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The ‘Five a Day’ Summer Challenge Blogs - Maths
By Sarah Collins
17 Aug

This is the second of four blogs using short bursts of physical activity and quick, focused exercises to motivate your child to move forward with their 11+ revision. With minimal desk time to give maximum results, we see these sessions as healthy eating for the brain!

As we outlined in Blog 1, exercising both before and between periods of study is proven to have an immediate and positive effect on both memory formation and concentration. Using this research, all the activities in these blogs are designed to boost concentration, confidence and build mental agility essential for achieving high marks in the 11+.

Each blog includes:

  • two activities, which include some form of physical activity
  • two short desk-based learning activities
  • answers and final review

Discussing the answers is an important part of the process to enable your child to check their understanding and improve accuracy.

If time is limited, pair exercises 1 and 2 on one day, then 3 and 4 on another; finally reviewing all the answers together shortly afterwards.

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The 11+ Maths Revision Five a Day Challenge

All of the activities in this blog relate to shapes, angles and compass directions. Many maths and non-verbal reasoning problems test children’s ability to view shapes from different angles, positions or in reflection. Some 11+ maths problems ask children to look at coordinates, which is not always taught as part of the curriculum, so the activities with compass bearings are helpful as an introduction to these questions.

1 Quirky Quadrilaterals

A game to practice reflecting shapes using small balls to map out the vertices (points where the sides of a shape meet). Two or more players (preferably outdoors).

Aim: To win as many shapes as possible in 15 minutes.

You will need:

  • A smartphone to time the game
  • Either 8 small balls or 8 pairs of socks rolled into balls
  • 2 pieces of string, each about 1 metre long
  • Paper, pen and a small mirror in case of dispute (optional)

Before beginning the game, nominate somebody to keep score. Set up the game by putting one piece of string on the ground to mark where the balls should be thrown from. The throwing area should be at least 6 metres square.

Use this link to help you revise quadrilaterals.

  • Set the smartphone timer for 15 minutes. Aim to make 10 shapes and reflections within this time.
  • Decide on the order of players.
  • Player 1 chooses a quadrilateral from the list below.
    • Square
    • Rectangle
    • Rhombus
    • Parallelogram
    • Kite
    • Trapezium
  • Player 2 now has to make this shape. They should stand behind the line and throw balls or socks to mark the vertices, ideally to an area of approximately 3m2 so that it is not too easy to do. Player 3 decides whether the shape is correct (this doesn’t have to be accurate) and if so, Player 2 gains a point.
  • Player 2 now gets the chance to challenge Player 1 by placing the second piece of string to mark a mirror line – see Diagram 1 (putting the line at an angle makes the game much harder)

Diagram 1

Diagram 1 - 11+ Maths Challenge

  • Player 1 now throws or puts the remaining balls or socks in position, showing where they think the shape would be reflected (see Diagram 2).

Diagram 2

  • If Player 3 thinks this is correct, Player 1 gains a point (draw the shape on a sheet of paper and use a mirror to check if there is any dispute). If Player 3 thinks it is incorrect, Player 2 has a go. Player 2 gains another point if it is correct but loses a point if it is not.
  • The play now moves on to Players 3 and 4 and so on around the group until the timer goes off.
  • The winning player is the one with the most points at the end of the game

Note down any reflections that were difficult for discussion in the review time.

2  Shape up   

Ask your child to complete this worksheet on shape, space and measures directly after playing the quirky quadrilaterals game (above) to help them focus on the task effectively.

Set a timer on your smartphone when they begin and explain that they should complete the test as quickly as possible. There may be some areas of maths your child has not covered in school, but that is fine; just ask them to do what they can.

Do not stop your child at the 10-minute point: timing the test is just intended to help them focus on the task. This is also good preparation for the 11+ exams as practicing timed tests improves speed and accuracy.

You can either mark the worksheet after they have finished or do this prior to the review at a later time or day.

Question 7 in this worksheet is a good introduction to the following activity.

3  Tricky treasure

Once your child has finished the worksheet, have a quick snack and enjoy this treasure trail game.

Compass games are helpful practice for questions involving directions and coordinates. As well as knowing the eight points of the compass, three figure bearings (shown on the diagram) allow us to describe direction more accurately. You can play this game either by using bearings or the names for the compass points. It is more difficult using bearings!

Compass - 11+ Maths Challenge

This game is suitable for two or more people.

Aim either:

  • To reach the treasure in 10 minutes (two people)
  • To be the first person to reach the treasure after 15 minutes (three or more people)

You will need:

  • A smartphone to time the game
  • A ball or frisbee
  • Something to hide as the ‘treasure’. This could be a treat of just an object to find with the prize being something like having the day off from the washing up.

Before beginning the game…

  • Decide who is going to hide the treasure and call out directions (‘The Caller’, everybody else is a ‘Seeker’)
  • Choose a landmark, such as a tree or large object to act as north (a clear landmark is more important than choosing true north)
  • Cake sure The Caller has hidden the treasure when nobody else is looking!
  • All players should spread out so they have space to throw and catch the ball.

The Caller can use the chart (above) to help them when giving directions. They can join in the catch game but do not take part in the treasure hunt.

  1. Set the timer for 15 minutes (or 10 if there are only two people playing)
  2. Choose who is going to start with the ball or frisbee and throw it randomly between two players, counting five successful catches. It is fine to make each other run around!
  3. On the fifth successful catch (unless this is The Caller and they must pass it on*), the Seeker is given a direction. This can either be a compass direction or bearing for example:
    Charlie – head six paces South East
    Prema – head four paces on a bearing of 225°
  4. If The Seeker goes in the wrong direction, they miss out on the next round of ‘catch’ (not relevant if only two people).
  5. Continue, with The Caller sending everybody around in circles, until the timer goes off.
  6. The Caller should then send the next ‘Seeker’ in the direction of the treasure. If they don’t head in the right direction, then continue the game until somebody does.

*If only two people are playing the game, The Seeker must successfully catch the object five times before taking instructions.

Make a note of any particular directions that were problematic for discussion in the review time.

4  Which way now?

Use this activity directly after completing the tricky treasure game (above) to help your child focus on the task effectively.

These questions are taken from page 111 of the Mathematics 11+ Revision Guide. Allow your child 15 minutes to complete the task in a quiet room. They will need paper, a pencil, eraser, ruler and, ideally, graph paper with 0.5cm squares which can be downloaded from the internet* (although they can draw the grid if necessary).

  1. The scale drawing shows five pupils standing on a patio made with square concrete slabs of side length 1m. Write down the compass direction and bearing of:
    1. Camilla from Flo
    2. Phoebe from Camilla
    3. Milly from Phoebe
    4. Flo from Paige
    5. Phoebe from Paige

Grid game - 11+ Maths Challenge

(10 marks)

  1. Complete these questions about compasses:
    • Draw an eight-point compass and label the directions and bearings.  (4 marks)
    • I face north-east when going towards the shops from my front door. I then turn 90° clockwise. In which direction am I now facing? (1 mark)
    2. On a copy of the diagram below, draw lines to show the path taken by following these instructions. The side of each square should be 0.5cm. Start at the dot. (7 marks)
    1. Go 1.5cm N
    2. Go 1cm W
    3. Go 1cm N
    4. Go 4cm E
    5. Go 2.5cm S
    6. Go 2cm NW
    7. Go 2cm SW. Draw and label the final position X.

Blank grid - 11+ Maths Challenge

*if downloading and printing graph paper from the internet, check the size of the squares after printing.

Questions involving directions are useful preparation for the following areas of the 11+ entrance exam:

  • Handling data problems
  • Coordinates
  • Spatial reasoning questions in non-verbal reasoning

5 Answers and final review

Mark activities 2 and 4 before you sit down for your review (answers listed in the sections below).

You may already be keeping a notebook for your child’s 11+ revision (see blog 1) and if not, it might be helpful to start one now.

Set aside 20 minutes to talk through this ‘Five a Day’ challenge. Talk generally about what your child did and didn’t enjoy when completing the activities. This may give you some clues to areas where they may need a little more work or support for their 11+ test preparation.

1 Quirky quadrilaterals

Review any reflection challenges your child found difficult and put them in your 11+ revision notebook so that they can come back to them at another time when making revision lists.

2 Shape up

Go through the answers to the questions and talk about any your child found difficult. Note down any areas your child may wish to revise in the 11+ notebook.

3 Tricky treasure

Review any of the directions or bearings your child found challenging in the game. Keep a copy of the compass diagram shown for future reference and revision.

4 Which way now?

Talk through the answers to the questions from this activity, noting any difficulties for further revision.

  1. Direction of children:
    1. east 090° (2)
    2. north-west 315° (2)
    3. north-east 045° (2)
    4. north-west 315° (2)
    5. north 000° (2)

2. Compass and directions

a. Eight-point compass showing directions and bearings (4)

Compass directions - 11+ Maths Challenge

b. South-east (1)

3. Grid as shown. ‘X’ should be marked for full 7 marks. (7)

Completed grid - 11+ Maths Challenge

How we can help

The written activities in this blog are taken from the Galore Park 11+ maths range.

You can find many more written and family activities in the 11+ Maths Revision Guide. This book is designed for quick bursts of 30-minute revision with separate topics broken into two- or four-page sections with questions at the end of each one.

11+ Maths Revision Guide

If you enjoyed the activities here, this guide can work as a way to provide a comprehensive revision programme. There is a range of tests covering each section in the book as well as a mock 11+ test at the end. Most importantly, all answers are explained so you can always help your child to understand the areas they would like to improve.

Follow on with 11+ maths practice papers when your child is ready to build their confidence and time their responses. Practice Papers 1 and 2 contain 13 model tests progressing in difficulty and pace to the most challenging tests set by any independent schools.

11+ Maths Practice Papers

Add in the 11+ maths workbooks for activities to practise these skills with hundreds of additional tests for use in specific areas where a little more confidence is needed and you can be assured that your child can face the exams with the best possible preparation. 

11+ Maths Workbooks

Sarah Collins is the author of our 11+ Verbal and Non-Verbal Reasoning Study and Revision Guides and is an expert in all things 11+. Learn more about Sarah here.

Tags: 11+, 11+ Revision, 11 plus, Entrance exams, independent schools, learning, Mathematics, Maths, Maths at key stage 2, Parents, Practice Papers, pre-tests, revision, revision prep, Revision Tips, school entrance exams, Summer

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