Level Five > Number and Algebra

AO2: Use prime numbers, common factors and multiples, and powers (including square roots).

Children

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Two's Company

This unit presents students with several problems that develop the idea of binary (base two) arithmetic. In the course of solving the problems, students are required to look for patterns and relationships and describe them using symbols and mathematical language.

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Building as a General Rule

In this unit we are paying close attention to the general rule of a pattern for the first time. We look at odd and even numbers as well as multiples of small numbers. We also look at squares and cubes of numbers and see that it is possible to make more than one pattern from the same three initial terms.

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Powers of Seven

Solve problems that involve finding powers of a number

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Base 3

Write numbers in base 3

Do arithmetic in base 3

Explain the "links" between base 3 and decimal numbers

Devise and use problem solving strategies to explore situations mathematically (be systematic).

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Spheres

use powers and take square and cube roots (with or without a calculator)

devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram, use smaller cases).

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Doubling Up

Perform calculations with powers of numbers and square roots

Explain the relation between a square root and a square.

Devise and use problem solving strategies to explore situations mathematically. This problem uses be systematic, draw a picture, and think.

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My Son is Naughty

Find factors of numbers

Work systematically

Use logic to explain away certain possible number combinations.

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Square and Cube Roots

The fact that squaring and square roots are inverses is explored geometrically and numerically. Gauss’ method of determining square roots when only squares are available is developed. Finally a powerful method of calculating square roots that produces answers to any desired accuracy quickly is shown.

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Babylonian Mathematics I

This unit uses a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. This same catalyst is also used for the unit: Babylonian Mathematics 2. Areas under enlargement are discussed in the present unit, and lying behind the various activities in both these units is the idea of incommensurability, which means, roughly, ‘things which cannot be measured no matter how accurate the ruler’.

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Square Roots

Solve problems that involve exponents and square roots.

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Squaring

Solve problems that involve exponents and square roots.

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Cubes and Cube Roots

Solve problems that involve exponents and square roots.

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Recurring and Terminating Decimal Fractions

Solve problems by finding the prime factors of numbers.

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Prime Numbers

Solve problems by finding the prime factors of numbers.

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The Sieve of Eratosthenes

Solve problems by finding the prime factors of numbers.

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Factor Trees

Solve problems by finding the prime factors of numbers.

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Lowest Common Multiples

Identify highest common factors and least common multiples.

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Highest Common Factors

Identify highest common factors and least common multiples.

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Writing Very Large Numbers

Solve problems that involve exponents and square roots.

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Powerful Numbers

Solve problems that involve exponents and square roots.

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Digits on the Move

Know what happens when a number is multiplied or divided by a power of 10.

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Locating Square Roots

Solve problems that involve exponents and square roots.

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Systematic Prime Factorisation

Solve problems by finding the prime factors of numbers.

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The Five Number Game

Explain what it means to square number.

Explain what it means to cube a number.

Define prime numbers using their own language.

Devise and use problem solving strategies (use equipment).

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Thinking Inside the Square

These exercises, activities and learning activities are designed for students to use independently or in small groups to practise number properties. Some involve investigation and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity. The exercises can also be used as teaching activities with similar supporting work for students.

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The difference of two squares

These exercises and activities are for students to use independently of the teacher to practice number properties

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Powers of Numbers

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation and may become longer and more involved tasks with consequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

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Powers of Investigations

These investigations are designed for students to use in small groups to practise number properties. Some may become longer and more involved tasks with consequent recording/reporting. The time for each investigation will vary but is suitable for a 10 to 20 minute learning episode. These investigations target the higher level creative thinking skills.

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Base 2 and complementary arithmetic

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute independent activity. While the involve operating with number, the contexts for the number operations in these exercises are not formally in the curriculum, and are therefore most suitable as ‘broadening’ or extension work with more able students.

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Primates

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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Using Exponents

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

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