YOUR NEXT DISCOVERY

Exponents and Order of Operations in Maths

Read powers. Choose each step. Explain your answer.

5 Units22 MissionsAbout 4 hoursCourse map

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A square of turquoise tiles sits beside three separate tile layers and a golden raised marker. A playful invitation to explore powers.
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Four shelves show grouping, powers, multiplication with division, then addition with subtraction.

A CLOSER LOOK

Understand a power

Read a calculation with confidence. Know which step comes next and why.

See it. Try it. Make it yours.

  1. Understand a power

  2. Explore different bases

  3. Choose the next operation

Beginners aged 10 and above, including learners with limited English. · What to know before you start

Bring with you: Add, subtract, multiply and divide small whole numbers. Read the signs +, −, ×, ÷ and =. Recognise simple fractions. Add and multiply simple fractions and decimals. Short reminders are included. Read short English sentences with support if needed. No knowledge of exponents or operation order is assumed.

Read a calculation with confidence. Know which step comes next and why.

Understand repeated factors, whole-number powers, fraction and decimal powers, and every step in a mixed calculation. Explain grouping, spot mistakes and write expressions for real situations.

By the end, you can…

  • Read a power and explain its repeated factors.
  • Calculate powers of whole numbers, fractions and decimals.
  • Use grouping and the order of the four operations.
  • Use powers, nested groups and fraction bars in mixed expressions.
  • Write expressions, compare methods and repair mistakes.

For another Course

  • Negative or fractional exponents, logarithms, roots, scientific notation and general algebraic exponent laws.
  • Negative bases and signed-number arithmetic. These need a separate introduction to negative numbers.
  • The expression 0⁰ and ambiguous calculator strings such as 8÷2(2+2). Grouping is always explicit.

YOUR LEARNING PATH

One idea leads to the next.

0 of 22 Missions completed or proven
Unit 1

Understand a power

Read a power and explain its repeated factors.

  1. The same factor againMission 1 of 22Locked. Tell repeated multiplication from repeated addition.
  2. Read the small raised numberMission 2 of 22Locked. Name the base and exponent and expand a power.
  3. Squares and cubesMission 3 of 22Locked. Connect second and third powers to arrays and layers.
  4. One factor and a zero baseMission 4 of 22Locked. Distinguish exponent 1, base 1 and base 0.
Unit 2

Explore different bases

Calculate powers of whole numbers, fractions and decimals.

  1. Powers of tenMission 5 of 22Locked. Connect powers of ten with place value.
  2. Why a zero power is oneMission 6 of 22Locked. Explain the zero-power rule for a nonzero base.
  3. Powers of fractionsMission 7 of 22Locked. Raise the whole fraction to a power.
  4. Powers of decimalsMission 8 of 22Locked. Use equal parts to explain decimal powers.
  5. Will the power grow or shrink?Mission 9 of 22Locked. Compare powers by checking the base and exponent.
Unit 3

Choose the next operation

Use grouping and the order of the four operations.

  1. Why operation order mattersMission 10 of 22Locked. Read an expression as a precise calculation.
  2. Brackets keep a group togetherMission 11 of 22Locked. Evaluate a bracketed group before using its result.
  3. Multiply and divide: go left to rightMission 12 of 22Locked. Handle multiplication and division at equal priority.
  4. Add and subtract: go left to rightMission 13 of 22Locked. Handle addition and subtraction at equal priority.
  5. Combine the four operationsMission 14 of 22Locked. Choose operations by priority and position.
Unit 4

Put the rules together

Use powers, nested groups and fraction bars in mixed expressions.

  1. Put powers in their placeMission 15 of 22Locked. Evaluate powers after groups and before multiplication.
  2. Groups inside groupsMission 16 of 22Locked. Work from the innermost group outward.
  3. A fraction bar is a grouping signMission 17 of 22Locked. Evaluate the top and bottom groups before dividing.
  4. Fractions and decimals in mixed expressionsMission 18 of 22Locked. Apply the same order to fraction and decimal bases.
Unit 5

Explain and apply

Write expressions, compare methods and repair mistakes.

  1. Write the calculation for a situationMission 19 of 22Locked. Choose grouping and powers from a concrete situation.
  2. Same numbers, different expressionsMission 20 of 22Locked. Compare expressions by their exact grouping and values.
  3. Find the first wrong stepMission 21 of 22Locked. Identify and repair the first invalid change.
  4. Make every step countMission 22 of 22Locked. Choose, calculate and explain mixed expressions independently.Mastery Challenge

A Debsie Course · Beginners aged 10 and above, including learners with limited English.