Systematic Listing · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Listing every combination

Mathematics · Algebra · ages 10-11
Name ______________________   Date ____________

  1. Mia is listing all meal combos from 2 starters (soup, salad) and 3 mains (pasta, pie, fish). She has written: soup with pasta, soup with pie. What should she write next to keep her list systematic?

    • salad with pasta
    • soup with fish
    • fish with salad
    • pie with soup

  2. A cafe has 3 sandwiches (cheese, tuna, egg) and 2 drinks (milk, juice). How many different lunch combos of one sandwich and one drink are there?

    • 5
    • 6
    • 8
    • 9

  3. A cafe has 2 soups and 3 sandwiches. How many soup-sandwich combinations are possible?

    • 6
    • 5
    • 7

  4. To find the total number of combinations, you multiply the number of options in each group.

    Circle one:   True   False

  5. Priya lists outfits from 4 tops and 3 skirts in a table, with tops down the side and skirts across the top. How many cells should the table have?

    • 12
    • 7
    • 4

  6. Ben has 3 breads (white, brown, roll) and 2 fillings (cheese, ham). Which list shows all 6 combos written systematically?

    • white+cheese, brown+ham, roll+cheese, white+ham, brown+cheese, roll+ham
    • white+cheese, white+ham, brown+cheese, brown+ham, roll+cheese, roll+ham
    • roll+ham, roll+cheese, white+cheese, white+ham, brown+ham, brown+cheese
    • white+cheese, brown+cheese, roll+cheese, brown+ham, roll+ham, white+ham

  7. A restaurant has 4 starters and 5 mains. How many different meals of one starter and one main can it serve?

    Answer: ______________

  8. A restaurant has 3 starters (soup, salad, bruschetta) and 4 mains (fish, chicken, pasta, beef). To list every combination systematically, what should you do first?

    • Write down random pairs until you get bored
    • Only list the mains, since starters don't matter
    • Pick one starter and pair it with every main before moving to the next starter

  9. A sandwich shop has 3 breads, 2 fillings, and 2 spreads. How many different sandwiches of one bread, one filling, and one spread can it make?

    • 7
    • 12
    • 18
    • 24

  10. Ben has 3 starters and 4 mains. He lists 11 combinations and says he's done. What went wrong?

    • Nothing, 11 is correct
    • He is missing one combination, since 3 x 4 = 12
    • He has too many, since 3 + 4 = 7
LightMySky · lightmysky.comW1-mt_gu0NPDvlhY-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Listing every combination W1-mt_gu0NPDvlhY-s1

  1. soup with fish · A systematic list finishes one starter before moving on, so she writes soup with fish next.
  2. 6 · Each of the 3 sandwiches can pair with 2 drinks, so 3 times 2 is 6 combos.
  3. 6 · Pair each of the 2 soups with each of the 3 sandwiches: 2 x 3 = 6.
  4. True · That's the rule: total combinations equal the two group sizes multiplied together.
  5. 12 · A table with 4 rows and 3 columns has 4 x 3 = 12 cells, one for each combination.
  6. white+cheese, white+ham, brown+cheese, brown+ham, roll+cheese, roll+ham · A systematic list keeps one choice fixed and goes through the other choice, then moves on, so no combo is missed or repeated.
  7. 20 · Each of the 4 starters pairs with each of the 5 mains, and 4 times 5 is 20.
  8. Pick one starter and pair it with every main before moving to the next starter · Working through one starter at a time with every main keeps the list organised and stops you missing or repeating pairs.
  9. 12 · First multiply the breads and fillings: 3 times 2 is 6. Each of those 6 can take either of 2 spreads, so 6 times 2 is 12.
  10. He is missing one combination, since 3 x 4 = 12 · Every starter should be paired with every main, giving 3 x 4 = 12 combinations, so Ben missed one.
Worksheet · LightMySky