CAMBERWELL HIGH SCHOOL SUBJECT LEARNING MAP: Year 9 MATHS

Broad curriculum content

At Year 9 students will: Investigate Pythagoras’ Theorem and its application to solve simple problems involving right angled triangles. Investigate the mathematics behind the measurement of 2D and 3D shapes Continue to develop their mathematical literacy and ability to work mathematically by exploring and

developing the above content using the four proficiency strands Understanding, Fluency, Problem Solving and Reasoning.

UNIT TITLE: All shapes and sizesTOPIC: Pythagoras’ Theorem and Measurement

UNIT TIME FRAME: Term 1: 16 Lessons

Big IdeasAll physical objects and shapes can be quantified.

Enduring UnderstandingsAfter the details of the topic have been forgotten, students will understand that:

there is a distinct relationship between the three sides of a right angled triangle the physical properties of an object can be determined in one, two or three dimensions regular 2D and 3D shapes can be viewed as a combination of simpler components Mathematics is everywhere and that their understanding of Pythagoras’ Theorem and Measurement can be used to help

them make meaningful connections with the world around them in such areas as design, architecture, nature and construction

Essential QuestionsHow can you find the unknown side length of a right angle triangle?How do we calculate and compare surface area and volume of different prisms?How do I to use visualisation skills to solve worded problems?

Standards:

Measurement and Geometry: AC Year 9

Pythagoras & Trigonometry: Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles

Using units of measurement: Calculate the areas of composite shapes. Calculate the surface area and volume of cylinders and solve related problems. Solve problems involving the surface area and volume of right prisms.

What will students know, understand and be able to do?

Knowledge Understanding SkillFacts:Pythagoras’ TheoremPerfect square numbers

Key Vocabulary:hypotenuseperfect squaresquare root

For any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangleTo apply Pythagoras's theorem to composite shapes and 3D situations, right-angled triangles must be formed within the shapes

Label the hypotenuse of a RATFind the side length of a RAT using Pythagoras’ TheoremIdentify the basic shapes that have been combined to make a composite shapeUse mathematical reasoning to find unknown side lengths of worded problems, composite shapes and 3D

The distance between two points can be determined by constructing a RAT.

shapesDetermine the distance between 2 points on a Cartesian plane

Key skills:RoundingUse the language of mathematics to express ideas preciselyUse CAS calculator to evaluate answersVisualisation of the problemCreate and use pictures, manipulative, models and symbols to organise, record and communicate mathematical ideas

Facts:Conversion charts for length, area, volume and capacity1cm3 = 1 mLCircumference and area of circle formulasArea of triangle formulaArea of rectangle, kite, trapezium and parallelogram formulasSurface area and volume of right prisms (cylinders, triangular prisms and cuboids)

Key Vocabulary:perimetercircumferencediameterradiusareavolumecapacityparallelogramtrapeziumsurface area

Perimeter is the length around an object.To determine the area of a composite shape, the object must be broken up into its basic componentsThe net of a solid is useful when determining its surface area.The surface area of an object is found by adding together the area of each of its surfaces.Surface area and volume are two different measurements.Volume is used to represent the space occupied by a solid while capacity is used to represent the amount a container can hold.Measurements can be represented in different ways.The area and volume of any object is maintained if the orientation of the object is changed or the object is rearranged by subdividing.

Convert between units of measurement of length, area, volume and capacity.Convert between volume and capacity units.Calculate the perimeter and area of triangles, quadrilaterals, circles and composite shapes.Adapt the formula for the area of a circle for the area of a sector.Determine the surface area and volume of right prisms using nets and formulas. Apply knowledge of surface area and volume to solve real-life problems.Use Pythagoras' theorem in measurement calculations if necessary.

Key skills:RoundingUse the language of mathematics to express ideas preciselyUse CAS calculator to evaluate answersVisualisation of the problemCreate and use pictures, manipulative, models and symbols to organise, record and communicate mathematical ideas

LEARNING EVIDENCE

1. What data will be used to establish entry points for each student?

Ontrack data – initial overview

2. Formative Assessments:

i. Assessment for Learning what prior learning is evident?

Pythagoras’ Theorem Measurement

ii. Assessment as learning How will we know that students are learning? What opportunities have we provided to our students to demonstrate their learning in multiple forms?

Pythagoras’ Theorem

Student work program

(multiple exit points)

Distance between two

points

Pythagoras in 3D

Worded Problems

Buffet

Shortest Path Problem Revision Task

Measurement

Student work program (multiple entry and exit points)

P and A problem solving task

Bicycle length problem solving task

Netball Court problem solving task

ERQ: Swimming Pool

ERQ: Water tanks

ERQ: Cameron’s swimming pool

3. What Summative Assessment (Assessment OF Learning) will be collected to demonstrate student’s learning growth?

Assessment Task

Becoming aware of the

level

Working towards the

levelAt the level Above the

levelWell above

the level

D C- C B APythagoras’ Theorem:Topic Test (multiple entry and exit points)

Use Pythagoras’ Theorem to calculate the unknown side length of a right angle triangle when given a diagram

Apply Pythagoras’ Theorem to calculate the unknown side length of a right angle triangle when given a diagram

Apply Pythagoras’ Theorem to calculate the unknown side length in composite shapes and simple worded problems

Apply Pythagoras’ Theorem to calculate the unknown side lengths in 3D problems and complex worded problems

Measurement:Packaging Investigation (tiered exit from the learning)

Able to convert between units of measurement for length.Calculate the perimeter and area of triangles, rectangles and parallelograms.Calculate the volume of a rectangular prism.

Able to convert between units of measurement for area.Calculate the circumference and area of circles and quadrilaterals and solve simple problems.Calculate the volume of rectangular and triangular prisms and solve simple problems.

Convert between units of measurement for volume.Calculate the area and perimeter of composite shapes involving circles, triangles and quadrilaterals.Calculate the volume and surface area of right prisms and cylinders.

Use mathematical knowledge and reasoning to solve perimeter and area of composite shape problems involving circles, triangles and quadrilaterals.Use mathematical reasoning and knowledge to solve problems involving the surface area and volume of

Apply knowledge and reasoning to solve surface area and volume problems involving composite solids.

right prisms and cylinders.