Download Medium Term Planning Year 4 Theme 7 Theme Title: Solve

National Curriculum Aims:
Medium Term Planning
Year 4 Theme 7 Theme Title: Solve problems involving position and direction
KEY THEMATIC IDEAS: connecting the strands and meeting National Curriculum aims
SIMMERING SKILLS AND ACTIVITIES within and beyond the daily
Fluency
The main focus of this theme is to provide varied opportunities for pupils to apply and deepen their geometrical
reasoning and use the language of position and direction to describe, translate and plot shapes and points. Using a
coordinate grid in the first quadrant pupils will construct both the x and y axes labelling the integers correctly. Pupils
will plot coordinates presented in pairs (4,6) and be able to visualise the position of missing vertices and sides, giving
the coordinates for these and applying their prior knowledge of 2D shapes and their properties (including the
different types of triangles). Pupils will be able to follow instructions to translate shapes in the first quadrant: Move
the shape 4 units up and 2 units left, using the vertices to translate accurately to a new position. Pupils will describe
the new position in relation to patterns in coordinates: The shape has moved 3 up, so the x coordinate stays the same
and 3 is added to the y coordinate. Using the coordinate grid, pupils will reflect shapes across a horizontal and vertical
mirror line, giving the coordinates of the new shape and describing any patterns in the coordinates of the original
and reflected shape. Pupils will begin to find the surface area of rectangles using a grid to count centimetre squares
and find other rectangles with the same area. Building on prior work around the algebraic formula for calculating
perimeter, and in preparation for Year 5, they could begin to reason about area, applying their knowledge of factors
and linking this to arrays and multiplication. Throughout the theme, children will continue to classify and compare
geometric shapes according to their properties: opposite angles of a rhombus are equal, while adjacent angles of a
trapezium are equal. Pupils order and compare angles up to 180°, and compare the size of angles in shapes using the
terms acute and obtuse. Can you draw a quadrilateral with 3 acute angles and one obtuse? Is it possible?
N.C.
 Describe positions on a 2D grid as
STATUTORY
Reasoning
Geometry: position, direction, motion
coordinates in the first quadrant
 Describe movements between positions as
 Recognise and show families of common equivalent fractions
 Order fractions with the same denominator
 Compare the size of fractions with the same denominator and order
on a number line
 Find 1/2, 1/4, 1/3, 3/4 of a quantity of money using mental strategies
 Order quantities of money from smallest to largest when presented in
decimal notation
 Round any number to the nearest 10,100 or 1000
 Round 2 and 3 digit numbers and quantities of money to the nearest
10p and whole pound
 Recall multiplication and division facts to 12 x12 and derive other
facts
 Divide one and two digit numbers by 10 and 100
 Count in multiples of 6,7,9,25 and 1000
 Read the time to 5 minutes
Geometry: Properties of shapes
Measurement
 Compare and classify geometric shapes, including quadrilaterals and  Measure and calculate the perimeter of a
triangles, based on their properties and sizes
 Identify acute and obtuse angles and compare and order angles up
to two right angles by size
 Identify lines of symmetry in 2D shapes presented in different
rectilinear figure (including squares) in
centimetres and metres
 Find the area of rectilinear shapes by counting
squares
orientations
 Complete a simple symmetric figure with respect to a specific line of
symmetry
NON-STATUTORY
Problem-Solving
translations of a given unit to the left/right
and up/down
 Plot specified points and draw sides to
complete a given polygon
Approximately 3 weeks
Pupils should draw a pair of axes in one quadrant, with equal scales and integer labels. They
should read, write and use pairs of coordinates
(2, 5), including using coordinate-plotting ICT
tools
© Wandsworth & Merton Local Authorities, 2014
Pupils continue to classify shapes using geometrical properties,
extending to classifying different triangles (e.g. isosceles, equilateral,
scalene) and quadrilaterals (e.g. parallelogram, rhombus, trapezium)
Pupils compare and order angles in preparation for using a
protractor and compare lengths and angles to decide if a polygon is
regular or irregular..
Pupils draw symmetric patterns using a variety of media to become
familiar with different orientations of lines of symmetry; and recognise
line symmetry in a variety of diagrams including where the line of
symmetry does not dissect the reflected shape.
They relate area to arrays and multiplication
Pupils understand and use a greater range of
scales in their representations.
Perimeter can be expressed algebraically as
2(a + b) where a and b are the dimensions in the
same unit.
National Curriculum Aims:
Medium Term Planning
Year 4 Theme 7 Theme Title: Solve problems involving position and direction
EXEMPLAR QUESTIONS AND ACTIVITIES: connecting the strands and meeting National Curriculum aims
KEY QUESTION ROOTS to be used and adapted in different contexts
Fluency
Working backwards: The co-ordinates of corners of a rectangle that has a width of 5 are (7, 3) and (27, 3). What
are the other two co-ordinates?
What’s the same, what’s different? What is the same and what is different about the diagonals of these 2-D
shapes?
Visualising: If you translated the square 4 up, what would the new coordinates be?
What if…...vertex B was translated 2 right, what would your new shape look like? Can you name it?
Work backwards: The steps to translate shape A to position B are 5 left, 7 down. How would you translate shape B
to position A?
Always, sometimes, never true….isosceles triangles can have a right angle
Convince me….. that the shape you have translated is congruent to the original shape
Translate the
shape 4 units to
the left.
Translate the
shape 2 units up.
Give the coordinates of the
acute angles...the obtuse angles.
10
9
8
Reasoning
Translate the shape
2 units down and 3
units to the right.
Translate the shape
1 unit to the left
and 3 units down.
Plot coordinates
(3,6) (5,6) (6,9)
and a fourth to
make a trapezium.
Player 1: Pick a task card
and plot the shape in the
first quadrant.
Player 2: Pick a translation card and translate
the shape on the same
grid.
Partners check each
other’s work.
7
Reflect shapes across horizontal and
vertical mirror lines.
6
Can pupils plot the coordinates of the
new shape. Can they see a pattern in the
coordinates?
5
4
3
Pupils choose a point and
translate the point to complete the shape e.g. 2 down,
3 right.
2
1
1
2
3
4
5
6
7
Problem-Solving
Is it possible to draw
a shape with:
 3 sides
 1 obtuse angle?
8
9
Approximately 3 weeks
See Wandsworth LA Calculation Policy for more detail on
developing mental and written procedures!
Can some of the key thematic ideas be delivered as part of a
mathematically-rich, creative topic?
Suggested ideas:
Design a Tudor knot garden. Using a 100cm squared grid, pupils
design a garden following a design brief with particular criteria:
 24cm2 of gravel pathway
 Two symmetrical rectangular flowerbeds with an area of 16cm 2
each
 A paved area with an area of 20cm2
 Two grassy areas with the same surface area
Pupils use their knowledge of arrays and factors to create areas
meeting the given measurements. Can pupils create more than one
design that meets the brief? Can they fit the areas in to the 100cm
squared grid without overlapping?
Non-Routine Problem:
Eight Hidden Squares (NRich— http://nrich.maths.org/6280
Can you find the eight hidden squares?
These 28 points all mark the vertices (corners) of eight hidden squares.
Each of the 4 red points is a vertex shared by two squares.
The other 24 points are each a vertex of just one square.
All of the squares share just one vertex with another square.
All the squares are different sizes.
10
Partners challenge
each other to draw
shapes with the
given properties.
Where would these shapes
fit in the carroll diagram?
Why?
Move one vertex to
make a different
triangle. What are its
properties?
10
What are the
properties of this
shape?
How many obtuse
angles? How many
acute angles?
9
8
7
Use Numicon shapes to
create symmetrical patterns
across a horizontal, diagonal
and vertical mirror line and
a combination of two or
three.
© Wandsworth & Merton Local Authorities, 2014
Is it possible to draw a
shape with:
 4 sides
 1 pair of parallel sides
 1 pair of sides of
equal length?
Is it possible to draw a
shape with:
 4 sides
 All acute angles?
At least one line
of symmetry
No lines of
symmetry
No right
angles
Draw the line
of symmetry.
Describe how you
translated the vertex.
6
5
4
What are the coordinates
of the fourth vertex of this
rhombus?
3
At least
one right
angle
Draw a four-sided
shape that fits
these criteria.
What would it be
called?
Join two vertices with another line to
make a triangle? Describe it. What type
of triangle is it?
2
1
1
2
3
4
5
6
7
8
9
10