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Workbook 1 · Numbers and place value · Answer guide
Accept equivalent correct explanations. Invite the learner to show how they checked.
1. Draw or arrange 7 counters. Write its numeral and explain the difference between the quantity and its written symbol.
Seven is the quantity; 7 is one written representation. Other languages and numeral systems can represent the same quantity.
2. Show zero on a units rod. Why does an empty active area matter?
Zero has no active beads. It also preserves a position in a numeral: 205 differs from 25.
3. Expand 68 into place values. What does each active bead on the tens rod represent?
68 = 6 × 10 + 8 × 1. Each tens bead represents ten.
4. Read 205. Which rod is empty? Explain why the numeral still has three digits.
2 hundreds, 0 tens, 5 units. The zero tens digit preserves place value.
5. Show 3.4. Why is a tenths bead different in value from a units bead?
3 units + 4 tenths. Adjacent decimal places differ by a factor of ten.
6. Predict 9 + 1. Describe the exchange rather than simply writing 10.
Exchange ten units for one ten; zero units remain.
7. Is a larger bead ten times the area of its neighbour? Explain the design limitation.
No. Bead sizes are visual cues and are not proportional measures of their values.
8. In base four, how many beads are needed per position? What does 13 in base four mean in decimal?
Three beads per position. 13₄ = 1 × 4 + 3 = 7 in decimal.