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Grade 8 Data Handling Worksheets β€” Two-Way Records and Frequency

Eighth grade sorts data two ways at once. "Travel to school. Walk: 12 boys, 9 girls. Bus: 8 boys, 11 girls." holds four numbers that can be totalled along two different directions, and every question on these sheets needs at least one of those totals β€” none of them can be answered by copying a figure that is already printed.

Relative frequency follows from it: once a group total exists, the part can be expressed as a fraction, a percentage or a decimal, and the three levels of that sub-skill ask for one each.

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Data Handling Β· Grade 8

Grade
Topic
SkillEach skill is a different kind of question, with its own levels.
Level
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10

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Grade 8 Β· 3 pages Β· A4

Data Handling Practice

Grade 8 β€’ Two-Way Records β€’ Down a column
Name:Date:

Add the numbers in the group named and write the total.

  1. 1) Lunch taken. Packed: 17 juniors, 10 seniors. Hot: 23 juniors, 29 seniors. How many juniors are there in all?
    Answer:
  1. 2) Lunch taken. Packed: 11 juniors, 28 seniors. Hot: 33 juniors, 17 seniors. How many juniors are there in all?
    Answer:
  1. 3) Travel to school. Walk: 9 boys, 16 girls. Bus: 26 boys, 11 girls. How many boys are there in all?
    Answer:
  1. 4) Club chosen. Art: 34 Year 7, 19 Year 8. Chess: 40 Year 7, 11 Year 8. How many Year 8 are there in all?
    Answer:
  1. 5) Club chosen. Art: 8 Year 7, 11 Year 8. Chess: 14 Year 7, 29 Year 8. How many Year 8 are there in all?
    Answer:
  1. 6) Travel to school. Walk: 8 boys, 11 girls. Bus: 24 boys, 31 girls. How many boys are there in all?
    Answer:
  1. 7) Homework done. On time: 40 boys, 33 girls. Late: 5 boys, 7 girls. How many boys are there in all?
    Answer:
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Page 1 of 3

Add the numbers in the group named and write the total. (continued)

  1. 8) Homework done. On time: 35 boys, 34 girls. Late: 14 boys, 37 girls. How many girls are there in all?
    Answer:
  1. 9) Lunch taken. Packed: 4 juniors, 31 seniors. Hot: 16 juniors, 5 seniors. How many juniors are there in all?
    Answer:
  1. 10) Travel to school. Walk: 8 boys, 34 girls. Bus: 16 boys, 32 girls. How many boys are there in all?
    Answer:
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Page 2 of 3

Answer Key

  1. 1. 40
  2. 2. 44
  3. 3. 35
  4. 4. 30
  1. 5. 40
  2. 6. 32
  3. 7. 45
  4. 8. 71
  1. 9. 20
  2. 10. 24
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Page 3 of 3

What each level generates

Grade 8 two-way records β€” the exact skill behind each difficulty setting, straight from the generator.

  1. Level 1Along a row
  2. Level 2Down a column
  3. Level 3Row against column

Grade levels follow the progression common to most English-language curricula β€” not one specific national curriculum. Every level shows exactly what it generates, so you can check the fit with your own program. See the full scope & sequence β†’

Why every question needs a total

The failure mode of a two-way data question is that it can be answered by retrieval. "How many girls walk?" is printed in the record, so a child answers it without ever engaging with the second dimension. Every question here asks for a row total, a column total, a grand total or a comparison between two of them, so the structure has to be used.

The third level goes further and asks whether a row total or a column total is larger, which requires both to be computed and neither to be guessed. That is the reading a two-way record exists to teach.

Relative frequency is data, not chance

Relative frequency sits on a boundary that is worth being explicit about. Asked about spins of a spinner or rolls of a dice, it is probability β€” a chance process observed over the long run. Asked about a surveyed group, it is data: a part of a whole that has already been counted.

Every item here is the second kind. The sheets ask what fraction of the pupils surveyed chose something, never what fraction of the spins came up red, and no question on this topic mentions a spinner, a dice or a coin. That keeps the boundary clean, and the Probability pages for Grades 4 to 8 now occupy the other side of it: every question there is about a chance process that has not happened yet, and neither page had to move.

Frequently asked questions

β–ΈWhat is a two-way record?

Data sorted by two things at once β€” for example, how pupils travel and whether they are boys or girls. Each entry belongs to one row and one column, so the same four numbers can be totalled in two different directions.

β–ΈWhat is relative frequency?

The part divided by the whole. If 40 children were asked and 12 chose walking, the relative frequency of walking is 12 out of 40 β€” which is 3/10 as a fraction, 30% as a percentage, or 0.3 as a decimal.

β–ΈWhich form should the answer be in?

The instruction line on each sheet says. The three levels ask for a simplified fraction, a percentage and a decimal in turn, so the required form is never ambiguous.

β–ΈIs relative frequency the same as probability?

They are closely related but these sheets stay on the data side. Every question is about a group that has already been surveyed, not about a chance process like a spinner or a dice. The chance side is covered on the Probability pages for Grades 4 to 8.

β–ΈDo the sheets show a drawn two-way table?

No β€” the record is written out in words, with each row and its two entries stated in turn. The reading is the same; the layout is not a printed grid.

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