PracticeQuestionsYears 1–7
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Problems with two unknowns

Year 6 · Upper Key Stage 2 · 6AS/MD-4 — Solve problems with two unknowns

Draft — awaiting teacher review

Builds on: Additive and multiplicative relationships (Year 6), Ratio and proportion (Year 6)

I

Concept Anchor

With two unknown numbers you need two facts. Draw a bar for each. Take away the difference first, then share what is left equally.

20??

Worked example

Two numbers add to 20. One is 6 more than the other.

  1. 1.Take off the extra 6: 20 − 6 = 14.
  2. 2.Now the two bars are equal: 14 ÷ 2 = 7.
  3. 3.The smaller is 7. The larger is 7 + 6 = 13.
  4. 4.Check: 13 + 7 = 20 and 13 − 7 = 6.
II

Guided Check

Two numbers add to 15. One is twice the other. What are they?

    III

    Independent Diagnostic Practice

    Q1Year 66AS/MD-4 — Sum and difference·Fluency·●●○Draft — awaiting teacher review

    Two numbers add to 20. Their difference is 6. What is the larger number?

    Q2Year 66AS/MD-4 — Two unknowns in context·Reasoning·●●●Draft — awaiting teacher review

    A pen and a pencil cost £1.20 together. The pen costs 80p more than the pencil. How much is the pencil?

    Q3Year 66AS/MD-4 — One is a multiple of the other·Problem Solving·●●●Draft — awaiting teacher review

    a+b=10a + b = 10 and a=4ba = 4b. What is the value of aa?