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Line Up Task Original Task Extension Ideas Task 1Task 2 Task 3Task 4Task 5Task 6 Task 7Task 8Task 9 NC Level 3 to 7

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Line Up Original Four numbers are equally spaced on a number line. Find the numbers represented by P and Q Home 75PQ120

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Line Up Home Easier Let the outside numbers be both even or odd and find the middle number Let one of the outside numbers be odd and one even and find the middle Variation Make the biggest – smallest a multiple of 3 and find P and Q Make the biggest – smallest a multiple of 4 and find P, Q and R etc… Present the problem as split the line in the ratio 2:1 … orthe first gap is twice as large as the second Use negative numbers or decimals If 80 is in the middle then what could P and Q be? What is the link between P, Q and 80? P+Q = 2x80 Find P P80Q 3050Q 2028Q

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Line Up Home Extension If P and Q are integers what could the outside numbers be? As above but insert P, Q and R equally spaced Looking at the diagram below what could P and Q be? What is the rule for finding pairs of values for P and Q? 2(Q-P)=120-Q or 3Q = 120+2P etc… Try different number of spacings Express the problem as a ratio: If PQ: QR = 3:1 then what could P,Q & R be? Include Negative numbers Decimals Fractions PQ120 PQR ½P¾

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Three numbers are equally spaced on a number line. Find the number represented by P Line Up 1 Change the outer values: Both even Both odd Odd/Even Change the outer values: Both even Both odd Odd/Even Home 60P120

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Four numbers are equally spaced on a number line. Find the numbers represented by P and Q Home 75PQ120 Line Up 2 Change the outer values Use Negatives Extend to P, Q and R Change the outer values Use Negatives Extend to P, Q and R

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Four numbers are placed on a number line. Find the numbers represented by P and Q Home 75PQ129 Line Up 3 Change the outer values Use negatives Express the position of P and Q in terms of ratios Extend to P, Q and R Change the outer values Use negatives Express the position of P and Q in terms of ratios Extend to P, Q and R

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The difference between P and Q is 140 Find the numbers represented by P and Q Home Line Up 4 Change the outer values Use Negatives Extend to P, Q and R Change the outer values Use Negatives Extend to P, Q and R P 0 Q

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Three numbers are equally spaced on a number line. Find possible values for P and Q What is the relationship between P and Q Line Up 5 Change the centre number Make the centre number negative Change the centre number Make the centre number negative Home P60Q

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Numbers are equally spaced on a number line. Find the numbers represented by P & Q Line Up 6 Change the 75 and 89 Change the position of P & Q Introduce negatives Change the 75 and 89 Change the position of P & Q Introduce negatives Home 7589PQ

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Three numbers are equally spaced on a number line. Find the number represented by P Line Up 7 Change the outer values Introduce P & Q Change the outer values Introduce P & Q Home 1/2P3/4

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Numbers are equally spaced on a number line. Find possible values for P and Q What is the relationship between P and Q Line Up 8 Change the 120 Home PQ120

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Numbers are equally spaced on a number line. Find possible values for P and Q What is the relationship between P and Q Line Up 9 Vary the number of increments Change the 120 Introduce R Vary the number of increments Change the 120 Introduce R Home PQ120

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Note 8– Sine Rule The “Ambiguous Case”

Note 8– Sine Rule The “Ambiguous Case”

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