Composite Shapes: a week of ready-to-teach maths

Five days of lessons for Year 4 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out shape pieces and composite cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the shape pieces and the composite cards once; they are reused across the week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

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. A composite shape is made by joining familiar shapes: squares, rectangles, triangles and circles. Children build composite shapes from pieces, split them back into their parts, and draw real things with familiar shapes. Solid objects work the same way: a rocket is close to a cylinder with a cone on top.

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.

Familiar shapes and objects

The familiar shapes here are the square, rectangle, triangle and circle; the familiar objects are the cube, rectangular prism, triangular prism, cylinder, cone and sphere. Most shapes split more than one way, and any split into familiar shapes is right. A square is a special rectangle, so splitting into squares is no mistake.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 builds composite shapes from pieces and Day 2 takes them apart. Day 3 sorts composite shapes from simple ones and shows that the same pieces can make different shapes. Day 4 uses familiar shapes to draw real things, and Day 5 does the same with solid objects. It builds on naming shapes and objects by their features in Year 3 (AC9M3SP01).

Materials for the week (one trip)

• From the classroom: scissors, rulers, coloured pencils, a tub of solid blocks or containers (cubes, prisms, cylinders, cones and spheres), and this pack printed.
• Optional: pattern blocks or tangram pieces, and a few classroom objects to draw.
• Cut out once, use all week: the shape pieces and the composite cards.

Words for the word wall

composite shape, simple shape, familiar shape, square, rectangle, triangle, circle, join, split, part, approximate, cube, prism, cylinder, cone, sphere

Dear families

This week in maths, Year 4 learns that many shapes are made by joining familiar shapes, and that real things can be drawn with them: a bus is close to a long rectangle with two circles for wheels.

Try this at home

• Look at a house, a car or a bike. Which shapes could you draw it with?
• Fold and cut a sheet of paper into squares and triangles, then join them into a new shape.
• Find things at home that are close to a cylinder, a cube or a sphere.
• Build a tower from boxes and tins. Which objects is it made of?

Shapes I found this week

Fill one row a day. Write what you found and the shapes in it.

Printed from the free seegongsik Composite Shapes teaching pack · seegongsik.com/au/y4/space/AC9M4SP01/pack

Shapes made from shapes

A composite shape is made by joining two or more familiar shapes. Children cover outlines with cut-out squares, rectangles and triangles, then draw lines to show where the pieces meet. Most outlines can be covered in more than one way, and every way is right when the pieces leave no gaps and do not overlap.

We are learning to

• join familiar shapes to make a composite shape,
• cover an outline with pieces, with no gaps and no overlaps,
• record how a composite shape was made.

Success criteria

• I can build a shape from pieces and draw lines where the pieces meet.
• I can find more than one way to build the same shape.

You need

The shape pieces (cut-out sheet 1), one set per child or pair, and scissors. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after cutting out the pieces; start Session B with Part A.

Watch for these ideas

• Leaving gaps or overlapping pieces, so the outline is not covered exactly.
• Thinking there is only one right way to build a shape.
• Naming the whole shape after one piece: the house is not a triangle.

Answers

• Part A, one way each: the house takes two rectangles and a big triangle; the T-shape takes a square and two rectangles; the arrow takes a rectangle and a big triangle; the sailboat takes two squares, a rectangle and four small triangles.
• Other ways are right too: two squares cover a rectangle and two small triangles cover a big one. Part B: any shape made from exactly three pieces.

Shapes made from shapes

A. Cover each outline with your pieces. Draw lines where the pieces meet.

B. Make a shape of your own from exactly three pieces. Draw it.

Breaking a shape apart

Splitting a composite shape is building it backwards: lines drawn inside the shape cut it into familiar shapes. An L-shape splits into two rectangles, and it splits two ways, with a line down or a line across. Children split shapes into as few rectangles as they can, then into rectangles and triangles, and name the parts.

We are learning to

• split a composite shape into familiar shapes,
• split a shape into as few parts as we can,
• find two different ways to split the same shape.

Success criteria

• I can draw lines to split a shape into rectangles and triangles, and name them.
• I can split the same shape in two different ways.

You need

A ruler and a pencil each, and yesterday’s shape pieces for anyone who wants to check. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the rocket.

Watch for these ideas

• Drawing a line that leaves a part that is not a familiar shape, such as a smaller L.
• Cutting a shape into lots of small squares when two rectangles would do.
• Thinking a shape has only one right split.

Answers

• Part A: the L-shape 2, the U-shape 3, the staircase 3, the Z-shape 2. Part B: the rocket is a rectangle and three triangles; the pencil is a rectangle and a triangle; the table is three rectangles.
• Part C: a line down beside the tall part gives a tall rectangle and a short one; a line across above the base gives a short rectangle on a long one.

Breaking a shape apart

A. Split each shape into as few rectangles as you can. How many?

B. Split each shape into familiar shapes. Name the shapes.

C. Split this L-shape into two rectangles in two different ways.

Composite or simple?

A simple shape is one familiar shape: a circle, a square, a triangle or a rectangle. A composite shape is two or more of them joined edge to edge. The same pieces can make different composite shapes: a square and a triangle make a house with the triangle on top, a signpost with it at the side and a shield with it below.

We are learning to

• tell a composite shape from a simple one,
• see the familiar shapes inside a composite shape,
• join the same pieces in different ways to make different shapes.

Success criteria

• I can say whether a shape is composite and explain why.
• I can match a composite shape to the shapes that make it.

You need

The composite cards (cut-out sheet 2), one set per pair, cut out before the lesson. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the card game.

Watch for these ideas

• Calling a square composite because it can be cut into two triangles. It is already one familiar shape.
• Thinking a composite shape must be big or complicated: two pieces are enough.
• Expecting the same pieces always to make the same shape.

Answers

• Part A: composite 1 (house), 4 (L-shape), 6 (plus sign), 7 (flag); simple 2 (circle), 3 (triangle), 5 (square), 8 (rectangle).
• Part B: each is a square and a triangle; the line goes where they join, on top, at the side and below. Part C: any two shapes made from a rectangle and two triangles. Cards: the key is on the cards sheet.

Composite or simple?

A. Tick the box under each composite shape.

B. Each shape is made of a square and a triangle. Draw a line to show them.

C. Draw two different shapes. Make each one from a rectangle and two triangles.

Drawing real things

Real things are seldom perfect shapes, but familiar shapes can stand in for them: a bus is close to a long rectangle with two circles for wheels. This is approximating. The drawing is close enough to show the thing, not an exact copy. Children draw six objects with familiar shapes and name the shapes they used, then draw something from the classroom for a partner to guess.

We are learning to

• draw a real object with familiar shapes,
• name the shapes we used in a drawing,
• see that an approximation is close, not exact.

Success criteria

• I can draw an object with familiar shapes so that someone else can tell what it is.
• I can list the shapes I used.

You need

Rulers and coloured pencils, the shape pieces, and three or four classroom things to draw, such as a book, a lunchbox and a cup. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the first three objects; start Session B with the window.

Watch for these ideas

• Drawing every detail instead of the main shapes.
• Thinking an approximation is wrong because it is not exact.
• Forgetting circles: wheels, plates and clocks are close to circles.

Answers

• Part A, one way each: a bus as a long rectangle, two circles for wheels and small squares for windows; a bike as two circles for wheels and a triangle for the frame; a table as a long thin rectangle for the top and two thin rectangles for legs; a window as a rectangle split into four squares; a bookshelf as a tall rectangle with three rectangles for shelves; a car as a long rectangle with a shorter one on top, and two circles for wheels.
• Any drawing is right if it uses familiar shapes and someone can tell what it is. Part B: answers vary.

Drawing real things

A. Draw each thing with familiar shapes. Write the shapes you used.

B. Draw something in the classroom with familiar shapes. Can a partner guess it?

Composite objects

Solid objects can be composite too. A rocket is close to a cylinder with a cone on top, and an ice cream is a sphere sitting in a cone. Children name the familiar objects that make six composite objects, match everyday things to the familiar object each is closest to, then build one of their own from blocks.

We are learning to

• name the familiar objects in a composite object,
• match an everyday thing to the familiar object it is closest to,
• build and draw a composite object.

Success criteria

• I can name the parts of a composite object.
• I can build an object from blocks and say what it is made of.

You need

A tub of solid blocks or containers (cubes, rectangular and triangular prisms, cylinders, cones and spheres) for each group. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B by building with the blocks.

Watch for these ideas

• Naming flat shapes for solids: a tin is a cylinder, not a circle or a rectangle.
• Seeing only the biggest part of an object and missing the rest.
• Thinking a sphere and a circle are the same thing.

Answers

• Part A: a rocket is a cylinder and a cone; an ice cream is a cone and a sphere; a house is a cube and a triangular prism; a snowman is two spheres and a cylinder; a lollipop is a sphere and a cylinder; a robot is a cube and a rectangular prism.
• Part B: a water tank to the cylinder; a tent to the triangular prism; a tennis ball to the sphere; a tissue box to the rectangular prism; an ice cube to the cube; a party hat to the cone. Part C: answers vary.

Composite objects

A. Which familiar objects make each one?

B. Draw a line from each thing to the familiar object it is closest to.

C. Build an object from two or more blocks. Draw it and name its parts.

Shape pieces

One set per child or pair. Cut on the dashed lines. The pieces are the size of the Day 1 outlines, so print this sheet and the Day 1 worksheet the same way. Keep the pieces in an envelope for the week.

4 circles

Teacher note: two squares cover a rectangle and two small triangles cover a big triangle, so most outlines can be built more than one way.

Composite cards

One set per pair, for the Day 3 game. Cut out the twelve cards and lay them face up. Match each shape to the card that names its parts.

Teacher note: A T-shape with G, H plus sign with J, K house with E, F arrow with D, C rocket with L, I table with B.

What we know: Composite Shapes

1. Tick the composite shapes.

   A □

   B □

   C □

   D □
2. Draw one line to split this shape into two rectangles.
3. This shape is made of a __________ and a __________.
4. How many squares make this shape? ____
5. A tin of soup is closest to which object? Ring one: cube · cylinder · cone
6. Draw a tree using a circle and a rectangle.
7. This tower is made of a __________ and a __________.
8. Draw a composite shape made of a rectangle and two triangles.

Answers and marking guide

Answers

1. A and C (a pennant flag and a step); the others are simple shapes.
2. A line down at the corner gives a tall rectangle and a short one; a line across gives a short rectangle on a long one. Either is right.
3. A rectangle and a triangle.
4. 5.
5. Cylinder.
6. A circle on top of a rectangle trunk.
7. A cube and a cylinder, in either order.
8. Any shape made from exactly one rectangle and two triangles, such as a boat or a fish.

A quick three-level guide

Eight questions, three ideas. A child at standard sees the familiar shapes inside a composite shape, splits and builds shapes from them, and uses them to draw real things.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: building, splitting, composite or simple, drawing real things, and composite objects.