Maths Mixed age Year 5/Year 6 Weekly Plan: Autumn
Week 10: Shape and fractions
No starter
Monday
Y5 Objectives: Identify, visualise and describe properties of 3D shapes; Use these properties to sort 3D shapes; Compare and order fractions with related denominators; Add and subtract
fractions with related denominators.
Y6 Objectives: Identify, describe and build 3D shapes using nets; compare and order fractions with unrelated denominators; Use common multiples to express fractions in the same
denomination; Add and subtract fractions and mixed numbers with unrelated denominators.
Very quick Starter
Whole class teaching
Guided group and independent paired/indiv practice activities
Plenary
Sort 3D shapes according to their properties; Visualise 3D shapes from 2D drawings;
Y5 Activity, TA if available to work with Easier group
Sort the
Recognise nets for a cube.
Put a selection of 3D shapes on each table, both regular and shapes in a
Arrange chn in a circle so that they can all see a collection of 3D shapes. Hold up the cube and the
irregular. Chn each secretly choose one of the shapes. They Venn
cuboid. What is the same about these 2 shapes and what is different? (e.g. Have the same number of
write its name and list some its properties. They take it in
diagram
faces, vertices and edges, have flat faces, one has only squares faces – it is regular.) How could we sort
turns to read out the properties of their mystery shape, 1 at made from 2
these shapes into 2 sets, so that every shape appears in 1 but not both sets, i.e. there is no overlap?
a time. The first child in the rest of the group to correctly
overlapping
Discuss how ‘has triangular faces’ and 'has square faces’ will not do because a shape could have both or guess the shape scores a point. Next they secretly choose
hoops, but
neither. Draw out the language used in Carroll diagrams, e.g. ‘has at least one triangular face’, ‘has no
another shape and attempt to draw it. They take it in turns
without the
triangular faces’, ‘is a prism’, ‘is not a prism’, ’is regular’, ‘is irregular’ so that the 2 headings are the
to show the rest of the group. If the group can guess it, the
headings.
opposite of one another (mutually exclusive). You may need to sort the shapes according to criteria the child who drew it scores a point.
Can the rest
chn give, even if they are incorrect, to show this. Once you have sorted the shapes, discuss how each
of the class
Y6 Activity
group can be sorted again into 2 different sets. Draw a Carroll diagram and help chn to write names of
guess them?
Chn identify which nets which will make a cube (see
shapes they have sorted in the correct places. Repeat with other criteria. Make sure that chn realise
Repeat with
resources). They choose one and record its properties
that the faces are called 2D shapes (2 dimensions) and the solids are called 3D shapes (3 dimensions).
another
including how many pairs of parallel faces it has.
Send Y5 away now to work with TA or independently.
way.
Harder: If chn finish challenge them to draw as many nets
Show a net of a cube and ask chn to sketch it on paper. Point to one of the faces. This face is going to
as they can that would make an ‘open’ cube, i.e. 1 with a
be at the bottom when I make it. Which face do you think will be parallel to this face when I make the
‘lid’.
shape? Ask chn to mark on their copies of the net. Take suggestions, if there is consensus colour in that GUIDED: Work with chn who find it difficult to imagine 3D
face and the base, and make the cube to check. Unfold it again. Point to the base again. Which faces do objects from 2D drawings, encouraging them to cut the
you think will be perpendicular, at right angles, to this face when I make it up again? Mark them with a
nets out and try to make a cube if necessary.
cross on your net. Take feedback, mark the 4 faces with a cross, and make up the cube to check.
© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
MATHS Mixed age Y5/Y6 Week 10 Autumn
Wednesday
Week 10: Shape and fractions
Very quick Starter
Whole class teaching
Visualise 3D shapes from 2D drawings; Describe properties of prisms & pyramids;
Recognise and build pyramids and prisms, making nets.
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm.
Can chn name each 3D shape? Hover over each to confirm. Ask if chn find any of the
drawings difficult to imagine in 3D. If so, click on the shape and play the animation.
Remind chn that there are lots of sorts of pyramids, with different 2D shapes on their
bases, and there are lots of different prisms, with different 2D shapes at each end.
Show animations of triangular, pentagonal and octagonal prisms at
http://www.learner.org/interactives/geometry/3d_prisms.html. What do prisms have
in common? Draw out that the 2 end faces are the same; they are polygons as they
have straight sides, and are joined by rectangles (which could include squares). Show
animations of triangular, pentagonal and octagonal-based pyramids at
http://www.learner.org/interactives/geometry/3d_pyramids.html. What do pyramids
have in common? They have a polygon as 1 face and triangles as the other faces. Show
chn the 2 nets (see resources) and ask chn to discuss which will make a prism and
which will make a pyramid, and how they know. What sort of prism will this net make?
What sort of pyramid will this net make? Ask a child to make the nets into 3D shapes to
check. Use sticky tape to secure the edges. Work with a partner to sketch a net for a
hexagonal-based pyramid. Share chn’s sketches. Repeat for a hexagonal prism.
No starter
Tuesday
Maths Mixed age Year 5/Year 6 Weekly Plan: Autumn
Factors
Put chn into 4 teams.
Give numbers 24, 28, 36
and 48, one to each
team. Roll a 1–9 dice. If
the number rolled is a
factor of their number,
chn put up their hand
and the team score a
point. Carry on playing.
Why is it not fair? (28
has fewer factors.)
Repeat but teams
choose their own 2-digit
number. Team score a
point each time the
number rolled is factor
of their number.
Guided group and independent paired/indiv practice activities
Plenary
Y5 Guided group report
GUIDED: Y5 Easier
Y5 Harder
back. (The number of faces
Give chn a sheet of
Give pairs of chn a sheet of prisms
is the number of sides of
pyramids (see resources).
(see resources). Chn write the shape
the 2D non-triangular face,
They record the name of
of the two end faces, then the
the non-triangular shape,
number of faces & vertices in a table. plus 1. The number of
vertices is the same.)
the numbers of faces and
If they have difficulty visualising the
Discuss why this is. (A
vertices in a table. After
3D shape, give them scrap
triangular face is attached
the first few can they
paper/tape to make 3D models.
to each side of the nonpredict the number of
After the first few, can they predict
triangular face.) Ask chn
faces and vertices?
the number of faces and vertices?
exploring prisms to report
Y6 Activities, TA if available
back what they found. (The
Activity 1: Chn draw and make their own nets for triangular prisms
number of faces is the
and cuboids. Allow them to experiment and find out how the lengths
number of sides of the 2D
of the end faces need to correspond to the edges of the central ‘tube’. shape at each end, plus 2,
Activity 2: Chn look at http://www.korthalsaltes.com/index.html of
the number of vertices is
different polyhedra. Choose a polyhedron to make, other than one
twice the number of sides
they have already made and print out the net for their chosen shape.
of the 2D shape at each
Afterwards they each write a description of their polyhedron. Use
end.) Discuss why this is.
their shapes and descriptions to form a display. [Abacus txtbk 1 p.76]
Compare and order fractions with related denominators;
Y5 Easier TA if available
Y5 Harder
Write: Fractions
Compare and order fractions with unrelated denominators; Use common
Chn compare pairs of
Chn compare pairs of with bigger
multiples to express fractions in the same denomination.
fractions by writing them
fractions then order
denominators
Write 3/8 and ¼ on the board. Which do you think is bigger? Can you persuade us!? as the same sort of
trios by writing them
(numbers on the
Suggest that we can write both fractions as 1/8s. Write 2/8 < 3/8 under the pair of
fraction, using a fraction
as the same sort of
bottom) are bigger.
fractions and agree that this means 3/8 is definitely bigger than ¼. Repeat with 2/5
wall up to 1/12s to help
fraction (see
Do you think that’s
and 3/10. Ask chn to discuss in pairs which they think is the biggest out of 5/6, 2/3
(see resources). [Abacus
resources).
right? Discuss with
and 7/12. Draw out that we can write ALL of them as 1/12s! Write the equivalent
txtbk 1 p.53]
your partner. Take
fractions under each. Now we can write them in order. It was very difficult to see,
feedback. Discuss
GUIDED: Y6 Easier
Y6 Harder
until we wrote them all as the same sort of fraction.
how it depends on
Chn compare
Send Y5 away now to work with TA or independently. Write 5/6 and ¾ on the
the numerator, but
then order trios
board. Which do you think is bigger? Perhaps 5/6 is bigger than ¾ as it is only 1/6 off
if fractions have
of fractions by
a whole number, as opposed to ¼. Say that we can prove this by writing them as
the same
writing them as
the same sort of fraction. Together list a few common multiples of 4 and 6. Explain
numerator, then
the same sort of
that we can use this to help us decide what denominator to use when writing
those with larger
fraction (see
these fractions as the same sort. Agree 12 is the smallest common multiple, and
denominators are
resources).
ask chn to write both fractions as 1/12s, then compare them. We could have written
smaller.
both as 1/24s, but then would have had to simplify them. Repeat with 5/6 and 7/9.
© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
MATHS Mixed age Y5/Y6 Week 10 Autumn
Friday
Thursday
Maths Mixed age Year 5/Year 6 Weekly Plan: Autumn
Week 10: Shape and fractions
Very quick Starter
Whole class teaching
Guided group and independent paired/indiv practice activities
Turn improper fractions Add fractions with related denominators;
Y5 Easier
GUIDED: Y5 Harder
into mixed numbers
Add fractions with unrelated denominators.
Chn work out ½ + Chn practise adding pairs of
and vice versa
Write ½ + ¾ on the board. Ask chn to discuss in pairs what they think the answer ¼, ½ + 1/6, ½ + 1/8
fractions, first with a total of
Chn shuffle 1 to 6 digit
might be. Discuss how they might be able to imagine two of the quarters being
and ½ + 1/10 using less than 1, then with a total
cards (Y5) or 1 to 9 digit added to the half to make 1, and the other quarter being added, but this is not
a fraction wall to
of more than 1 (see
cards (Y6), take 2 to
easy and we are only adding halves and quarters! Explain that we can make it
help write ½ as
resources). Help them to use a
make an improper
easier by writing both fractions as the same sort just like we do when comparing ¼s, 1/6ss, 1/8s and
fraction wall if necessary (see
1
fraction, and then write fractions. Rewrite the addition underneath as 2/4 + ¾. Now we can see straight
/10s.
resources day 3).
as a mixed number.
away that the answer 5/4. How can we write that as a mixed number? Write 2/3 + Y6 Easier
Y6 Harder
How many can they find 1/6 on the board. What can we do this time? Ask a child to rewrite the addition
TA if
Give chn a set of fractions (see
in 3 minutes? They use
underneath, both fractions written as sixths: 4/6 + 1/6 = 5/6. The addition was
available
resources). They look for pairs of
the 1 and 2 others to
really easy once we had fractions written as the same sort! Repeat with ½ + 5/8,
As Year 5
fractions that they can write as the
make a mixed number,
writing the answer as an improper fraction first, then as a mixed number. Write
Harder. Or same type, but both must have new
e.g. 13/7. They write this ½ + 2/3 on the board. This time we can't write one fraction as the same type as
[Abacus
denominators. They write at least 4
as an improper fraction. the other. Ask chn to discuss with a partner what could be done to help. Take
txtbk 1
additions with a total of more than 1,
How many can they
feedback. Draw out changing both to 1/6s. Ask Y6 chn to do this, and then Y5s
p.83]
and at least four with a total of less
write in 3 minutes?
find the answer. Repeat with other subtractions such as ½ + 2/5 and 2/3 + 2/5.
than 1.
Mental
Subtract fractions with related denominators;
Y5 Easier
Y5 Harder
multiplication
Subtract fractions with unrelated denominators.
Children practise
Chn choose a fraction from 1 set, and
Remind chn that
Write the following subtractions on the board: ¾ – ½, 7/10 – 2/5, ¾ – 3/8. Point
subtracting pairs
then look for a fraction in the second
we can multiply by to the first. We might be able to imagine ½ taken from ¾, but as yesterday
of related
set such that they can write both
4 by doubling twice we can write the fractions as the same sort, and then subtract. Ask chn to
fractions, mainly
fractions as the same sort, then
and multiply by 5
work in pairs. The first writes both fractions in the subtraction as the same
unit fractions (see subtract (see resources). Challenge
by halving and
type, and the second works out the subtraction. Take feedback and agree the resources).
them to find at least 8 subtractions.
multiplying by 10
answers as ¼, 3/10 and 3/8.
GUIDED: Y6 Easier
Y6 Harder
(or vice versa). Ask Send Y5 away now to work with TA or independently. Write ¾ – 2/3 on the
Chn work out ½ + 1/3, ½ + Chn work out the following
them to multiply
board. Ask chn to discuss with a partner what could be done to help. Take
¼, ½ + 1/5…then ½ - 1/3, ½ subtractions: 2/3 – ½, ¾ - 2/3, 4/5
1
each of the
feedback. Draw out changing both to /12s. Ask chn to do this, and then find
- ¼, ½ - 1/5… first
– ¾, 5/6 – 4/5 and so on. What
1
2
2
4
following numbers the answer. Repeat with other subtractions such as ½ – /5, /3 – /5 and /5 –
agreeing in pairs how to
do they notice about the
by 4 and 5: 72, 48,
¾. Write 11/7 – 3/7 on the board and ask chn to discuss in pairs how they
write both fractions as
answers?
54, 96, 78.
might work this out. Take feedback. Draw out writing 1½ as an improper
the same type. [Abacus
fraction, 8/7 then subtracting 3/7 to give 5/7. Ask chn to work out 12/5 – 4/5.
txtbk 1 p.85]
© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Plenary
Write these
additions on the
board: 5/6 + 1/3, ½ +
¼, 3/7 + 1/14, ½ + 7/10.
Ask chn to discuss in
pairs which additions
they think will have a
total of more than 1
and which will have a
total of less than 1.
Give one to each of
the quarter of the
class, and then check
against chn’s
predictions.
Ask chn to check
these subtractions
with addition:
½ – 3/8 = 1/8
7
/8 – ¾ = 3/8
7
/10 – ½ = 3/10
4
/5 – 3/10 = ½.
Y6 check the first
two and:
11/6 – 5/6 = 4/6
2¼ - ¾ = 1½.
MATHS Mixed age Y5/Y6 Week 10 Autumn
Maths Mixed age Year 5/Year 6 Weekly Plan: Autumn
Week 10: Shape and fractions
Resources:
 A collection of 3D shapes
 Two hoops
 Monday: Year 6 activity sheet cube nets (see resources)
 3D shapes at http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm
 Animations of triangular, pentagonal and octagonal prisms at http://www.learner.org/interactives/geometry/3d_prisms.html
 Animations of triangular, pentagonal and octagonal-based pyramids at http://www.learner.org/interactives/geometry/3d_pyramids.html
 Tuesday: picture of two nets (see resources)
 Tuesday: Year 5 activity sheet of prisms (Harder group) (see resources)
 Tuesday: Year 5 activity sheet of pyramids (Easier group) (see resources)
 Tuesday: Y6 Abacus txtbk 1 p.76
 Access to different polyhedra on: http://www.korthalsaltes.com/index.html and facility to print out
 Paper, scissors and tape
 1-9 dice (or 0 to 9 and roll again if it lands on 0)
 Wednesday: Comparing and ordering fractions activity sheets (Y5 Easier, Y5 Harder, Y6 Harder) (see resources)
 Wednesday: Y5 Abacus txtbk 1 p.53; Y6 txtbk 1 p.63
 Fraction wall – up to 1/12s and up to 1/15s (see resources)
 1 to 9 digit cards
 Thursday: Adding fraction activity sheets (Y5 Harder/Y6 Easier and Y6 Harder) (see resources)
 Thursday: Y6 Abacus txtbk 1 p.83
 Friday: Year 5 Subtracting fractions (easier and harder versions) (see resources)
 Friday: Y6 Abacus txtbk 1 p.85
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Scroll down for outcomes
© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
MATHS Mixed age Y5/Y6 Week 10 Autumn
Maths Mixed age Year 5/Year 6 Weekly Plan: Autumn
Week 10: Shape and fractions
Outcomes
Tuesday
Outcomes for most children
Wednesday
Thursday
Friday
1. Use a range of mathematical
vocabulary to describe 3D shapes.
2. Sort 3D shapes according to
their properties using Carroll
diagrams.
1. Visualise 3D shapes from 2D
representational drawings.
2. Describe properties of prisms
and pyramids.
1. Compare and order fractions
with related denominators.
1. Add fractions with related
denominators.
1. Subtract fractions with related
denominators.
1. Recognise nets for a cube.
1. Make nets and use to make
polyhedral.
1. Compare and order fractions
with unrelated denominators.
1. Add fractions with unrelated
denominators.
1. Subtract fractions with
unrelated denominators.
Year 6
Year 5
Monday
Year 6
Year 5
Default (outcomes for children not on statements but not able to reach the outcomes for most children)
1. Use a range of mathematical
vocabulary to describe 3D shapes.
2. Sort 3D shapes according to
their properties using Venn
diagrams.
1. Visualise 3D shapes from 2D
representational drawings.
2. Describe properties of prisms
and pyramids.
1. Compare pairs of fractions with
related denominators.
1. Add unit fractions with related
denominators.
1. Subtract unit fractions with
related denominators.
1. Recognise nets for a cube.
1. Make nets and use to make
polyhedral.
1. Compare pairs of fractions with
unrelated denominators with
support of a fraction wall.
1. Add fractions with related
denominators.
1. Add and subtract fractions with
unrelated denominators with
support.
Only record names of children who struggled or exceeded these outcomes
© Original plan copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
MATHS Mixed age Y5/Y6 Week 10 Autumn