Maths Year 4 Spring Shape

Day 1 Teaching
Introduce the terminology for circles: radius, diameter, and circumference. Show children a compass and model how to use it to draw a circle. Discuss drawing circles with specified radii. Observe that the diameter is double the radius.
Group Activities
-- Use compasses to draw circles with measured radii.

Day 2 Teaching
Show a large 50p coin and agree (having noted slightly curved sides and rounded corners) that it is a heptagon. Children draw irregular heptagons. Identify types of angle within it. Explain that all polygons have straight sides and are closed. Discuss what makes a good description of a polygon.

Group Activities
-- Identify the properties of polygons and use this to sort them.
-- Draw 2-D shapes based on given properties.

Day 3 Teaching
Show children five different triangles and discuss their similarities and differences. Look at the number of sides and angles, lines of symmetry, length of sides, sizes of angles. Name the triangles as: equilateral, isosceles, right angled, scalene. Note that a right angled triangle can also be isosceles. Sort triangles according to different properties, e.g. has a right angle or not.
Group Activities
Use the in-depth problem-solving investigation ‘Egyptian Rope’ from NRICH as today’s group activity.
Or, use this activity:
-- Identify right angles and other properties in triangles; classify them.

• A circle: pre-drawn and annotated (circumference, radius, diameter)
• Compasses, large pieces of paper, glue, sticky notes and rulers
• cm cards (see resources)
• Range of sharp coloured pencils and scissors
• Picture of 50p coin (or large mock 50p coin)
• ‘Polygons to sort’ sheet (see resources)
• Paper equilateral triangle
• Additional activity sheets (see resources)

Day 1
2-D shapes (pre-requisite skills)

Suggested for Day 2
Telling the time (simmering skills)

Suggested for Day 3
Complete symmetrical drawings (simmering skills)

Day 1
Draw circles of given radii using compasses.

Day 2
Guess the shape game.

Day 3
Name triangles and identify right angles and other properties.

• Always true, sometimes true or false?
  The circumference of a circle is the distance across the centre from one side to the other.
  The radius of a circle is half the diameter.
  A circle is a special type of polygon.
  A pentagon is a regular five-sided polygon.
  A polygon has eight sides.
• Draw triangles to match each description.
  With a right angle and the shortest side is 3cm.
  Two sides and two angles are equal.
  No equal angles; one side twice as long as one other side.
• Make as many generalisations as you can about this collection of shapes (see download).

In-depth Investigation: Egyptian Rope
The ancient Egyptians were said to make right-angled triangles using a rope which was knotted to make 12 equal sections. If you have a rope knotted like this, what other triangles can you make? Egyptian Rope from nrich.maths.org.

Recognising acute, right and obtuse angles

Day 1 Teaching
Show a variety of 3-D shapes. Write the words: face, edge, vertex (plural: vertices) and polyhedron on the board. Revise their meanings and ask children to use these words to describe one of the shapes to a partner. Discuss the properties of different shapes, using these terms.

Group Activities
-- Make and describe 3-D shapes, identifying faces, edges and vertices.
-- Make 3-D models using cubes.

Day 2 Teaching
Show children a selection of 3-D shapes. Explain that we will sort these into prisms and pyramids and those which are neither. Identify the properties of prisms and those of pyramids and ensure children understand that there are different examples of each. Sort using other headings/criteria.
Group Activities
Use the in-depth problem-solving investigation ‘Soma Cube’ as today’s group activity.
Or, use these activities:
-- Make, describe and classify 3-D shapes.

• A collection of 3-D shapes: cubes, cuboids, cylinders, spheres, cones, prisms, pyramids and tetrahedra
• Shape construction equipment
• Interlocking cubes
• ‘Cube Models’ sheet (see resources)
• Isometric paper (see resources)
• Straws and modelling clay
• ‘Skeletons’ sheets 1 and 2 (see resources)
• Two hoops and card or paper for labels

Day 1
Use clues to identify 3-D shapes (pre-requisite skills)

Suggested for Day 2
Counting on and back in ones from 4-digit numbers through 1000s and 100s (simmering skills)

Day 1
List the properties of 3-D shapes.

Day 2
Sort 3-D shapes into given Venn diagrams.

• Create a net for a tetrahedron. Fold it up to ensure that it works. Is this the only way to draw a net for a tetrahedron?
• Imagine a 3 by 3 by 3 cube hanging in front of you with just the front face facing you.
  The cube is made up of three 3 by 3 layers, that is 27, small cubes.
  You drill a hole through the four corner cubes that are facing you, all the way through to the back.
  A friend looks down on the cube, from above, and they also drill four holes through their four corner cubes all the way through to the bottom.
  You and your friend then examine all the 27 small cubes.
  How many small cubes will then have holes drilled in them?
• Find out what a dodecahedron is. Build one using a construction kit, then write a description of it, using all your best mathematical shape language for someone who has never seen one.

In-depth Investigation: Soma Cube
Children create specified 3-D shapes using 2-D representations and then combine these to create other 3-D shapes including a cube.

Solid Specials
Looking at the relationship between 2-D and 3-D shapes

Day 1 Teaching
Draw horizontal and vertical axes from 0 to 10 on a square background on the Interactive Whiteboard. The x-axis goes across. Ring 2 points: (2, 5) and (6, 1). Show children how we write these as co-ordinates. Children give more co-ordinates to make a square. Repeat with co-ordinates for another square and a triangle.
Group activities
Use the in-depth problem-solving investigation ‘Coordinate Challenge’ from NRICH as today’s group activity.
Or, use this activity:
-- Plot (x, y) co-ordinates and use them to construct 2-D shapes (in the first quadrant) of a co-ordinate grid.

Day 2 Teaching
Draw a triangle on a grid. Children write co-ordinates for each corner. Move the triangle 2 squares to the right and discuss how each vertex has moved 2 squares. Explain that this shape has been translated. Repeat with other shapes moving up, down, left or right. Children sketch and label the new co-ordinates.
Group Activities
-- Translate 2-D shapes up, down, left or right in the first quadrant of a co-ordinate grid.

Day 3 Teaching
Launch the Coordinates ITP. Stress that the x co-ordinate comes before the y one. Use the grid to show the co-ordinates of vertices of different polygons, including a ‘house-shaped’ pentagon.
Group Activities
-- Plot co-ordinates in the first quadrant and describe translations.
-- Apply knowledge of co-ordinates in the first quadrant.

• Interactive Whiteboard
• Squared paper and 0-9 cards
• ‘Co-ordinates’ sheet, including one enlarged copy (see resources)
• ITP: Co-ordinates
• Counters, two 1-6 dice and coloured pencils
• Coin with T (translation) labelled on one side and D (destination) labelled on the other
• Cali and the Co-ordinate System game from www.math10.com

Suggested for Day 1
Convert from 24-hour clock to 12-hour am/pm (simmering skills)

Suggested for Day 2
Roman numeral clocks (simmering skills)

Suggested for Day 3
Roman numerals (simmering skills)

Day 1
Plot x and y coordinates in one quadrant on a graph to draw 2-D shapes, including missing co-ordinate points.

Day 2
Give the x and y coordinates of shapes on a grid after moving them up, down, left or right.

Day 3
Imagine translating shapes and finding new co-ordinates.

• Draw a 6 × 6 grid and label the x and y axes. Mark these co-ordinates:
  A (1, 1) B (1, 4) C (4, 1).
  Join these and name the shape created.
  Add another point so that if you join all four vertices you create a 4-sided shape that is not a square.
• Sam says that if she draws a square on a co-ordinate grid, then two of its corners will always have the same ‘x’ co-ordinate and two will have the same ‘y’ co-ordinate.
  Is she correct? Explain how you know.
• Bill draws a triangle on his grid. He moves it two spaces ‘down’ the grid. The new co-ordinates of its vertices are:
  (2,1) (6, 1) (3, 5)
  Write the co-ordinates of the triangle before its translation.

In-depth Investigation: Co-ordinate Challenge
Use clues about the symmetrical properties of capital letters to place them on the coordinate grid. Co-ordinate Challenge from nrich.maths.org.

The Lily Pond
Describe a route for Frog to jump across all the leaves to visit Snail. The Lily Pond from nrich.maths.org.

Day 1 Teaching
Display a pattern drawn on one side of a line of symmetry (see resources). Discuss the concept of ‘line of symmetry’ and begin to complete each pattern. Provide copies for children who complete each symmetrical pattern. Children create their own symmetrical patterns, colouring just 12 squares lines of symmetry.
Group Activities
-- Create symmetrical patterns across one or two lines of symmetry.

Day 2 Teaching
Draw an irregular but symmetrical hexagon. Ask children to say whether it has a line of symmetry. Then draw half of an irregular but symmetrical octagon. Children need to draw the other half. Discuss shapes with two lines of symmetry and draw one, identifying the two lines. Model how to use a mirror to check for symmetry, perhaps using the Symmetry ITP.
Group Activities
Use the in-depth problem-solving investigation ‘Tremendous Tiles’ as today’s group activity.
Or, use these activities:
-- Identify the lines of symmetry on 2-D shapes; draw shapes with a given number of lines of symmetry.
-- Identify whether shapes are symmetrical. Draw the lines of symmetry on 2-D shapes.

• ‘Symmetrical patterns’ sheets 1 and 2 (see resources)
• Squared paper
• ITP: Symmetry
• ‘Shapes for sorting’ sheet (see resources)
• Mirrors, rulers and a set of 2D shapes (regular, irregular, symmetrical, not symmetrical)

Suggested for Day 1
Draw irregular polygons (simmering skills)

Suggested for Day 2
Compare pairs of numbers with 2 decimal places (simmering skills)

Or

Suggested for Day 2
Count on or back in steps of 50 and 100 (simmering skills)

Day 1
Complete patterns across one or two lines of symmetry.

Day 2
Complete drawings of 2-D shapes to make them symmetrical.

• Shade 4 more spaces on this grid (see download) to create a pattern with two lines of symmetry.
• Draw a shape with exactly four lines of symmetry. It does not need to be a polygon.
• Explore all possible symmetrical designs that can be created by shading whole squares of a 1 × 1, 2 × 2 and 3 × 3 grid. Watch out for patterns that are simply rotations of other patterns.
  Predict how many designs might be possible on a 4 × 4 grid. Try it.

In-depth Investigation: Tremendous Tiles
Children explore creating patterns of tiles with three asymmetrical blocks. They look for and identify lines of symmetry, creating patterns with at least two lines of reflective symmetry.

Colouring Triangles
Make symmetrical patterns by colouring the set of triangles. Colouring Triangles from nrich.maths.org.

Day 1 Teaching
Draw a succession of given angles (see Teaching and Activities document). Ask children which are larger/smaller than 90°. Identify acute (sharp) angles as less than 90° and obtuse (blunt) angles as being between 90° and 180°. Compare angles by placing them on top of one another.
Group Activities
-- Compare and classify angles.

Day 2 Teaching
Show a number of different triangles. Discuss what they have in common and how they are different. Remind children of the previous learning on triangles of different types and identify these. Then focus on the types of angles in each.
Group Activities
-- Explore the angle properties of different types of triangles.

Day 3 Teaching
Remind children of the definition of a quadrilateral. Ask children to draw a quadrilateral (different to their neighbour’s), then to mark right angles with a little square, acute angles with ‘a’ and obtuse angles with ‘o’. Did their neighbour’s shape have the same number of each type of angle?
Group Activities
Use the in-depth problem-solving investigation ‘Rabbit Run’ from NRICH as today’s group activity.
Or, use this activity:
-- Investigate the angle properties of quadrilaterals.

Day 4 Teaching
Draw a parallelogram and a trapezium. Both are quadrilaterals. Children describe each, including what is the same and different. Both have 2 parallel sides (same distance away from each other, like train tracks). Move on to sort other quadrilaterals by properties, including a square, rhombus and oblong.
Group Activities
-- Draw quadrilaterals, based on properties including types of angles.
-- Compare and classify quadrilaterals, based on properties including types of angles.

• Interactive Whiteboard set square
• ‘Comparing and ordering angles’ sheet (see resources)
• Set squares, scissors, protractors and coloured card
• Flipchart, whiteboards and pens
• Paper copy of triangle 2 (equilateral triangle) from Day 2
• Elastic bands and geoboards
• Rulers
• ‘Sorting quadrilaterals’ sheet (see resources)
• Venn rings (or hoops)
• Sticky notes

Suggested for Day 1
Count on and back in steps of 0.01 through multiples of 0.1 and 1 (simmering skills)

Suggested for Day 2
Multiply and divide numbers by 10 and 100 (simmering skills)

Suggested for Day 3
Division fact bingo for 8 times table (simmering skills)

Suggested for Day 4
Division facts for 7 times table (simmering skills)

Day 1
Compare and order angles, and identify if they are acute or obtuse.

Day 2
Identify acute, obtuse and right angles in triangles.

Day 3
Identify acute, obtuse and right angles in quadrilaterals.

Day 4
Sort quadrilaterals into Venn diagrams based on their properties.

• True or false?
  A triangle cannot have two right angles.
  A triangle with one right angle cannot be isosceles.
  A quadrilateral cannot have exactly three right angles.
  A quadrilateral can always be divided into two triangles by drawing just one straight line.
• Sketch the following:
  A triangle with one obtuse angle.
  A quadrilateral with two obtuse angles.
  A triangle with three sides of identical length.
  A quadrilateral that has two lines of symmetry but no right angles.
  A quadrilateral with two pairs of parallel lines but no right angles.

In-depth Investigation: Rabbit Run
Help Ahmed to build a run for his rabbit using planks of different lengths. Rabbit Run from nrich.maths.org.

Jig Shapes
Complete the shape jigsaw and describe the shapes for a partner. Can they guess which shape you are describing? Jig Shapes from nrich.maths.org.