Source: https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-1-1-problem-solving-with-measures [Revision notes](https://senecalearning.com/en-gb/revision-notes.md) › [Primary](https://senecalearning.com/en-gb/revision-notes/primary.md) › [Maths](https://senecalearning.com/en-gb/revision-notes/primary/maths.md) › [Maths: Year 5 & 6 National Curriculum](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum.md) › Problem Solving with Measures # Problem Solving with Measures Maths: Year 5 & 6 National Curriculum, topic 8.1.1 ## Remembering Key Facts You need to remember some key facts in order to answer problem solving questions in measures. Let's recap some of the key facts: ### Conversion of units ![Conversion of units](https://image-v2.cdn.app.senecalearning.com/2018-05/a1ee7110-2869-4cf6-80b7-099d01c5f458/shutterstock_555956572.jpg) - Remember that: - 1,000 g = 1 kg - 1,000 m = 1 km - 1,000 ml = 1 l ### Units of length ![Units of length](https://image-v2.cdn.app.senecalearning.com/2019-08/631e5dd4-9544-4d14-a62c-8c20b8934b98/Slides%20(72).png) - Remember that: - 10 mm = 1 cm - 100 cm = 1 m - 1,000 m = 1 km ## Problem Solving Questions in Measures Let's have a look at some examples of problem solving questions involving measures before you can have a go at your own. ### Question 1 ![Question 1](https://image-v2.cdn.app.senecalearning.com/2019-08/5f95cc43-015e-4fed-983e-71213e2ef8c8/Slides%20(4).png) - When Year 6 measure the length of different ropes they find one is 1.3 m long. - The other is 500 cm long. - What is the total length of both of these ropes? ### First step ![First step](https://image-v2.cdn.app.senecalearning.com/2019-08/356be3ae-bb67-4e67-bcfc-bd8f1d847065/Slides%20(2).png) - Both lengths need to be in the same units to be able to add them together. - Convert the length of rope 2 into metres. ### Then add the rope lengths ![Then add the rope lengths](https://image-v2.cdn.app.senecalearning.com/2019-08/012a6b55-c8d0-4885-a54a-a7e70994516d/Slides%20(5).png) - Now that the rope lengths are in the same units, you can add them together. - The total length of both ropes is 1.3 m + 5 m = 6.3 m ### Question 2 ![Question 2](https://image-v2.cdn.app.senecalearning.com/2019-08/76a45c4f-61be-4e82-9347-17d90ab62f3d/Slides%20(6).png) - There are 3 children swimming lengths in a swimming pool. - One child swims 50.7 m, another swims 4700 cm and the other swims 10 m. - How far did the children swim altogether? ### First step ![First step](https://image-v2.cdn.app.senecalearning.com/2019-08/c6e59026-c61b-4dcb-b51b-e0a6b031c96e/Slides%20(7).png) - All distances need to be in the same units to be able to add them together. - Convert child 2's distance into metres ### Then add the distances ![Then add the distances](https://image-v2.cdn.app.senecalearning.com/2019-08/629a2a8a-b254-498b-ae1d-95f9e8268e06/Slides%20(8).png) - Now that the distances are in the same units, you can add them together. - The total distance the children swam is 50.7 m + 47 m + 10 m = 107.7 m - You could use column addition to work out the answer. ## Test yourself on Problem Solving with Measures - How many centimetres are in 1 m? - How many millimetres are in 1 cm? - How many metres are in 1 km? - How many grams are in 1 kg? - How many millilitres are in 1 l? [Practise this topic for free](https://app.senecalearning.com/classroom/course/cc410aae-4be5-4c7a-9492-ee552574ade2/section/36375575-4c41-45bf-8071-c1c7b3a389f5/session) - Previous topic: [7.3.2 Combining Two Variables](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-3-2-combining-two-variables.md) - Next topic: [8.2.1 Conversion Between Miles & Kilometres](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-2-1-conversion-between-miles-and-kilometres.md) ## Maths: Year 5 & 6 National Curriculum contents ### 1 Year 5 - Number - 1.1 Number & Place Value - [1.1.1 The Value of Digits to Millions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-1-the-value-of-digits-to-millions.md) - [1.1.2 Smallest & Biggest Numbers to Millions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-2-smallest-and-biggest-numbers-to-millions.md) - [1.1.3 Ordering Numbers to Millions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-3-ordering-numbers-to-millions.md) - [1.1.4 Counting in Powers of 10](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-4-counting-in-powers-of-10.md) - [1.1.5 Counting in Negative Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-5-counting-in-negative-numbers.md) - [1.1.6 Rounding Numbers up to 1,000,000](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-6-rounding-numbers-up-to-1000000.md) - [1.1.7 Reading Roman Numerals](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-1-7-reading-roman-numerals.md) - 1.2 Addition & Subtraction - [1.2.1 Written Methods for Adding Large Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-2-1-written-methods-for-adding-large-numbers.md) - [1.2.2 Written Methods for Subtracting Large Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-2-2-written-methods-for-subtracting-large-numbers.md) - [1.2.3 Mental Addition & Subtraction](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-2-3-mental-addition-and-subtraction.md) - [1.2.4 Rounding to Check Your Answer](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-2-4-rounding-to-check-your-answer.md) - 1.3 Multiplication & Division - [1.3.1 Multiples](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-1-multiples.md) - [1.3.2 Factors](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-2-factors.md) - [1.3.3 Prime Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-3-prime-numbers.md) - [1.3.4 Prime Factors](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-4-prime-factors.md) - [1.3.5 Composite Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-5-composite-numbers.md) - [1.3.6 Factor Trees](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-6-factor-trees.md) - [1.3.7 Multiplication by a 1 Digit Number](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-7-multiplication-by-a-1-digit-number.md) - [1.3.8 Long Multiplication Using Column Method](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-8-long-multiplication-using-column-method.md) - [1.3.9 Times Tables](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-9-times-tables.md) - [1.3.10 Division](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-10-division.md) - [1.3.11 Multiplying & Dividing by 10, 100 & 1,000](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-11-multiplying-and-dividing-by-10-100-and-1000.md) - [1.3.12 Square & Cube Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-3-12-square-and-cube-numbers.md) - 1.4 Fractions & Decimals - [1.4.1 Compare & Order Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-1-compare-and-order-fractions.md) - [1.4.2 Identifying Equivalent Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-2-identifying-equivalent-fractions.md) - [1.4.3 Add & Subtract Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-3-add-and-subtract-fractions.md) - [1.4.4 Mixed Numbers & Improper Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-4-mixed-numbers-and-improper-fractions.md) - [1.4.5 Multiplying Fractions by Whole Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-5-multiplying-fractions-by-whole-numbers.md) - [1.4.6 Converting Between Decimals & Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-6-converting-between-decimals-and-fractions.md) - [1.4.7 Rounding Decimals](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-7-rounding-decimals.md) - [1.4.8 Ordering Decimals](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/1-4-8-ordering-decimals.md) ### 2 Year 5 - Measurement - 2.1 Measures - [2.1.1 Metric Measurements](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/2-1-1-metric-measurements.md) - [2.1.2 Imperial Measurements](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/2-1-2-imperial-measurements.md) - 2.2 Perimeter & Area - [2.2.1 Perimeter](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/2-2-1-perimeter.md) - [2.2.2 Area](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/2-2-2-area.md) - 2.3 Time - [2.3.1 Units of Time](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/2-3-1-units-of-time.md) ### 3 Year 5 - Geometry - 3.1 Properties of 3D Shapes - [3.1.1 Types of 3D Shapes](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-1-1-types-of-3d-shapes.md) - [3.1.2 Faces, Edges & Vertices](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-1-2-faces-edges-and-vertices.md) - 3.2 Properties of 2D Shapes - [3.2.1 Polygons](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-2-1-polygons.md) - 3.3 Angles - [3.3.1 Angles in Degrees](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-3-1-angles-in-degrees.md) - [3.3.2 Types of Angle](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-3-2-types-of-angle.md) - [3.3.3 Finding Missing Angles](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-3-3-finding-missing-angles.md) - 3.4 Position & Direction - [3.4.1 Reflection & Translation](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/3-4-1-reflection-and-translation.md) ### 4 Year 5 - Statistics - 4.1 Graphs - [4.1.1 Line Graphs](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/4-1-1-line-graphs.md) - [4.1.2 Tables](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/4-1-2-tables.md) - [4.1.3 Timetables](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/4-1-3-timetables.md) ### 5 Year 6 - Number - 5.1 Number & Place Value - [5.1.1 The Value of Digits to Ten Millions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-1-1-the-value-of-digits-to-ten-millions.md) - [5.1.2 Ordering Numbers to Millions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-1-2-ordering-numbers-to-millions.md) - [5.1.3 Rounding](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-1-3-rounding.md) - [5.1.4 Negative Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-1-4-negative-numbers.md) - 5.2 Multiplication & Division - [5.2.1 Multiplication by a 2 Digit Number](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-2-1-multiplication-by-a-2-digit-number.md) - [5.2.2 Division](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-2-2-division.md) - [5.2.3 Multiples](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-2-3-multiples.md) - [5.2.4 Factors](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-2-4-factors.md) - [5.2.5 Primes](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-2-5-primes.md) - 5.3 Mental Maths - [5.3.1 Multiplying & Dividing by 10, 100 & 1,000](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-3-1-multiplying-and-dividing-by-10-100-and-1000.md) - [5.3.2 Addition & Subtraction](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-3-2-addition-and-subtraction.md) - [5.3.3 Adding & Subtracting 10, 100 & 1,000](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-3-3-adding-and-subtracting-10-100-and-1000.md) - [5.3.4 Multiplication & Division](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-3-4-multiplication-and-division.md) - 5.4 Order of Operations - [5.4.1 BIDMAS](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-4-1-bidmas.md) - 5.5 Problem Solving - [5.5.1 Addition & Subtraction Multi-step Problems](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-5-1-addition-and-subtraction-multi-step-problems.md) - [5.5.2 Problem Solving with Proportion](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-5-2-problem-solving-with-proportion.md) - 5.6 Fractions & Decimals - [5.6.1 Simplifying Fractions Using Equivalents](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-1-simplifying-fractions-using-equivalents.md) - [5.6.2 Ordering Different Types of Fraction](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-2-ordering-different-types-of-fraction.md) - [5.6.3 Adding & Subtracting Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-3-adding-and-subtracting-fractions.md) - [5.6.4 Adding & Subtracting Mixed Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-4-adding-and-subtracting-mixed-numbers.md) - [5.6.5 Multiplying Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-5-multiplying-fractions.md) - [5.6.6 Dividing Fractions by Whole Numbers](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-6-dividing-fractions-by-whole-numbers.md) - [5.6.7 Converting Between Decimals & Fractions](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-7-converting-between-decimals-and-fractions.md) - [5.6.8 Dividing Decimals](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/5-6-8-dividing-decimals.md) ### 6 Year 6 - Ratio & Proportion - 6.1 Ratio - [6.1.1 Using Ratios](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/6-1-1-using-ratios.md) - [6.1.2 Simplifying Ratios](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/6-1-2-simplifying-ratios.md) - 6.2 Percentages - [6.2.1 Calculating Percentages](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/6-2-1-calculating-percentages.md) - 6.3 Scale - [6.3.1 Scale of 2D Shapes](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/6-3-1-scale-of-2d-shapes.md) ### 7 Year 6 - Algebra - 7.1 Sequences - [7.1.1 Describing Sequences](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-1-1-describing-sequences.md) - [7.1.2 Finding Gaps in Sequences](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-1-2-finding-gaps-in-sequences.md) - 7.2 Missing Number Problems - [7.2.1 Missing Number Problems](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-2-1-missing-number-problems.md) - 7.3 Equations - [7.3.1 Balancing Equations](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-3-1-balancing-equations.md) - [7.3.2 Combining Two Variables](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/7-3-2-combining-two-variables.md) ### 8 Year 6 - Measurement - 8.1 Problem Solving - [8.1.1 Problem Solving with Measures](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-1-1-problem-solving-with-measures.md) - 8.2 Unit Conversion - [8.2.1 Conversion Between Miles & Kilometres](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-2-1-conversion-between-miles-and-kilometres.md) - 8.3 Perimeter, Area & Volume - [8.3.1 Area](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-3-1-area.md) - [8.3.2 Volume](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-3-2-volume.md) - [8.3.3 Nets](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-3-3-nets.md) - [8.3.4 Faces, Edges & Vertices](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-3-4-faces-edges-and-vertices.md) - 8.4 Angles - [8.4.1 Types of Angle](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-4-1-types-of-angle.md) - [8.4.2 Finding Missing Angles](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-4-2-finding-missing-angles.md) - [8.4.3 Finding Missing Angles in Triangles](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-4-3-finding-missing-angles-in-triangles.md) - [8.4.4 Vertically Opposite Angles](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-4-4-vertically-opposite-angles.md) - 8.5 Circles - [8.5.1 Parts of a Circle](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-5-1-parts-of-a-circle.md) - 8.6 Coordinate Grids - [8.6.1 Positions on Coordinate Grids](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-6-1-positions-on-coordinate-grids.md) - [8.6.2 Reflection & Translation](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/8-6-2-reflection-and-translation.md) ### 9 Year 6 - Statistics - 9.1 Displaying Data - [9.1.1 Pie Charts](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/9-1-1-pie-charts.md) - [9.1.2 Line Graphs](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/9-1-2-line-graphs.md) - 9.2 Averages - [9.2.1 Mean](https://senecalearning.com/en-gb/revision-notes/primary/maths/maths-year-5-and-6-national-curriculum/9-2-1-mean.md)