unit overview - cpb-ap-se2.wpmucdn.com · convince yourself that you your ways will work. convince...

CNPS - GINGERBREAD PLANNER 2019

Unit Overview

Overview Lessons

‘Current understanding suggests it is important not to focus on teaching number

to the detriment of geometry. Also, it should not be assumed that a student

having difficulty with number will also struggle with geometry’

Teaching mathematics: Foundations to Middle Years; D. Siemon, K. Beswick K.

Brady, J. Clark, R. Faragher, E. Warren

Exploring shapes Recreating Prisms and pyramids

Nets and Cubes exploring Building views

Nets and Cubes part 2 City Views

Using isometric paper to draw 3D

shapes

Gingerbread house creation

Pyramids and Prisms

Assessment Curriculum

TBD – Gingerbread design and analysis

Essential Assessment – Shape post

GRADE 3/ 4

Make models of three-dimensional objects and describe key features (VCMMG142)

Compare the areas of regular and irregular shapes by informal means (VCMMG169)

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies(VCMMG170)

Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects(VCMMG171)

GRADE 5 - Connect three-dimensional objects with their nets and other two-dimensional

representations (VCMMG198)

GRADE 6 - Construct simple prisms and pyramids (VCMMG228)

GRADE 7 - Draw different views of prisms and solids formed from combinations of

prisms (VCMMG260)

https://victoriancurriculum.vcaa.vic.edu.au/Curriculum/ContentDescription/VCMMG142







MATHEMATICAL MINDSETS

Learning Goals

The tasks given to you are intended to get you to think and explore. Some people find working visually and spatially challenging, while others find this a strength.

Your goal: I can show bravery by exploring multiple ways of seeing and thinking during tasks.


Exploring regular shapes M

ath

Fo

cu

s Exploring how two dimensional shapes can be made by combining and splitting common shapes.

We are aiming to build an understanding of visualising and manipulating 2D shapes before moving into 3D.

Refe

ren

ces

References: MAKING SHAPES – p150, Peter Sullivan

La

un

ch

& E

xp

lore

Launch (5 minutes)

If these gingerbread houses came in kit of 2D pieces, what would the ‘kit’ look like?

Explore (20 minutes)

Teacher prompts: Can you tell me the features of the shapes you have recorded? Eg. Does it have parallel lines? Are

your shapes regular or irregular? Are the shapes convex or concave? Do you have an angles, lines or shapes that are

Congruent? – objects that are exactly the same size and shape.

Enabler: Draw the shapes you can see

Resources

A combination of any of these:

Kinder squares

White boards

Geosticks

Geoboards

Attribute blocks

North School has access to:

Whiteboards

Kindersquares

Attribute blocks


Extender: How would you describe each shape? Make a list of words that would be useful to describe a pentagon.

Ma

kin

g C

on

nec

tio

ns

Summarise and Consolidate (15 minutes)

Draw and name all the regular shapes that you can make:

If you have 6 equilateral triangles all the same

If you have 3 rhombuses all the same

If you have 3 trapeziums all the same

Review/Reflection (5 minutes)

Have you tried flipping and turning the shapes?

How could a systematic approach help you with this task?

What have you noticed when you have been exploring putting shapes together?

Can you think of when this would be useful in real life?

Have you made any connections between this and fractions or angles?


NETS AND CUBES: Exploring M

ath

Fo

cu

s Students understand ways to create simple prisms and pyramids.

Draw different views of prisms and solids formed from combinations of prisms

Refe

ren

ces

NETS and CUBES, P164, P. Sullivan (see part 2)

La

un

ch

& E

xp

lore

Launch (5 minutes)

Some students created this model. What nets could be used for each shape?


Enabler: draw a net that could be used to make a cube

Extender: Find all the ways to create each shape

Teacher prompts

Justify how you know it will form a cube

Resources

Has some great reading to accompany the

activity.


Collaboration – get together with another group. Convince yourself that you your ways will work. Convince a skeptic

that your variations will work. Together do you think you have all the possible combinations?

Ma

kin

g C

on

nec

tio

ns


Cube challenge

Explore how many ways you could create the yellow cube from the picture.

Record the possibilities in a shared space (we used our whiteboard). Prove that your net will make a cube when folded.

*allow students to cut out and make their nets

Allow time for students to share their ideas with the class and create robust discussions.

Invite students to pick a net from the collection and see if they can make it to see if it works.


NETS AND CUBES – Part 2. M

ath

Fo

cu



Ref

ere

n

ce

s NETS and CUBES, P164, P. Sullivan

La

un

ch

& E

xp

lore

Launch (5 minutes)

Allow students time to explore the different nets for cubes from the last session. Introduce and explore the

important language: faces, vertices, edges, parrallell, congruent etc.


Resources

Nets and Cubes prompt

Ma

kin

g

Co

nn

ec

tio

ns Summarise and Consolidate (15 minutes)

Share strategies students have used with an emphasis on ‘students imagining the connections between the cube and the nets.’


USING ISOMETRIC PAPER TO DRAW 3D OBJECTS M

ath

Fo

cu



Ref

ere

n

ce

s USING ISOMETRIC PAPER TO DRAW 3D OBJECTS, P158, P. Sullivan

La

un

ch

& E

xp

lore

Launch (5 minutes)

Give students isometric paper and dice. Challenge students to see if they can draw a cube on the isometric paper.


USING ISOMETRIC PAPER TO DRAW 3D OBJECTS

An object is made using 4 cubes. Use isometric dot paper to draw what the object might look like. Give as many

different answers as you can. (links to Maths300 cubecity – revision for us)

*Provide isometric paper

*Provide linking cubes

Resources

Isometric paper

Ma

kin

g C

on

nec

tio

ns


This is a drawing of an object. Using isometric paper, see if you can copy it.

What three different objects can you see in the drawing?

This activity was really fun and the students were very excited about it.

Additional – draw the picture in different ways to try to emphasis the objects.


SQUARE, DIAMOND or RECTANGLE? M at h

Fo

cu s Students develop an understanding of the attributes of shape.

Ref

ere

n

ce

s

La

un

ch

& E

xp

lore

Launch (5 minutes)

Here is a square. I have rotated it to look like this. Is this still a square or is a diamond or even a rectangle?


Invite students to collaborate, discuss and respectfully debate their opinion.

Question: ‘What makes a shape a shape?’ or ‘What makes a square a square.

Explore definitions.

https://www.mathsisfun.com/definitions/square.html has some great tools.

Resources

Ma

kin

g

Co

nn

ec

tio


Invite discussion and record key terms.

I heard that a diamond isn’t a real shape and should be called a rhombus. What do you think?

https://www.mathsisfun.com/definitions/square.html


PYRAMIDS AND PRISMS M

ath

Fo

cu

s Students can describe the key features of prisms and pyramids

Pyramid – https://www.mathsisfun.com/definitions/prism.html

Prism - https://www.mathsisfun.com/definitions/pyramid.html

Ref

ere

n

ce

s Open-ended maths activities; P. Sullivan, P. Lilburn, P97

La

un

ch

& E

xp

lore

Launch (5 minutes)

What is the difference between a pyramid and prism?

Use skewers and chic peas to build examples of prisms and pyramids. Be prepared to justify what makes them a prism

or a pyramid.


Enabler: What 3D shapes can you make?

Extender: Create a definition that helps identify Prisms and Pyramids

Language - continue to explore important language to identify and describe features: faces, vertices, edges,

parrallell, congruent etc.

Resources

Skewers

Chic peas

prompt:

Ma

kin

g

Co

nn

e

cti

on

s Summarise and Consolidate (15 minutes)

https://www.mathsisfun.com/definitions/prism.html

https://www.mathsisfun.com/definitions/pyramid.html


Create a class ‘kid friendly’ version of what the difference between a pyramid and a prism is.


RECREATING PRISIMS AND PYRAMIDS M

ath

Fo

cu



Ref

ere

n

ce

s

La

un

ch

& E

xp

lore

Launch (5 minutes)

If I was to recreate this gingerbread house, what prisms and pyramids would I need?

Extension:

What would this construction look like from different perspectives?


Reference class definition.

Resources

Isometric paper

Ma

kin

g C

on

nec

tio

ns


Using TINKERCAD, can you recreate the Gingerbread house – recording the prisms and pyramids used (use the simpler one).

*REVISED – TINKERCAD has been unreliable at CNPS so use isometric paper instead.

*This will require access to TINKERCAD, user accounts and some experience in Tinkercad education. This task could be done using isometric paper.

*Take screenshots of the house from different perspectives

Entry level

Ambitious level


Alternative / supplementary lessons

GINGERBREAD HOUSE CREATION

M at h

Fo

cu s

Ref

ere

n

ce

s

La

un

ch

& E

xp

lore

Launch (5 minutes)


Resources

Ma

kin

g

Co

nn

ec

tio



Building Views M at h

Fo

cu s Students connect 3D objects with 2D representations and visual what objects look like from different perspectives.

Wa

rm U

p

References

D Clarke / Charles Lovitt – Building Views

https://maths300.com/members/m300full/163lbuil.htm

Demonstrated by Charles Lovitt, Doug Clarke and Peter Burrows during PMSS course. Also found in the following spots

La

un

ch

& E

xp

lore

Launch (5 minutes)

Students are given the 1st investigation sheet and create the solutions to the puzzles.


Enabler: Guide students to understand what the numbers mean. What do you think the 3 represents?

Extender: Prove to a skeptic that you’ve completed each board.

Resources

Kinder squares

Attribute blocks

Whiteboards

Ma

kin

g

Co

nn

ec

tio

ns


The second set of investigations require more strategic thinking in strategy and amounts of blocks being used.

Review/Reflection (5 minutes)

What strategies are you using to check your answers?

https://maths300.com/members/m300full/163lbuil.htm


How do you know that you have the ‘minimal’ amount of blocks?

How did you record your answers?

How did your thinking change during this activity? – prompting for students to say that when looking at the view it doesn’t matter how close or far the block are.

Share the ways in which you recorded your answers.

What is something you know now, that could have helped you at the beginning of the lesson?


CITY VIEWS M at h

Fo

cu s

Refe

ren

ce

s

Mindset mathematics Grade 5: Boaler, Munson, Williams

City Views

La

un

ch

& E

xp

lore

Launch (5 minutes)

The follow are different views of a city. Build the city and prove to a skeptic that your city matches the plan.

Resources

Linking cubes



For each puzzle students try, ask them to consider the following:

How are they showing each building?

How do they show height?

Are there multiple possible cities that match the views you were given?

Do you have suggestions for the puzzle creators for how to make the puzzle clearer or more interesting?

Enabler:

Extender:

Ma

kin

g C

on

nec

tio

ns


Create a plan for someone to recreate this gingerbread city.

Enabler: Choose one building. How will you show how high the roof would be?

Extension: Convince yourself that your plan works, trial it with a friend to see if it works.

unit overview - cpb-ap-se2.wpmucdn.com · convince yourself that you your ways will work. convince...

Documents