Download 2d shape - Primary Mathematics

Theme: Properties of 2D shapes
Year Target
Yr 1
Understanding
shape
Shape and
space
activities
booklet
Group Target
Must
Should
Shape tools
Further
examples of
pitch and
expectations:
Foundation to
year 1
Use everyday
language to
describe
features of
familiar 2D
shapes.
Use
mathematical
names for
common 2D
shapes, sort
shapes and
describe some
of their features.
Year 1
Information
- Divide and
rule1
- Divide and
rule2
Use language
such as ‘circle’
or ‘bigger’ to
describe the
shape and size
of flat shapes.
Key Resources
/ Models and
Images
Outcomes
2 D shapes
Feely bag
Crayons/pencils/p
aper/ Sand
Understand and use in a practical context the
vocabulary: shape, flat, straight, curved, round,
corner, side, sort, circle, triangle, rectangle, square,
Plasticine / Biscuit
Dough and shape
cutters
Geo boards
Objects with
different shaped
faces
Digital camera
Shapes Songs.
For example
Dave Godfrey
“Number Fun”
songs.
Shape fan
3d shape
properties
Picture a rectangle in your head. Can you tell me
about it so that I can picture it? When you imagine a
square, how many edges does it have? How is it like
this square? Is it different in any way?
ICT files
Problem solving
materials
Number lines
Odd one out
5rectangles
Identify circles, squares, triangles and rectangles.
Draw arrows to show which shapes
belong in the set.
Shut your eyes. Listen while I describe a shape to you
... Now open your eyes. Can you pick up the shape I
was describing? Now describe a shape for someone
else to guess.
Can you make a different pattern using the same
numbers/shapes? What comes next? How did you
work that out?
Which two of the
shapes would fit
together to make
new shape? Tick the
two shapes.
Look at the shapes. Listen to this
description of one of them. Can you tell which shape
is being described?
Put your hands into this big box. Can you find
something soft? An object with corners? Something
round? Something spiky?
Look at this collection of objects or shapes. Shut your
eyes while I pick one up and hide it. Open your eyes.
Tell me which object or shape I have hidden.
Picture a triangle in your head. Start at the top and
walk around the sides of the triangle. How many sides
do you walk around? How many corners does the
triangle have?
Think of a shape. Without saying its name, can you
describe it so that I can find your shape in the box?
Can you describe your shape to your partner so that
your partner can picture it?
Draw a line on this square to make two
triangles. You may use a ruler.
Find two shapes with only
straight sides. Draw a circle
around them.
Here are five rectangles of the same size. How many
different bigger rectangles can you make using two or
more of the rectangles?
Tell me where in the classroom you can see a circle,
a square, a triangle, ... What about a cube? Can you
see a cone anywhere?
- teaching
written
strategies
I've hidden an object/shape/wooden numeral in this
cloth bag. Pass it round and tell me what you think it
is. How do you know?
five
These shapes have been sorted.
Put a cross on the shape which is
in the wrong place.
Could
- teaching
mental
calculation
strategies
- exemplification
of standards
Imagine a big triangle painted on the floor. How many
corners does it have? How many sides?
Sort and classify shapes using Venn and Carroll
diagrams, e.g. identify all the 2-D shapes with a
square corner or all the 3-D solids with a rectangular
face
1b-1a
Yr 2
Must
Use everyday
language to
describe
features of
familiar 2D
shapes.
Understanding
shape
Shape and
space
activities
booklet
Should
Shape tools
Further
examples of
pitch and
expectations:
year 2
Identify lines of
symmetry in
simple shapes
and recognise
shapes with no
lines of
symmetry.
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Use
mathematical
names for
common 2D
shapes, sort
shapes and
describe some
of their features.
Could
2 D shapes
Feely bag
Shape Songs e.g.
Dave Godfrey
“Number Fun”
Geo boards
Objects with different
shaped faces
Hoops for sorting
Digital camera
Mirrors
Paper shapes
Rulers
Programmable robot
Understand, use and begin to read the
vocabulary: shape, flat, straight, curved, round,
corner, side, sort, circle, triangle, rectangle,
square, pentagon, hexagon, octagon,
How do you know that this shape is a square?
What is special about it?
Two of these shapes are not
hexagons. Which are they?
Look at these two shapes. What is the same about
them? What is different?
Watch as I slowly reveal a shape from behind a ‘wall'.
What could it be? How do you know? What could it
not be? Why?
This shape is made from four identical
squares touching edge to edge.
Here are five identical triangles.
ICT files
Use some or all of the triangles to make a bigger
triangle.Is there another way to do it?
Problem solving
materials
Choose a shape to match the properties described
by the teacher and name it:
Line of symmetry
Spot the shapes
Making shapes
Creating shapes
Number lines
Odd one out
Jack and the
beanstalk
Coloured shape
Triangles and
pentagons
Bucket and spade
6triangles
Look at the symmetrical picture that I have given you.
Draw a line of symmetry on it.
Find a shape that has five corners and five sides
(pentagon) Has four straight equal sides (square)
Refer to the properties of shapes such as the
number of corners and sides.
I have begun to make a symmetrical shape with
these coloured blocks. Can you complete the
shape? How can you check that it is symmetrical?
Programme the robot to draw squares and
rectangles
Describe this shape/solid to a friend. Can they
guess what it is?
Sort these 2-D shapes. Put all the pentagons in
this circle. Now choose another way to sort them.
What do all the shapes that you have put in the
circle have in common?
Make different shapes from four identical squares
touching edge to edge. Record and name each
different shape that you make by counting sides.
How many rectangles can you
count in this diagram?
What about this diagram?
Sort shapes on a Carroll
diagram, to extend their
understanding of 'not'. For
example, they sort shapes into
red/not red and rectangles/not
rectangles .
Use these geostrips to show me what a right angle
looks like
Point out some right angles in the classroom. For
those we can reach, how could we check?
Which of these shapes has a right
angle?
Two of these shapes have no lines of
symmetry. Which are they?
This shape has been folded in half along
the dotted line. Imagine opening it up.
How many sides does the opened shape
have? Draw the shape that you think will
be made when the folded shape is
opened up.
2c-2b
Year Target
Yr. 3
Group Target
Must
Use
mathematical
names for
common 2D
shapes, sort
shapes and
describe some
of their features.
Understanding
shape
Shape and
space
activities
booklet
Should
Shape tools
Further
examples of
pitch and
expectations:
Name and
classify
polygons, using
criteria such as
number of right
angles, whether
or not they are
regular,
symmetry
properties.
year 3
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Identify lines of
symmetry in
simple shapes
and recognise
shapes with no
lines of
symmetry.
Could
Key Resources /
Models and
Images
2 D shapes
Feely bag
Geo boards
Objects with different
shaped faces
Hoops for sorting
Set square (to
identify right angles)
Rulers
Digital camera
Mirrors
Paper shapes
Logo/programmable
robot
ICT files
Names and
properties of 2D and
3D shapes
Shape sort
3d shape facts
Quadrilateral-triangle
Venn diagram sorter
Problem solving
materials
Create new shapes
Sorting shapes
Describing position
Rows of coins
Odds and evens
Straw squares
Circle sums
Guess who?
Outcomes
Use, read and begin to write the vocabulary: shape,
flat, straight, curved, vertex, vertices, side, edge,
sort, semi-circle, triangle, rectangle, square,
quadrilateral, pentagon, hexagon, octagon, circular,
right-angled
Combine these three shapes to make a shape with
at least one line of symmetry. Describe the shape
you have made. How many different shapes can
you make?
In this drawing there are triangles, rectangles,
squares and other quadrilaterals. Show me these
shapes. Are there any pentagons? What about
octagons?
Know that a quadrilateral is any shape with four
straight sides
Refer to properties such as: reflective symmetry, the
number of sides and vertices, whether sides are the
same length, whether or not angles are right angles.
Find a quadrilateral that has two angles that are
smaller than right angles and two that are bigger
than right angles.
Which shapes always have four right angles?
Draw two lines to complete the square.
Sketch the reflection of a
simple 2-D shape in a
mirror line along the edge,
using a mirror to help, For
example:
Describe angles in 2-D shapes , identifying whether
each angle is equal to, greater than or smaller than
a right angle.
Place a set of
shapes in the
correct place
in this table.
Fold 2D shapes along lines of symmetry and create
symmetrical shapes e.g. fold and cut paper to make
squares, octagons and stars.
Shade more squares so that this
rectangle has one line of
symmetry.
Select from a set of shapes a shape that has: no
right angles; all sides equal;.
One of the shapes does not belong in this set. Find
the odd one out. Explain how you found it.
Draw the reflection of this
shape in the mirror line.
Use a set-square and a ruler to draw a square with
sides of 12 cm.
How many right angles are there in this
pentagon? How could you check?
2a-3c
Yr. 4
Must
Identify lines of
symmetry in
simple shapes
and recognise
shapes with no
lines of
symmetry.
Understanding
shape
Shape and
space
activities
booklet
Shape tools
Should
Further
examples of
pitch and
expectations:
Name and
classify
polygons, using
criteria such as
number of right
angles, whether
or not they are
regular,
symmetry
properties.
year 4
Unit plans: Autumn
unit 4
Autumn unit 6
Spring unit 4
Spring unit 6
Summer unit 5
Summer unit 6
2D-3D shapes
Feely bag
Geo boards
Objects with different
shaped faces
Hoops for sorting
Paper shapes
Set square (to
identify right angles
/perpendicular lines)
Rulers
Digital camera
Mirrors
Logo/programmable
robot
ICT files
Names and
properties of 2D and
3D shapes
Properties of 3D
shapes
3D shape properties
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Could
Recognise
parallel and
perpendicular
lines, and
properties of
rectangles and
triangles.
Shape quiz
3d shape facts
Carroll diagrams for
sorting shapes
Quadrilateral-triangle
Venn diagram sorter
Problem solving
materials
Reflecting shapes
Rows of coins
Odds and evens
Straw squares
Circle sums
Tangram
3 by 3 grid
Guess who?
name equilateral triangles, isosceles triangles and
heptagons,
Use logo/programmable robot to draw shapes when
given their properties.
know that polygons are closed flat shapes with
straight sides.
recognise symmetrical polygons, both regular and
irregular, and cases where a polygon has no lines of
symmetry, or one, two or more lines of symmetry;
for example, they try to draw a hexagon with no
lines of symmetry, one line of symmetry, two lines of
symmetry, etc
investigate problems such the maximum number
of right angles in a triangle, quadrilateral, pentagon,
Refer to properties
such as: reflective
symmetry, the
number of sides and
vertices, whether
sides are the same
length, whether or
not angles are right
angles, e.g.
investigate a statement such as: 'The number of
lines of symmetry in a regular polygon is equal to
the number of sides of the polygon' by finding
examples that match it.
Classify 2-D shapes
according to their
lines of symmetry.
Identify particular shapes from a mixed set.
For example, which of these shapes are hexagons?
Use a set of regular and irregular polygons, and
criteria written on cards, such as 'is a regular
polygon', 'is an irregular polygon', 'has no lines of
symmetry', 'has at least one line of symmetry', 'has
no right angles', 'has one right angle', etc. Select a
card, e.g. 'is an irregular polygon'.
name equilateral, isosceles and right-angled
triangles
Know the angle and side properties of isosceles and
equilateral triangles, and use them: for example, to
make triangular patterns.
Use these triangular tiles to make a symmetrical
shape. Can you take one tile away and keep your
shape symmetrical? Can you change one or more
tiles so it is no longer symmetrical?
Sketch the reflection of a
simple shape in a mirror line
parallel to one edge, where
the edges of the shape or
the lines of the pattern are
parallel or perpendicular to
the mirror line.
Sort a set of
polygons using
this sorting
diagram.
This is half a symmetrical shape. Tell me how you
would complete it. How did you use the line of
symmetry to complete the shape?
Construct different polygons by paper folding or on
a pinboard, name new shapes and discuss
properties such as lines of symmetry.
Here are five shapes on a
square grid.
Which two shapes have a
line of symmetry?
3c-3b
Yr. 5
Must
Classify
polygons, using
criteria such as
number of right
angles, whether
or not they are
regular, and
symmetry
properties.
Understanding
shape
Shape and
space
activities
booklet
Should
Shape tools
Recognise
parallel and
perpendicular
lines, and
properties of
rectangles and
triangles.
Further
examples of
pitch and
expectations:
ICT files
Shape quiz
Carroll diagrams for
sorting shapes
Quadrilateral-triangle
Venn diagram sorter
year 5
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Unit plans: autumn unit
8
Spring unit 5a
Spring unit 5b
Spring unit 7
Summer unit 8
Summer unit 9
2 D shapes
Feely bag
Geo boards
Objects with different
shaped faces
Hoops (Venn
diagrams)
Paper shapes
Set square (to identify
right
angles/perpendicular
lines)
Rulers
Digital camera
Mirrors
Could
Name, describe
and classify
quadrilaterals
using criteria
such as parallel
sides, equal
angles and
equal sides.
Problem solving
materials
Virtual pinboard
investigation
How many triangles?
Triangles; Symmetry
Spot the shapes 2
Four by four
All square; four
triangles;Tangram; 3
by 3 grid; Guess
who?;
Use, read and write: two-dimensional, side, angles,
centre, radius, diameter, congruent, circle, semicircle, triangle, equilateral triangle, isosceles
triangle, quadrilateral, rectangle, oblong, square,
pentagon, hexagon, heptagon, octagon, polygon
Look at this shape (or a shape that is drawn on a
square grid). Tell me whether each of these
statements is true or false.
The shape has exactly two right angles.
The shape has two pairs of parallel lines.
The shape has one line of symmetry.
The shape is a quadrilateral.
Here is part of a shape on a
square grid. Draw two more
lines to make a shape which
has a line of symmetry. Use
a ruler.
Recognise properties of rectangles such as: All four
angles are right angles; Opposite angles are equal
and parallel; The diagonals bisect one another.
Use a pinboard to make shapes.
For example, make:
• different triangles on 3
3 pinboard;
• different squares on a
5 5 pinboard.
Discuss properties such as which of these triangles
are scalene, or which has the greatest area.
Here is a regular octagon. Join
three of the dots to make an
isosceles triangle. Use a ruler.
Join three dots to make a different
isosceles triangle.
Now join three dots to make a
right-angled triangle. Join three dots to make a
scalene triangle.
This grid is made of hexagons.
Draw the reflection of the shaded
shape on the grid.
Predict and test which other shapes have diagonals
of equal length or diagonals that bisect each other
Know how to check if two lines are parallel?
perpendicular?
Select two 'sorting' cards, such as: has exactly two
equal sides and has exactly two parallel sides. Can
you show me a polygon that fits both of these
criteria? What do you look for?
Know some of the
properties of triangles:
• equilateral triangle: all
three sides are equal
in length and all three
angles are equal in size;
• isosceles triangle: two
equal sides and two
Here is a shaded square on a
grid. Shade in three more
squares so that the design is
symmetrical in both mirror lines.
complete patterns with two lines of symmetry, using
for example peg boards or a suitable computer
program.
solve problems involving symmetry such as: Place
eight squares together (edge to edge) to make a
shape with two lines of symmetry. How many
different shapes can you make?
investigate the line symmetry of regular polygons,
Suggest a general statement based on their
findings.
equal angles;
• scalene triangle: no two sides or angles are equal;
• right-angled triangle: one of the angles is a right
angle.
identify shapes that have pairs of parallel or
perpendicular sides or edges.
Investigate the number of different shapes that can
be made by placing four identical equilateral
triangles edge to edge
Imagine cutting off a corner of the square in one
straight cut. Draw the shape you cut off. Now draw
the shape you have left. What are the names of
your two shapes?
3a-4c
Yr. 6
Must
Understanding
shape
Shape and
space
activities
booklet
Should
Recognise
parallel and
perpendicular
lines, and
properties of
rectangles and
triangles.
Name, describe
and classify
quadrilaterals
using criteria
such as parallel
sides, equal
angles and
equal sides.
Shape tools
Further
examples of
pitch and
expectations:
year 6
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Could
Know and use
side, angle and
symmetry
properties of
equilateral,
isosceles and
right-angled
triangles.
Unit plans:
Autumn unit 8
Autumn unit 10
Spring unit 8
Summer unit 3
Summer unit 7
Summer unit 11
Springboard
Lesson 11
Lesson 14
Lesson 17
Lesson 28
2 D shapes
Feely bag
Geoboards
Objects with different
shaped faces
Hoops
Paper shapes
Set square (to
identify right angles/
perpendicular lines)
Rulers
Digital camera
Mirrors
ICT files
Rotations and
coordinates
Quadrilateral rummy
Problem solving
materials
Chalk problem;
Reasoning about
shapes; Angles ;
Virtual pinboard
investigation; How
many triangles?;
Triangles; Symmetry ;
Spot the shapes 2;
Four by four;
Albert Square; All
square;
Tangram; 3 by 3 grid;
Equilateral triangles;
Guess who?;
Recognise, and know properties of: cube, cuboid
(rectangular prism), sphere, cylinder, cone, pyramid,
prism, triangular prism, hemi-sphere, tetrahedron,
octahedron, dodecahedron, polyhedron.
Know that perpendicular lines are at right angles to
each other and that parallel lines are the same
distance apart.
Name various triangles (isosceles, equilateral,
scalene, right-angled) and quadrilaterals (square,
oblong, parallelogram, rhombus, kite, trapezium).
Sort quadrilaterals and triangles by given criteria
e.g. has parallel sides, has equal sides etc.
Know properties such as:
A parallelogram has its opposite sides equal and
parallel
A rhombus is a parallelogram with four equal sides
A trapezium has one pair of opposite sides parallel
A kite has two pairs of adjacent sides equal
A rectangle had four right angles and its opposite
sides are equal.
A square is a rectangle with equal sides.
Identify a shape from a set of given properties.
How many triangles can you
see in this diagram?
How can you make sure that
you have counted them all?
What is the same about a rhombus and a kite?
What is different?
Name a shape that has one pair of parallel sides,
but no pairs of perpendicular sides.
What do you notice about the opposite sides of this
parallelogram? Is it true for all parallelograms? What
about this trapezium?
By moving just one point, can
you change this shape into a
kite? A rhombus? A nonisosceles trapezium?
Which quadrilaterals have diagonals that intersect at
right angles?
How would you check if two lines
are parallel? Perpendicular?
Give me instructions to get me to draw a rhombus
using my ruler and a protractor.
Which of these shapes has two
pairs of parallel sides?
On the square paper, use a ruler to draw a
pentagon that has three right angles.
Draw two straight lines from
point A to divide the shaded
shape into a square and two
triangles.
Draw the reflection of this shape.
The shape below is
rotated 90 clockwise about point A.
Draw the shape in its new position on
the grid.
How many different shapes can be made by placing
two identical equilateral triangles edge to edge?
What about 3, 4, 5, … identical equilateral triangles?
Use compasses to draw a circle. Use a ruler and
protractor to draw a regular pentagon with its
vertices on the circumference of the circle.
Program an on-screen turtle to draw regular
polygons or specific quadrilaterals
Use a computer program to
transform shapes.
Predict and discuss the patterns
made.
Investigate the different
polygons that can be made
using tangram pieces.
For example,
reassemble the five
tangram
pieces to form hexagons.
4b-4a
Yr. 6
Must
Understanding
shape
Shape and
space
activities
booklet
Should
Recognise
parallel and
perpendicular
lines, and
properties of
rectangles and
triangles.
Name, describe
and classify
quadrilaterals
using criteria
such as parallel
sides, equal
angles and
equal sides.
Shape tools
Further
examples of
pitch and
expectations:
year 6 into year
7
Information
- Divide and
rule1
- Divide and
rule2
- teaching
mental
calculation
strategies
- teaching
written
strategies
- exemplification
of standards
Could
Know and use
side, angle and
symmetry
properties of
equilateral,
isosceles and
right-angled
triangles.
Unit plans:
Autumn unit 8
Autumn unit 10
Spring unit 8
Summer unit 3
Summer unit 7
Summer unit 11
Springboard
Lesson 11
Lesson 14
Lesson 17
Lesson 28
2 D shapes
Feely bag
Geoboards
Objects with different
shaped faces
Hoops
Paper shapes
Set square (to
identify right angles/
perpendicular lines)
Rulers
Digital camera
Mirrors
ICT files
Rotations and
coordinates
Quadrilateral rummy
Problem solving
materials
Chalk problem;
Reasoning about
shapes; Angles ;
Virtual pinboard
investigation; How
many triangles?;
Triangles; Symmetry ;
Spot the shapes 2;
Four by four;
Albert Square; All
square;
Tangram; 3 by 3 grid;
Equilateral triangles
8pointquadrilateral
overlapping squares
Know the labelling convention
for:
• triangles – capital letters for the
vertices (going round in order,
clockwise or anticlockwise)
and corresponding lower-case
letters for each opposite side, the triangle then
being described as ABC;
Using a 3 by 3 array on
a pinboard, identify the
eight distincttriangles
that can be constructed
(eliminating reflections,
rotations or
translations). Classify
the triangles according to their side, angle and
symmetry properties.
• equal sides and parallel sides in diagrams.
How many DIFFERENT
quadrilaterals can be made by joining
the dots on the circle?
What different shapes can
you make by overlapping two
squares?
Imagine a square with its diagonals drawn in.
Remove one of the triangles. What shape is left?
How do you know?
• Imagine a rectangle with both diagonals drawn.
Remove a triangle. What sort of triangle is it? Why?
• Imagine joining adjacent mid-points
of the sides of a square. What shape
is formed by the new lines?
Explain why.
• Imagine a square with one of its corners cut off.
What different shapes could you have left?
• Imagine an isosceles triangle. Fold along the line
of symmetry. What angles can you see in the folded
shape? Explain why.
Use Logo to write instructions to draw a
parallelogram.
Sarah draws a quadrilateral. It has these properties:
1. it has 2 long sides the same length;
2. it has 2 short sides the same length;
3. it does NOT have any right angles;
4. it does NOT have reflective symmetry.
What is the mathematical name for Sarah’s
quadrilateral.
An isosceles triangle has a perimeter of 12cm. One
of its sides is 5cm. What could the length of each of
the other two sides be? Give both answers.
Here is a kite.
Write the coordinates of
point D
• Imagine a square sheet of paper. Fold it in half and
then in half again, to get another smaller square.
Which vertex of the smaller square is the centre of
the original square?
Imagine a small triangle cut off this corner. Then
imagine the paper opened out. What shape will the
hole be? Explain your reasoning.
Imagine what other shapes you can get by folding a
square of paper in different ways and cutting off
different shapes.
Here is a pentagon drawn on
a coordinate grid. The
pentagon is symmetrical.
What are the coordinates of point C?
5c-5b