Line Up Task

Original Task

Extension Ideas

Task 1 Task 2

Task 3 Task 4 Task 5 Task 6

Task 7 Task 8 Task 9

NC Level 3 to 7

Line Up Original

Four numbers are equally spaced on a number line.

Find the numbers represented by P and Q

Home

75 P Q 120

Line Up

Home

EasierLet the outside numbers be both even or odd and find the middle numberLet one of the outside numbers be odd and one even and find the middle

VariationMake the biggest – smallest a multiple of 3 and find P and QMake 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 …

or the first gap is twice as large as the secondUse 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 = 2x80Find P

P 80 Q

30 50 Q

20 28 Q

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 spacingsExpress the problem as a ratio: If PQ: QR = 3:1 then what could P,Q & R be?

Include Negative numbersDecimalsFractions

P Q 120

P Q R

½ P ¾

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

Home

60 P 120

Four numbers are equally spaced on a number line.

Find the numbers represented by P and Q

Home

75 P Q 120

Line Up 2

Change the outer valuesUse NegativesExtend to P, Q and R

Four numbers are placed on a number line.

Find the numbers represented by P and Q

Home

75 P Q 129

Line Up 3

Change the outer valuesUse negativesExpress the position of P and Q in terms of ratiosExtend to P, Q and R

The difference between P and Q is 140

Find the numbers represented by P and Q

Home

Line Up 4

Change the outer valuesUse NegativesExtend to P, Q and R

P 0 Q

Three numbers are equally spaced on a number line.

Find possible values for P and QWhat is the relationship between P and Q

Line Up 5

Change the centre numberMake the centre number negative

Home

P 60 Q

Numbers are equally spaced on a number line.

Find the numbers represented by P & Q

Line Up 6

Change the 75 and 89Change the position of P & QIntroduce negativesHom

e

75 89 P Q

Three numbers are equally spaced on a number line.

Find the number represented by P

Line Up 7

Change the outer valuesIntroduce P & QHom

e

1/2 P 3/4

Numbers are equally spaced on a number line.

Find possible values for P and QWhat is the relationship between P and Q

Line Up 8

Change the 120Home

P Q 120

Numbers are equally spaced on a number line.

Find possible values for P and QWhat is the relationship between P and Q

Line Up 9

Vary the number of incrementsChange the 120Introduce RHom

e

P Q 120