Enhancing Decimal Skills: Length Reasoning Practice

Reasoning With Lengths This resource is intended to provide extra practice and examples based on the resources found on Don Steward s Median blog: https://donsteward.blogspot.com/search/label/lengths These resources have been used as AO2 practice for addition/subtraction of decimals, as well as isolating finding missing lengths before introducing compound area/perimeter of rectilinear shapes. A suggested use is outlined below: Consolidation/Assessment: The consolidation sheet can be used either as an assessment tool to direct pupils to specific skills or to assess after. The skills in each section are outlined below: Sheet 1: Finding a missing length with three lengths Sheet 2: Finding missing lengths with extra information Sheet 3: Finding three lengths given the total and overlaps Sheet 4: Finding a missing length using information not labelled on the diagram Sheet 5: Finding a missing length by extending beyond the lines given

Consolidation/Assessment In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. 1) 20km a 2) 5.4m b 3.8m 12.3km 4.6km 4) 3) 97.3ft 76.1cm 132.9ft 176.8ft f c d e 143.9ft 52.9cm 55.8cm 5) 83.18mm 65.12mm 39.86mm g

Sheet 1 In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. a = 6.25 - 4.1 a = 2.15m e.g. a 6.25m 28cm 13cm 4.1m b c 63ft 17ft 42.7m d 18.3m 10.4km e 6p 36.02km p Write an expression for f in terms of p f 4k Write an expression for g in terms of k g 3k

Sheet 2 In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. e.g. 16km a = 16 4.3 a = 11.7km a 28cm 10.3km 9cm 4.3km 10cm b 45ft 10ft 73ft c 42.7m 55.6ft d 18.3m 10.4km e 13.1km f 20.3km 16p 3p 9p 8k g Write an expression for g in terms of k 11k Write an expression for f in terms of p 5k

Sheet 3 In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. e.g. a = 28.5 21.37 a = 6.8cm 28.5cm b = 19.4 6.8 b = 12.6cm 42cm a b c c = 28.5 19.4 c = 9.1cm e f d 21.37cm 28cm 19.4cm 30cm i 97ft h 135ft 98ft 68.4m g 82.9m j k l p 36.3m n m 102km 12p 75.1km 62.3km 16p 5k q r s 9p x 13k 17k Write an expression for x, y and z in terms of k y 11k Write an expression for q, r and s in terms of p z

Sheet 4 In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. e.g. 32.9 26.2 = 6.7 32.9 29.05 = 3.85 32.9ft 15cm 26.2ft a 32.9ft 6.7 + 3.85 = 10.55 14cm a = 32.9 10.55 a = 22.35ft 29.05ft 18cm b 9cm c 64ft 74ft 49ft 53.5m 59ft 54.56m 70.4m d 33.96m 7km 6.2km e f 9.9km 9.4km 25p 22p 14p 16p 12k Write an expression for g in terms of k g 19k 14k 10k Write an expression for f in terms of p

Sheet 5 In each question, all the dashed lines are parallel to each other. All the solid lines are also parallel to each other. 37.5mm e.g. 28.4mm 17.8mm 23cm a a = (28.4 + 17.8) 37.5 a = 46.2 37.5 a = 8.7mm 27cm 14cm b 109ft 129ft c 53ft d 74m 60.8m 39.9m 22km 19.8km e 32.1km f 29.2km 35p 28p 22p 23p 178k Write an expression for g in terms of k 283k g 205k 149k Write an expression for f in terms of p

Answers Consolidation/Assessment b) 15.4km e) 20.3cm g) 21.8mm a) 1.6m d) 32.6cm c) 23.2cm f) 100ft Sheet 1 b) 15cm c) 46ft d) 24.4m e) 46.42km f) 5p g) 7k Sheet 2 b) 19cm c) 28ft d) 24.4m e) 30.7km f) 12p g) 13k Sheet 3 e) 16cm h) 60ft k) 32.1m n) 35.4km r) 5p y) 7k d) 12cm g) 38ft j) 36.3m m) 39.9km q) 7p x) 6k f)14cm i) 37ft l) 14.5m p) 26.9km s) 4p z) 4k Sheet 4 b) 11cm c) 48ft d) 37.66m e) 12.3km f) 23p g) 15k Sheet 5 b) 10cm c) 31ft d) 26.7m e) 39.3km f) 30p g) 227k