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Level Three > Geometry and Measurement

Angles

Achievement Objectives:

Purpose:

This unit of work is based on the Māori medium unit Koki, and investigates:

• contexts where angles are important, such as the turning of hands on a clock
• how rotation and degree angle measures are connected
• estimating and measuring angles.
Specific Learning Outcomes:

Students will learn

• about whole, half and quarter turns
• to use the degree unit for angle measures
• how degree measures relate to turns
• to estimate the size of angles
• to use a protractor to measure and draw angles
• about everyday contexts related to angles
Description of mathematics:
• An angle is an amount of turn
• Degree is the standard unit of measurment for angle
• There are 360 degrees in a full turn
Required Resource Materials:
protractors
cardboard or light sticks and a clip to make ‘angle arms’
copymasters
Activity:

Session 1

• How many full turns have I completed?
• Show me a [half/quarter/three quarter turn].
• How much more of a turn do you need to complete a full turn?
• Start off facing toward the river/lake/mountain. If you made a [half/quarter, three quarter/one and a half turn] what would you be looking at?
• Show me a turn that is more than a quarter but less than a half. What fraction of a turn might that be?

Get the students to think about how they might represent different turns on a piece of paper. Discuss the need for two ‘arms’ to show an angle. Angles they could show:

• a full turn
• two full turns
• a half turn
• two/three/four … half turns
• a quarter turn
• two/three/four/five … quarter turns
• a turn in between a half and three quarters

Session 2

Revise work from Session One by getting students to make ‘angle arms’. Working in pairs one student could make an angle and the other student could say what fraction of a turn, or how many turns the angle is.

Possible turns that could be shown:

• A little bit bigger than a quarter turn
• Exactly half way between a quarter turn and a three quarter turn
• One and a half turns

Copymaster 1 contains some follow up work for students to consolidate this learning.

Session 3

Show a full turn in a diagram or with the ‘angle arms’. Explain that a full turn is divided up in to 360 small fractions of a turn. Each of these small fractions of a turn are called a degree.

Compare this with a metre being divided up in to 1000 smaller lengths each called a millimetre. Just as the abbreviation ‘mm’ is used for millimetre, the symbol ° is used for degree.

Use the ‘angle arms’ to show the main fractions of a full turn and get students to work out how many degrees are in these fractions of a turn. Strategies used to find a half, a quarter and three quarters of 360 could be discussed.

These angle measures could be consolidated by asking students to show or draw angles such as:

90° 45° 180° 270° in between 270° and 360° about 100° about 300° …

Copymaster 2 has some independent work to consolidate this learning.

Session 4

Discuss the importance of the 90° angle and its other name of ‘right angle’. Also introduce the symbol for right angle.

Look in the built environment for examples of right angles.

Look for the occurrences of right angles in the natural environment.

Possible discussion questions for right angles:

• What helps you to draw a right angle in your book?
• How many right angles are there in a full turn. How would you show this in a diagram?
• How many right angles are there in a straight line?
• Draw an angle which is about half a right angle. How many degrees is that? How could you make an accurate half right angle (folding).
• How many right angles are there in a square/rectangle/hexagon …?
• How many right angles can you have in a triangle?
• Can you draw a rectangle where the diagonals cross over each other at an angle of 90°?

Session 5

In this session students learn how to use a protractor to draw and measure angles.

Give each student (or pair of students a protractor). Get them to identify these parts:

• the centre of the protractor
• the base line
• the inside scale
• the outside scale

Get students to identify 90° and 180° angles on the protractor.

The following pictures and instructions help students to use the protractor correctly to measure an angle. As in all measurement tasks it is good idea for the students to first estimate the approximate size of the angle (in relation to known angles such as 45°, 90°, 180° etc)

1. Place the protractor on the angle so that the base line of the protractor is directly on top of one of the arms of the angle.
2. Move the protractor so that the centre lines up with the corner of the angle.
3. Choose which scale to take the reading off. Get students to think about where 0° is in relation to the angle and count up the scale from there. Also have them think about the measurement that is consistent with their estimate.

Copymaster 3 has some angles to measure and draw for students to practice using the protractor.

Wind Up Investigation

Get students to list the joints in the body that can turn.

Draw an ‘angle arm’ diagram to show the maximum angle each joint can turn.

Estimate the maximum angle that each of the joints can turn.

Investigate a way to measure more accurately the maximum angle each joint can turn.

Compare results for different students. Are they the same, similar, or are there big differences? Discuss why might this be.

Discuss what it would be like if you joints could turn double the amount that they can.

AttachmentSize
Angles_CM_1.pdf26.9 KB
Angles_CM_2.pdf67.8 KB
Angles_CM_3.pdf68.73 KB

Direction and Position

This unit of work is based on the Māori medium unit Te Ahunga me te Taunga, and investigates the main compass directions, degree measures of direction and the use of a grid system to define locations on a map.

The Number Partner

This unit uses one of the digital learning objects, the number partner, to support students as they investigate possible pairings for numbers from 10 to 30. It is suitable for students working with Advanced Counting and Early Additive strategies (Stage 4-5 of the Number Framework). It includes problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

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In this unit we work on word problems about climbing up steps and riding in a lift. We learn about different types of problems that can be modelled on number lines. We practice mental calculations with sums to 10 and to 20.

Ratios and Rates

The purpose of this series of lessons is to synthesise students’ fraction and decimal place value knowledge to enable them to work with rates and ratios with understanding and competence.

This unit supports teaching and learning activities in the Student Fractions e-ako 13 and 14 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages.

This is the eighth and final in a series of units developing fractional understanding. This unit builds upon these previous units of work:

Complementary to this unit is the seventh Place Value unit:

Percentages

The purpose of this series of lessons is to synthesise students’ fraction and decimal place value knowledge to enable them to work with percentages, with understanding and competence.

These sessions make strong use of concrete materials to consolidate students’ understanding, before requiring them to work with number properties. Discussion is an important part of all sessions.

This unit supports teaching and learning activities in the Student Fractions e-ako 12 and complements the learning activities in Book 7 Teaching Fractions, Decimals and Percentages.

This is the seventh in a series of units developing fractional understanding. This unit builds upon these previous units of work:

Complementary to this unit is the seventh Place Value unit:

Links to additional complementary units of work are included after Session 5.