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Hoshi coloured seven spaces on a calendar page to create an H-pattern. January Which sums between 80 & 90 are possible in an Manday Ternday Friday Saturday H-pattern on a calendar? 2 A. Calculate the sum of the numbers in the 7 9 10 H-pattern on the calendar page shown. 11 Repeat step "A" for THREE more H-patterns in 12 B. 13 14 15 16 17 other locations on the calendar page. 18 19 20 C. Describe, in words, how the sum of each 21 22 23 24 H-pattern is related to this middle number. 25 27 D. Consider the H-pattern shown above. Add TWO 29 30 31 numbers shaded with the same colour. How does the sum compare with the middle number in the H-pattern? Repeat for the two other pairs of shaded numbers. E. Repeat step D for each of your THREE H-patterns. F. Copy out and complete this H-pattern diagram, replacing each "?", with an an algebraic expression. ? ? N - 1 N N + 8 G.Use step D, E, or F to explain why your rule in step C is correct.

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