Cross-Sections and Right Prisms: a week of ready-to-teach maths
Five days of lessons for Year 6 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus twelve solid cards and twelve slice cards for Slice match, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Gather play dough and dental floss for Days 1 and 3, and pattern blocks and cubes for Day 4.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Cut out the Slice match cards for Day 5, one set for each pair.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: cut a solid straight through, parallel to its base, and the flat face you uncover is a cross-section, or slice. A right prism has the same slice all the way up, a copy of its base, and the base names it. Pyramids and cones have slices that shrink to a point; a sphere’s grow and then shrink; a cylinder’s stay the same, but its base is a circle, so it is not called a prism.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Words to watch
A cross-section is the flat face a straight cut uncovers; this week every cut is parallel to the base. The base of a prism is the face that repeats, whichever way the prism lies. A right prism has two identical polygon ends joined by rectangles that stand square to them. The apex is the point a pyramid or a cone rises to.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Slice it | Cut play-dough solids parallel to the base low, halfway and high, trace the slices, and compare everyday objects | A slice reveals a flat shape |
| 2 | Same all the way | Recognise right prisms by their matching slices, name them by their bases, and find the pattern in faces, edges and corners | Reading the cross-section’s shape; Cross-sections name the solid |
| 3 | Shrinking slices | Measure a pyramid’s slices on a side view, draw them, and compare pyramids, cones and spheres with prisms | A pyramid’s slices shrink |
| 4 | Build it in layers | Stack pattern blocks and layers of cubes into prisms, and count the cubes as one layer times the layers | A prism is its base, repeated |
| 5 | Prism or not? | Name mystery solids from their slices, decide which everyday objects are right prisms, and play Slice match | Telling a prism from the rest |
How the week builds
Day 1 slices solids and looks at what the cuts uncover; Day 2 finds the solids whose slices never change, the right prisms; Day 3 measures slices that shrink; Day 4 builds prisms layer by layer; and Day 5 sorts prisms from the rest. It builds on the Year 5 work of connecting solids to their nets (AC9M5SP01). It leads to the Year 7 work on the volume of right prisms (AC9M7M02), where the matching slices become the key to how much space a prism fills.
Materials for the week (one trip)
- For Days 1 and 3: play dough or modelling clay, and dental floss or a plastic knife for each pair.
- For Day 2: a collection of prisms, such as boxes, a new hexagonal pencil and wooden blocks.
- For Day 4: pattern blocks and about 60 interlocking cubes for each pair.
- For Day 5: the Slice match cards, one set for each pair. Rulers and coloured pencils all week.
Words for the word wall
cross-section, slice, parallel, base, right prism, triangular prism, rectangular prism, pentagonal prism, hexagonal prism, pyramid, cone, cylinder, sphere, apex, face, edge, corner
Dear families
This week in maths, Year 6 slices solids. We cut play dough straight across, look at the flat shape each cut uncovers, and find out why a prism has the same slice all the way up while a pyramid’s slices shrink.
Try this at home
- When you cut a carrot or a cucumber into rounds, compare the slices from the thick end and the thin end.
- Find a box, a tin and a new pencil. What shape would each slice be if you cut it across?
- Ask your child why a loaf of sandwich bread gives slices that are nearly all the same.
- Spot prisms around the house: what shape is each one’s base?
Slices we found
Fill one row a day. Name an object, draw its slice, and say whether the slices stay the same or change.
| Day | Object | Its slice | Same or changes? |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Cross-Sections and Right Prisms teaching pack · seegongsik.com/au/y6/space/AC9M6SP01/pack
Slice it
A cross-section is the flat face you uncover when you cut straight through a solid. This week every cut is parallel to the base: level slices, one above another. Children slice play-dough solids low, halfway and high, trace each slice, and find that some solids give the same slice every time while others change.
We are learning to
- describe a cross-section as the flat face a straight cut uncovers,
- cut solids parallel to the base and draw the slices,
- compare slices taken low, halfway and high.
Success criteria
- I can draw the slice of a play-dough cylinder cut parallel to its base.
- I can say whether a solid’s slices stay the same or change, and how.
You need
The worksheet, one per child, play dough and dental floss or a plastic knife for each pair, and a new pencil, a candle and a box to show.
Lesson flow (about 50 minutes)
| 10 min | Cut it Show the board (see the box). Children predict the slice before each press. Ask: “If we cut the box near the top instead, would the slice be bigger, smaller or the same?” |
| 25 min | Play-dough slices Pairs roll a cylinder and shape a cube and a square pyramid. They cut each one parallel to its base low, halfway and high, press each slice on paper and trace round it (Part B). Ask: “Which solid gave you three slices you could stack exactly on top of each other?” |
| 15 min | Everyday slices Children answer Parts A and C. Ask: “A carrot and a candle are both long and round. How are their slices different?” |
Two half-sessions instead? Split after the play-dough slices; start Session B with Part A.
Watch for these ideas
- Drawing the outside of the solid instead of the flat face the cut uncovers.
- Cutting at a slant, which changes the slice: keep the cut level, parallel to the base.
- Thinking every solid’s slices must get smaller higher up.
Answers
- Part A: (1) hexagon, the same; (2) circle, the same; (3) rectangle, the same; (4) circle, smaller towards the tip; (5) circle, bigger, then smaller.
- Part B: cylinder, circles the same; cube, squares the same; square pyramid, squares smaller towards the tip; slices vary a little with the cutting.
- Part C: (1) the cylinder and the cube; (2) the square pyramid: its squares get smaller towards the point; (3) the candle’s slices are all the same circle, the carrot’s circles shrink towards the tip.
Slice it
A. Everyday slices
Each object is cut across, parallel to its end. Draw the slice and say how the slices change along the object.
| Object | Draw the slice | Same, or how do they change? |
|---|---|---|
| a new hexagonal pencil, before it is sharpened | ||
| a round candle | ||
| a house brick | ||
| a carrot, cut into rounds | ||
| an orange, cut into rounds |
B. Play-dough slices
Cut each solid parallel to its base low down, halfway up and high up. Trace each slice in its box.
| Solid | Low | Halfway | High | Same or changes? |
|---|---|---|---|---|
cylinder | ||||
cube | ||||
square pyramid |
C. Same or changes?
1. Which play-dough solids gave the same slice at every height? ______________________________
2. Which solid’s slices changed? How? ______________________________________________
3. A carrot and a candle are both long and round. How are their slices different? ____________________
Same all the way
A right prism has two identical ends joined by rectangles that stand square to them, so every slice parallel to the base is a copy of the base. The base names the prism: a triangle base makes a triangular prism. Children name prisms from their slices and find the pattern in their faces, edges and corners.
We are learning to
- recognise a right prism by its matching slices parallel to the base,
- name a prism from the shape of its base,
- find the pattern in a prism’s faces, edges and corners.
Success criteria
- I can name a prism from its slice.
- I can predict the faces, edges and corners of a prism with a base of 10 sides.
You need
The worksheet, one per child, and a collection of prisms: boxes, a new hexagonal pencil and wooden blocks.
Lesson flow (about 50 minutes)
| 10 min | Name it Show the board (see the box). The class votes before each press. Ask: “Why is every slice of a cube a square, and not just a rectangle?” |
| 25 min | Prism hunt Groups hold each prism in the collection, find its base and run a finger along a slice. Then children do Parts A and B. Ask: “A prism with a base of 5 sides has 7 faces. Where do the other 2 come from?” |
| 15 min | Prism or not? Children answer Part C. Ask: “A cylinder has the same slice all the way up. Why do we not call it a prism?” |
Two half-sessions instead? Split after Part A; start Session B with the faces, edges and corners in Part B.
Watch for these ideas
- Naming a prism by its rectangle side faces instead of by its base.
- Counting only the faces they can see in a drawing.
- Thinking a cube is not a prism: it is a square prism whose sides are squares too.
Answers
- Part A: (1) hexagon, hexagonal prism; (2) triangle, triangular prism; (3) octagon, octagonal prism; (4) rectangle, rectangular prism; (5) pentagon, pentagonal prism.
- Part B (faces, edges, corners): triangle 5, 9, 6; square 6, 12, 8; pentagon 7, 15, 10; hexagon 8, 18, 12; octagon 10, 24, 16; 10 sides: 12, 30, 20; faces are the sides plus 2, edges 3 times the sides, corners 2 times the sides.
- Part C: (1) yes, a square prism: every slice is the same square; (2) no: its slices are all the same, but its base is a circle, not a polygon, and it has no rectangle sides.
Same all the way
A. Name the prism
The shaded top is a copy of the base. Draw each prism’s slice parallel to the base, and name the prism.
B. Faces, edges and corners
| Base | Sides of the base | Faces | Edges | Corners |
|---|---|---|---|---|
| triangle | 3 | |||
| square | 4 | |||
| pentagon | 5 | |||
| hexagon | 6 | |||
| octagon | 8 | |||
| decagon | 10 |
The rule for any prism, from the sides of its base: faces ______________ edges ______________ corners ______________
C. Prism or not?
1. Is a cube a prism? Why? ______________________________________
2. A cylinder’s slices are all the same circle. Is it a prism? Why? ____________________
Shrinking slices
A pyramid’s slices parallel to the base have the base’s shape, but they shrink as they go up and vanish at the apex. A cone does the same with circles. Seen from the side the pyramid is a triangle, so halfway up the slice is half as wide as the base. Children measure slices on a side view, draw them, and compare pyramids and cones with prisms.
We are learning to
- describe how the slices of a pyramid and a cone change,
- measure a slice’s width from a side view,
- compare a pyramid with the prism on the same base.
Success criteria
- I can find the width of a pyramid’s slice halfway up.
- I can explain why a pyramid is not a prism.
You need
The worksheet, one per child, play dough and dental floss for each pair, and rulers.
Lesson flow (about 50 minutes)
| 10 min | Shrink it Show the board (see the box). Children predict the slice before each press. Ask: “The base is a square. Is the slice near the top still a square?” |
| 25 min | Side view Children read the side view in Part A and draw the slices in Part B. Pairs check with a play-dough pyramid cut halfway up. Ask: “Halfway up, the slice is half as wide. Does it cover half as many squares?” |
| 15 min | Pyramid or prism? Children answer Part C. Ask: “Where would you cut an orange to get the biggest round? Why?” |
Two half-sessions instead? Split after Part A; start Session B with the drawings in Part B.
Watch for these ideas
- Thinking every slice of a pyramid is the same as its base, because the base is the shape they know.
- Measuring the slanted side of the side view instead of straight across.
- Thinking a slice half as wide covers half as many squares: it covers a quarter.
Answers
- Part A (width, squares covered): height 0: 8, 64; height 2: 6, 36; height 4: 4, 16; height 6: 2, 4; height 8: 0, 0.
- Part B: squares 6, 4, 2 wide; halfway up, 4 by 4 covers 16 squares, a quarter of the base’s 64.
- Part C: (1) 8: a prism’s slices are all the base; (2) 4, then 2; (3) through the middle, where the circles stop growing and start to shrink.
Shrinking slices
A. Read the side view
A square pyramid is 8 squares wide and 8 squares tall. The dashed lines are slices parallel to the base. Measure how wide each slice is.
| Height | Width of the slice | Squares it covers |
|---|---|---|
| 0 | 8 | 64 |
| 2 | ||
| 4 | ||
| 6 | ||
| 8 |
B. Draw the slices
Draw the slices at heights 2, 4, 6 as squares on the grid. Label each with its height.
C. Pyramid or prism?
1. A square prism has the same 8 by 8 base and is 8 tall. How wide is its slice at height 4? ______
2. A cone is 8 squares wide and 8 squares tall. How wide is its slice at height 4? ______ At height 6? ______
3. An orange is a sphere. Where would you cut it to get the biggest round? Why? ______________________
Build it in layers
A prism is its base repeated: stack identical layers straight up and you build a prism, which is why every level slice matches the base. Children build prisms from pattern blocks and from layers of cubes, and count the cubes in a prism as the cubes in one layer times the number of layers.
We are learning to
- build a prism by stacking identical layers,
- name the prism a stack of one shape makes,
- count the cubes in a prism as one layer times the layers.
Success criteria
- I can say which prism a stack of hexagon blocks makes.
- I can find the cubes in a prism with 12 cubes in each layer and 5 layers.
You need
The worksheet, one per child, pattern blocks, and about 60 interlocking cubes for each pair.
Lesson flow (about 50 minutes)
| 10 min | Stack it Show the board (see the box). Children predict the label before each press. Ask: “Six triangle layers make a prism. What is the slice through the third layer?” |
| 25 min | Block towers Pairs stack pattern blocks of one shape into towers (Part A), then build the cube prisms on the bases in Part B. Ask: “The L-shaped tower is a prism too. How do you know?” |
| 15 min | Layers count Children answer Part C. Ask: “96 cubes in 8 identical layers. How many in each layer, and what could the base look like?” |
Two half-sessions instead? Split after the pattern-block towers; start Session B with the cube prisms in Part B.
Watch for these ideas
- Thinking only boxes are prisms, so an L-shaped or a step-shaped tower cannot be one.
- Counting the cubes one by one instead of one layer, then the layers.
- Building towers that get narrower, and still calling them prisms.
Answers
- Part A: (1) a hexagonal prism; (2) a triangular prism; (3) a square prism; (4) a trapezoidal prism.
- Part B: (1) 12 in a layer, 5 layers, 60 cubes; (2) 5 in a layer, 4 layers, 20 cubes; (3) 6 in a layer, 3 layers, 18 cubes.
- Part C: (1) 12 cubes in each layer, for example a base of 12 squares such as 4 by 3; (2) no: its layers are not all the same, so its slices change.
Build it in layers
A. Pattern-block towers
Stack ten blocks of one shape straight up. Name the prism you built.
B. Cube prisms
Build each prism: cover the base with cubes, then stack the layers. Fill in the table.
| Base | Cubes in one layer | Layers | Cubes in the prism |
|---|---|---|---|
| 5 | |||
| 4 | |||
| 3 |
C. Layers count
1. A prism is built from 8 identical layers and uses 96 cubes. How many cubes are in each layer? ______ Draw a base it could have.
2. A tower of cubes gets narrower as it goes up. Is it a prism? Why? __________________________________
Prism or not?
A right prism has the same slice all the way up, on a polygon base. A cylinder’s slices stay the same too, but its base is a circle, so it is not called a prism; pyramids, cones and spheres have slices that change. Children name mystery solids from their slices, decide which everyday objects are right prisms, and play Slice match.
We are learning to
- name a solid from a description of its slices,
- decide whether an object is a right prism, and explain why using its slices,
- match solids to their slices.
Success criteria
- I can name a solid whose slices are circles that grow, then shrink.
- I can explain why a new hexagonal pencil is a prism but a sharpened one is not.
You need
The worksheet, one per child, and the Slice match cards (cut-outs), one set for each pair.
Lesson flow (about 50 minutes)
| 10 min | Prism or not? Show the board (see the box). The class decides before each press. Ask: “A cone and a cylinder both have circle slices. What is different about them?” |
| 25 min | Mystery solids Children work through Parts A and B, then share their reasons for Part C. Ask: “Which clue told you straight away that a solid could not be a prism?” |
| 15 min | Slice match Pairs play Slice match (cut-outs). Finish with the self-check quiz as a class game. Ask: “Which two cards were easiest to mix up? What told them apart?” |
Two half-sessions instead? Split after Part B; start Session B with Part C and Slice match.
Watch for these ideas
- Calling a cylinder a prism because its slices are all the same.
- Thinking a prism must stand on its base: a prism lying down is still a prism.
- Deciding from the name or the look of an object instead of from its slices.
Answers
- Part A: (1) hexagonal prism; (2) square pyramid; (3) cylinder; (4) sphere; (5) triangular pyramid; (6) rectangular prism.
- Part B: (1) yes, a hexagonal prism: same slices, polygon base; (2) no: near the tip the slices shrink to a point; (3) no, a cylinder: same slices, but a circle base; (4) yes, a rectangular prism: same slices, polygon base; (5) no, a square pyramid: slices shrink to the apex; (6) yes, a rectangular prism: same slices, polygon base.
- Part C: yes: cut parallel to the triangle ends instead, and every slice is the same triangle. A prism’s base is the face that repeats, whichever way it lies.
Prism or not?
A. Mystery solids
Each clue tells you the slices parallel to the base. Name the solid.
| 1 | Its slices are hexagons, all the same size. | |
| 2 | Its slices are squares that shrink to a point. | |
| 3 | Its slices are circles, all the same size. | |
| 4 | Its slices are circles that grow, then shrink. | |
| 5 | Its slices are triangles that shrink to a point. | |
| 6 | Its slices are rectangles, all the same size. |
B. Is it a right prism?
| Object | Yes or no | Why, using its slices |
|---|---|---|
| a new hexagonal pencil | ||
| a pencil sharpened to a point | ||
| a round candle | ||
| a house brick with no holes | ||
| a glass paperweight shaped like a square pyramid | ||
| a 30 cm ruler |
C. A prism lying down
A tent is shaped like a triangular prism lying on its side. Its slices parallel to the floor get narrower towards the top. Is it still a prism? Explain.
______________________________________________________________________________
______________________________________________________________________________
Slice match: solid cards
Cut out one set for each pair. The twelve solids stand on their bases; dashed lines are edges at the back.
How to play Slice match (Day 5)
- Lay the solid cards face up. Shuffle the slice cards and deal them out between the two players.
- Take turns: place one of your slice cards on the solid it belongs to, and say why, using the words same, shrink or grow.
- Your partner checks. A right match keeps the pair; a wrong one goes back. The most pairs wins.
Slice match: slice cards
Each card shows one solid’s slices parallel to its base: low down, halfway up and high up.
Teacher note, the matches: 1 = D (cube), 2 = I (rectangular prism), 3 = B (triangular prism), 4 = G (pentagonal prism), 5 = L (hexagonal prism), 6 = E (octagonal prism), 7 = J (cylinder), 8 = A (square pyramid), 9 = F (triangular pyramid), 10 = K (hexagonal pyramid), 11 = C (cone), 12 = H (sphere).
What we know: Cross-Sections and Right Prisms
Work on your own. Show your thinking if you can.
- A triangular prism is cut parallel to its base. What shape is the slice? ______________
- What is the name of a prism whose base is an octagon? ______________
- A prism’s base has 7 sides. How many faces, edges and corners does it have? Faces ______ Edges ______ Corners ______
- A square pyramid is 10 cm wide and 10 cm tall. How wide is its slice halfway up? ______
- Circle the solids whose slices parallel to the base are all the same: cube · cone · cylinder · sphere · triangular prism.
- Is a cone a prism? Explain using its slices. ______________________________________
- A prism is built from 6 identical layers of 10 cubes. How many cubes does it use? ______
- A solid’s slices, low, halfway and high, look like this. What is the solid? ______________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- A triangle, the same as the base.
- An octagonal prism.
- 9 faces, 21 edges, 14 corners.
- 5 cm, half the base’s width.
- cube and cylinder and triangular prism.
- No: its slices are circles that shrink to the point, and its base is a circle, not a polygon.
- 60 cubes.
- A sphere: its circle slices grow, then shrink.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Slices (Q1, Q5, Q8) | draws the outside of a solid, not the face a cut uncovers | describes slices parallel to the base as the same, shrinking or growing | predicts a solid’s slices from a picture or a description |
| Right prisms (Q2, Q3, Q6) | names a prism by its rectangle sides | names a prism by its base and explains its matching slices | finds the faces, edges and corners of any prism from its base |
| Shrinking slices (Q4) | thinks every slice of a pyramid is the base | finds a slice’s width from the height climbed | explains why halfway up covers a quarter of the base |
| Layers (Q7) | counts cubes one at a time | multiplies the cubes in a layer by the layers | finds a layer from the total and the layers |
Eight questions, four ideas. A child at standard describes how a solid’s slices behave and uses that to decide, and explain, whether it is a right prism.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Slicing | Prisms | Pyramids | Layers | Prism or not |
|---|---|---|---|---|---|
The five columns are the five days: slicing solids, right prisms, shrinking slices, building in layers, and telling a prism from the rest.