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from CambridgeMATHS Year 7 Chapter 2 uncorrected sample pages

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12 a Evaluate 32 × 42.

b Evaluate 122 c The rule a 2 × b 2 = (a × b)2 can be used to link 32 × 42 and 122. What are the values of a and b if 32 × 42 = 122? d Check this formula using other numbers. b Predict an answer for 11112 c Evaluate 11112 and test your prediction. b Add a new row to your table which gives the difference between each value and the previous one. c What patterns do you notice in the differences between consecutive square numbers? d Try to explain why these patterns occur. You could use a visual representation like dots arranged in squares, as below, to help illustrate.

13 a Evaluate 112 and 1112.

14 a List the square numbers from 12 to 202 in a table like the one below.

2H Number patterns CONSOLIDATING

Learning intentions

• To understand what a number pattern (or number sequence) is

• To be able to describe a pattern where there is a common difference (added or subtracted)

• To be able to describe a pattern where there is a common ratio (multiplied or divided)

• To be able to ﬁnd terms in a number pattern with a common difference or ratio

Past, present and future learning:

• This section consolidates and extends Stage 3 concepts

• It prepares students for future work in Linear Relationships in Stage 4 and beyond

• Expertise with these concepts may be required in non-calculator examinations such as NAPLAN and industry aptitude tests

Mathematicians commonly look at lists of numbers in an attempt to discover a pattern. They also aim to find a rule that describes the number pattern to allow them to predict future numbers in the sequence.

Here is a list of professional careers that all involve a high degree of mathematics and, in particular, involve looking at data so that comments can be made about past, current or future trends:

Statistician, economist, accountant, market researcher, nancial analyst, cost estimator, actuary, stock broker, data scientist, research scientist, nancial advisor, medical scientist, budget analyst, insurance underwriter and mathematics teacher!