## Measurement and Units for SATs Reasoning

Measurement is a key part of your Year 6 Maths SATs, especially in reasoning problems. You'll need to understand different units and how to convert between them, as well as calculate perimeter, area, and volume.

## Metric Units: Length, Mass, and Capacity

It's vital to know the common metric units and their conversions.

• Length:
• 1 centimetre (cm) = 10 millimetres (mm)
• 1 metre (m) = 100 centimetres (cm)
• 1 kilometre (km) = 1000 metres (m)
• Mass (Weight):
• 1 kilogram (kg) = 1000 grams (g)
• Capacity (Volume of liquid):
• 1 litre (l) = 1000 millilitres (ml)

Remember:

• To convert a larger unit to a smaller unit, you multiply. (e.g., metres to centimetres, multiply by 100)
• To convert a smaller unit to a larger unit, you divide. (e.g., grams to kilograms, divide by 1000)

## Time

You need to be confident with time conversions and calculations:

• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 day = 24 hours
• You should be able to read and interpret 12-hour and 24-hour clocks, and calculate durations. For example, knowing that 15:30 is 3:30 PM.

## Money

Calculations involving money often appear in reasoning questions. You'll need to work with pounds (£) and pence (p), remembering that £1 = 100p. Be careful with decimal places when converting between them (e.g., £2.50 is 250p).

## Perimeter, Area, and Volume

These are crucial geometric measurements:

• Perimeter: The total distance around the outside of a 2D shape. For a rectangle, it's 2 x (length + width). For compound shapes, add up all the side lengths.
• Area: The amount of surface a 2D shape covers.
• Rectangle: Area = length x width
• Triangle: Area = (base x height) ÷ 2
• Parallelogram: Area = base x perpendicular height
• Volume: The amount of space a 3D object occupies.
• Cuboid: Volume = length x width x height

## Reasoning Tips

• Read carefully: Understand what the question is asking.
• Identify units: Check which units are given and which unit the answer needs to be in.
• Show your working: This helps you track your steps and can earn partial marks.
• Estimate: Does your answer make sense?

## 2D and 3D Shapes

• 2D Shapes are flat shapes like triangles, squares, and circles.
• Polygons are 2D shapes with straight sides. A regular polygon has all sides and all angles equal (e.g., square, equilateral triangle).
• Quadrilaterals are polygons with four sides. Examples include:
• Square: 4 equal sides, 4 right angles, 2 pairs of parallel sides.
• Rectangle: 2 pairs of equal sides, 4 right angles, 2 pairs of parallel sides.
• Rhombus: 4 equal sides, opposite angles equal, 2 pairs of parallel sides.
• Parallelogram: Opposite sides equal and parallel, opposite angles equal.
• Trapezium: Exactly one pair of parallel sides.
• Kite: Two pairs of equal-length sides that are adjacent to each other.
• Triangles:
• Equilateral: All 3 sides equal, all 3 angles 60°.
• Isosceles: 2 sides equal, 2 angles equal.
• Scalene: All sides different, all angles different.
• Right-angled: One angle is 90°.
• 3D Shapes have length, width, and height (e.g., cubes, pyramids).
• They have faces (flat surfaces), edges (where faces meet), and vertices (corners).
• A net is a 2D pattern that can be folded to make a 3D shape.

## Angles

• Types of Angles:
• Acute angle: Less than 90°.
• Right angle: Exactly 90° (often marked with a square symbol).
• Obtuse angle: Greater than 90° but less than 180°.
• Reflex angle: Greater than 180° but less than 360°.
• Angle Rules:
• Angles on a straight line add up to 180°.
• Angles around a point add up to 360°.
• Angles in a triangle add up to 180°.
• Angles in a quadrilateral add up to 360°.
• Vertically opposite angles (formed when two straight lines cross) are equal.

## Position and Direction

• Coordinates: Used to locate points on a grid.
• The x-axis is horizontal, the y-axis is vertical.
• Points are written as (x, y). Remember "along the corridor, up the stairs" (or down for negative y).
• Year 6 covers all four quadrants, including negative coordinates (e.g., (-2, 3) or (1, -4)). The point (0,0) is the origin.
• Transformations: Ways to move shapes.
• Translation: Sliding a shape without turning or flipping it. Described by how many units left/right and up/down (e.g., (+3, -2) means 3 right, 2 down).
• Reflection: Flipping a shape over a mirror line (e.g., x-axis, y-axis, or lines like y=1). The reflected shape is the same distance from the mirror line as the original.
• Rotation: Turning a shape around a fixed centre of rotation. Described by the angle (e.g., 90°, 180°), direction (clockwise/anticlockwise), and centre of rotation.

## Understanding Statistics: Tables and Graphs

Statistics is all about collecting, organising, interpreting, and presenting data. In your Year 6 SATs, you'll need to show you can understand different ways data is displayed and use it to solve problems.

## Tables

Tables organise data into rows and columns.

• Read the headings carefully to understand what each row and column represents.
• Use tables to quickly find specific pieces of information or to complete missing data.

## Bar Charts and Pictograms

Bar charts (or bar graphs) use rectangular bars to compare different categories.

• Look at the x-axis (horizontal) for categories and the y-axis (vertical) for values.
• Always check the scale on the y-axis to read values accurately.
• Pictograms use pictures or symbols to represent data.
• The most important part of a pictogram is the key. The key tells you what each symbol, or part of a symbol, represents. Make sure to use the key correctly, especially when symbols are cut in half or quarters.

## Line Graphs

Line graphs are used to show how something changes over time.

• The x-axis usually represents time (e.g., hours, days, months).
• The y-axis represents the quantity being measured.
• Look at the points and the lines connecting them to identify trends – is the value increasing, decreasing, or staying the same? You might need to read values between marked points on the line.

## Pie Charts

Pie charts show how a whole is divided into different parts or proportions.

• Each slice (or sector) represents a fraction or percentage of the total.
• You'll often be asked to compare the sizes of different sectors or estimate simple fractions (like half or a quarter) of the total. Precise calculations of percentages or degrees are less common at Year 6, but understanding the concept of proportion is key.

## Timetables

Timetables display schedules for things like buses, trains, or events.

• Read across rows and down columns to find specific departure or arrival times.
• You might need to calculate the duration of a journey or event by finding the difference between start and end times.

## Solving Problems with Data

• Read the question carefully: Understand exactly what is being asked.
• Identify key information: Which graph or table, and which parts of it, do you need?
• Calculate: You might need to find totals, differences, or the mean (add all values and divide by the number of values).
• Be precise: Use the correct units and read scales accurately.
• Draw conclusions: What does the data tell you?

## Ratio and Proportion: Year 6 SATs Revision

This topic is all about comparing quantities and understanding how they relate to each other.

## Understanding Ratio

A ratio compares two or more quantities of the same type. It shows how much of one thing there is compared to another.

• Ratios are written using a colon (:) e.g., 2:3.
• The order matters! A ratio of 2:3 is different from 3:2.
• For example, if there are 2 red apples and 3 green apples, the ratio of red to green apples is 2:3.

## Simplifying Ratios

Just like fractions, ratios can be simplified by dividing all parts by their highest common factor (HCF).

• Example: The ratio 6:9 can be simplified by dividing both numbers by 3. So, 6:9 is the same as 2:3.
• Always simplify ratios to their simplest form if possible.

## Using Ratios to Find Quantities

You might need to share a total amount in a given ratio, or find missing amounts.

1. Add the parts of the ratio to find the total number of 'shares'.

2. Divide the total amount by the total number of shares to find the value of one share.

3. Multiply the value of one share by each part of the ratio to find the individual amounts.

• Example: Share 20 sweets in the ratio 1:4.
• Total shares: 1 + 4 = 5
• Value of one share: 20 ÷ 5 = 4 sweets
• Amounts: 1 x 4 = 4 sweets; 4 x 4 = 16 sweets. (Check: 4 + 16 = 20)

## Understanding Proportion

Proportion describes how two quantities change in relation to each other. If they are in direct proportion, as one quantity increases, the other increases by the same factor (and vice versa).

• Proportion often involves scaling up or down.
• Example: If 1 cake needs 2 eggs, then 2 cakes need 4 eggs, and 3 cakes need 6 eggs. The number of eggs is directly proportional to the number of cakes.

## Solving Proportion Problems

A common method is to find the value for 'one' (the unitary method).

• Example: If 3 pencils cost 90p, how much do 5 pencils cost?

1. Find the cost of 1 pencil: 90p ÷ 3 = 30p.

2. Find the cost of 5 pencils: 30p x 5 = 150p (£1.50).

• You can also use multiplication factors. If you want to make 3 times as many cakes, you need 3 times as much of each ingredient.

Remember, ratio compares parts, while proportion often relates to how a whole changes or how parts scale together. Both are crucial for problem-solving.

## Understanding Multi-step Word Problems

Multi-step word problems are a key part of the Year 6 SATs Maths Reasoning paper. Unlike simpler problems, they require you to perform two or more different mathematical operations (like addition, subtraction, multiplication, or division) to find the final answer. They test your ability to understand a situation, plan a solution, and execute it accurately.

## Strategies for Success

1. Read the Problem Carefully:

• Read the entire problem at least twice.
• Underline or highlight key information, including numbers and units (e.g., £, cm, kg).
• Identify exactly what the question is asking you to find. Don't rush to calculate before you understand the goal.

2. Break it Down into Smaller Steps:

• Most multi-step problems can be broken into a series of single-step problems.
• Think: "What do I need to find out first?" and "What do I need to do with that information next?"
• You might need to find a total, then a difference, or calculate a quantity per item, then multiply by the number of items.

3. Identify the Correct Operations:

• Look for keywords that suggest which operation to use:
• Addition (+): "total," "sum," "altogether," "increase," "more than."
• Subtraction (-): "difference," "how many left," "decrease," "less than," "take away."
• Multiplication (x): "product," "times," "groups of," "each" (when finding a total from multiple items).
• Division (/): "share equally," "per," "each" (when finding an amount for one item from a total).

4. Show Your Working Clearly:

• Write down each step of your calculation. This helps you to organise your thoughts and can earn you partial marks even if your final answer is incorrect.
• Label your steps (e.g., "Step 1: Calculate total cost," "Step 2: Find change").

5. Check Your Answer:

• Once you have a final answer, read the original question again. Does your answer make sense in the context of the problem?
• Consider if the magnitude is reasonable.
• You can also use inverse operations to check your calculations (e.g., if you added, subtract to check).

Practising these strategies will build your confidence and accuracy in tackling multi-step word problems.

## Time Calculations

Time questions often involve converting between units, calculating durations, and interpreting timetables. Remember the key conversions:

• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 day = 24 hours
• 1 week = 7 days
• 1 year = 12 months or 365 days (366 in a leap year)

12-hour and 24-hour clocks: Be confident switching between these. Remember that PM times in 12-hour format (except 12 PM) have 12 added to them for 24-hour format (e.g., 3 PM is 15:00). AM times are generally the same, except 12 AM is 00:00.

To calculate a duration, subtract the start time from the end time. If crossing midnight, it can be easier to calculate time to midnight, then time from midnight, and add them together. Always pay attention to the units given in the question (e.g., minutes, hours).

## Money Problems

Money questions require accurate calculations with decimals, often involving addition, subtraction, multiplication, and division. Key points:

• £1 = 100p. Always write money amounts with two decimal places, even if it's a whole number (e.g., £5.00) or ends in zero (e.g., £3.50).
• Calculating change: Subtract the cost of the item(s) from the amount paid.
• Problem-solving: Often involves multi-step calculations, such as finding the total cost of multiple items, sharing a cost equally, or comparing prices to find the best value. Read carefully to understand what is being asked.

## Scaling and Ratio

Scaling involves changing the size of something by a scale factor. This means multiplying or dividing all quantities by the same number.

• Recipes: If a recipe serves 4 people and you need to make it for 6, you'll need to find a scale factor. (e.g., 6/4 = 1.5, so multiply all ingredients by 1.5).
• Maps and Plans: A scale like 1:100 means that 1 unit on the map represents 100 units in real life. If a distance is 5 cm on a map with a scale of 1:200, the real distance is 5 cm * 200 = 1000 cm = 10 metres.

Ratio describes how quantities relate to each other. For example, a ratio of 2:3 means for every 2 parts of one thing, there are 3 parts of another. You might need to find a missing value in a ratio problem or share an amount in a given ratio. Remember to find the total number of parts in the ratio first.