group.

p2. Core: share 18 ribbons equally among 3 tables, then give each table 2 more ribbons. Write an expression for the final number at one table, then enter its value. Explain why the added 2 is not part of the divisor.

p3. Challenge: remove 8 counters from a collection of 24, then share the remaining counters equally among 4 groups. Write the expression for counters in one group and enter its value. Explain why 24 - (8 ÷ 4) represents a different sequence.

e1. Independent check: five packs each contain 7 blue counters and 4 yellow counters. Combine all five packs, then remove 3 counters from the combined collection once. Write a single numerical expression, label the part for one pack and enter the final number of counters. Explain where the subtraction belongs.

Transfer the idea

transfer. Without first evaluating, explain the difference between (24 - 8) ÷ 4 and (24 ÷ 4) - 8. Which describes removing 8 counters from the full collection before sharing the rest equally among four groups?