Year 9 Measurement and Geometry by Texas Instruments

Students calculate area composite shapes, surface area and volume of right prisms and solve related problems. They use geometric reasoning on enlargements and transformations to explain similarity and develop the conditions for triangles to be similar. Students investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles and use similarity to investigate the constancy of the sine, cosine and tangent ratios and solve related problems.

Year 9: Measurement and Geometry Classroom Activities		Download
Pythagoras and Trigonometry
Pythagoras Clue 1 Updated on October 21, 2024 Prepare for an adventure filled with ancient knowledge and mathematical intrigue! Your journey begins with the enigmatic Pythagoras and the secrets hidden within his famous theorem. This activity is Part 1 in a series that aims to build a basic understanding of this famous theorem and also links with the Fibonacci sequence in an engaging manner.		Download4
Pythagoras Clue 2 Updated on November 14, 2024 The investigation deepens as students continue their quest to uncover the connections between the Pythagoras’s theorem, the Pythagorean Circle and infamous Fibonacci sequence that will appear centuries later. In this episode students discover irrational secrets, numbers that can’t be tamed or fully expressed. While the Babylonians provide a numerical entry point, the hauntingly elusive square roots threaten to expand the number system.		Download
Pythagoras Clue 3 Updated on November 17, 2024 In Part Three of this activity series, students unravel cryptic clues that move the one step further on the mathematical bridge connecting the ancient world of Pythagoras with Fibonacci. Students progressively uncover the fascinating realm of continued and infinite fractions, connecting the rational and irrational worlds. Discover how simple ratios can evolve into infinite complexity.		Download
Pythagoras Squared A short investigation involving squares and triangles that leads to simple proof of Pythagoras's theorem. A beautiful illustration of the power of the Geometry environment and CAS functionality of TI-Nspire.		Download4
Standard ACMMG276 Pythagoras' theorem and trigonometry to solving threedimensional problems in right-angled triangles Standard ACMNA214 Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software Activity: How Long Two points are placed randomly in a 1cm x 1cm square. What would be the average distance between these two points? This wonderful problem has been constructed as an applicable exploration that uses Pythagoras’s theorem; however, extension opportunities reach well beyond year 12 mathematics. So what’s your guess? Fancy exploring the problem in 3D?	ACMMG276 ACMNA214	Download19
Standard ACMMG223 Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles Activity: Similar Signs Students investigate the ratio between the opposite side and hypotenuse of a right angled triangle as the triangle is dilated. Once students identify the outcome they explore changes to the angle and estimate ratios for specific angles.	ACMMG223	Download724
Standard ACMMG223 Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles Activity: Just Cos Students investigate the ratio between the adjacent side and hypotenuse of a right angled triangle as the triangle is dilated. Once students identify the outcome they explore changes to the angle and estimate ratios for specific angles. Note: Students should complete the “Similar Signs” activity first.	ACMMG223	Download396
Standard ACMMG223 Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles Activity: ACMMG223 – Trig Ratio Test - Year 9 Electronic, auto correcting formative or summative assessment for the Australian Mathematics Curriculum standard ACMMG223 using the TI-Navigator system including a companion PDF of the same.	ACMMG223	Download108
Standard ACMMG224 Apply trigonometry to solve rightangled triangle problems Activity: ACMMG224 - Trigonometry Test - Year 9 Electronic, auto correcting assessment for the Australian Mathematics Curriculum standard ACMMG224 using the TI-Navigator system including a companion PDF of the same. Content detail: "Apply trigonometry to solve right-angled triangle problems."	ACMMG224	Download169
Spirally Surds Students start by constructing the Spiral of Theodorus by hand using traditional pen and paper techniques. Once they have the general construction idea, they produce the spiral using the dynamic geometry facilities of TI-Nspire. The length of the hypotenuse is then explored as the spiral progresses.		Download14
Units of Measurement
Standard ACMMG218 Solve problems involving the surface area and volume of right prisms Activity: Water Bottles A wealth of freely available videos are available to introduce this activity. Students then explore a Fermi question with a view to estimating the quantity of single use water bottles that are disposed of annually in Australia. This quantity is then used to estimate the mass and volume of plastic and consider how deep this pile of plastic would be if it covered the school.	ACMMG218	Download83

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Pythagoras Clue 1

Pythagoras Clue 2

Pythagoras Clue 3

Pythagoras Squared

Standard ACMMG276

Standard ACMNA214

Activity: How Long

Standard ACMMG223

Activity: Similar Signs

Standard ACMMG223

Activity: Just Cos

Standard ACMMG223

Activity: ACMMG223 – Trig Ratio Test - Year 9

Standard ACMMG224

Activity: ACMMG224 - Trigonometry Test - Year 9

Spirally Surds

Standard ACMMG218

Activity: Water Bottles

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