T2 Week 3_Mathematics_G4_Symmetry

QaD Teacher Support Materials Focus: Identifying line and rotational symmetry Instructions Remember to download the ‘Weekly Class Report’ and use it to help plan the 15 – 20

minute Weekly Follow-up lesson.

Use the ‘Weekly Class Report’ to determine which group students will be in for the Suggested Activities (score 0 or 1 = Red, score 2 or 3 = Yellow, score 4 or 5 = Green).

Please refer to the ‘QaD Teacher Guide’, and also the ‘Using the Teacher Support Materials Video’ to assist you in understanding and using the ‘Weekly Class Report’ and the ‘Teacher Support Materials’.

QaD Weekly Questions These are the questions completed by the students this week. Please refer to these as you look at the Weekly Class Report. Each student will also need a copy of these questions.

Misconceptions Information (by Day) Use these with the Weekly Questions and the ‘Weekly Class Report’ to better understand student errors.

What TIMSS content and skills are assessed by Thursday’s question? This table shows the content and skills that Thursday’s question assesses. This is an international framework and may not align with your current curriculum. The QaD Thursday question attempts to assess long-term learning and higher order thinking.

Summary, focus and purpose of QaD Weekly Follow-up Lesson (by Group) This table connects the Weekly Class Report to the Follow-up Lesson with differentiated information for the three ability groups. It provides a quick overview of the focus and intent of the Weekly Follow-up Lesson for each of the Red, Yellow and Green groups. Use the table to focus the lesson, plan the activities and organise the required equipment.

Follow-up Lesson The Follow-up Lesson is the key component of the Teacher Support Materials document.

The Follow-up Lesson has been specifically developed to address student needs according to demonstrated ability. It is recommended that the format of this Follow-up Lesson have three parts:

Introduction (whole class)

Suggested Activities (in colour groups) Student worksheets have been provided for each colour Group. ‘Red Group Worksheet’ ‘Yellow Group Worksheet’ ‘Green Group Worksheet’

(Note: answers included on the page before the activities.)

Explicit instruction in solving the QaD ‘Thursday’ question (whole class)

T2 Week 3_Mathematics_G4_Symmetry

QaD Weekly Questions

Sunday In which of the following figures is the dotted line a line of symmetry?

Monday

How many lines of symmetry does this rectangle have?

A: 1

B: 2

C: 3

D: 4

Tuesday

Which of these shapes has rotational symmetry?

Wednesday

Which of these figures has rotational symmetry after half a turn only?

T2 Week 3_Mathematics_G4_Symmetry

Thursday

Each of these shapes has:

only line symmetry or

only rotational symmetry or

both line and rotational symmetry

Drag and drop each shape into the correct place in the table.

Only line symmetry Only rotational symmetry Both line and rotational

symmetry

T2 Week 3_Mathematics_G4_Symmetry

Misconception Information (by Day)

Sunday

A Plausible option

B Key

C Plausible option

D Plausible option

Monday

A Can only see one line of symmetry exists

B Key

C Believes there is a diagonal line of symmetry

D Believes there are two diagonal lines of symmetry as well as the correct lines of symmetry

Tuesday

A Key

B Plausible option

C Plausible option

D Plausible option

Wednesday

A Key

B Misunderstands that equilateral triangles have rotational symmetry after more than just half a turn

C Misunderstands that squares have rotational symmetry after more than just half a turn

D Misunderstands that circles have rotational symmetry after more than just half a turn

Thursday

Only line symmetry Only rotational symmetry Both line and rotational

symmetry

T2 Week 3_Mathematics_G4_Symmetry

What TIMSS content and skills are assessed by Thursday’s question?

(see TIMSS 2019 Mathematics Framework, IEA)

Summary, focus and purpose of QaD Weekly Follow-up Lesson (by Group)

Focus: Identifying line and rotational symmetry

Red (score 0 or 1) Yellow (score 2 or 3) Green (score 4 or 5)

What does

the Class

Report

show?

Has not attempted, has no understanding of line symmetry. Cannot identify lines of symmetry or identify how many lines of symmetry a shape may have.

Has a basic understanding of line symmetry but is not familiar with rotational symmetry.

Has a sound understanding of rotational and line symmetry and is able to analyse 2D shapes to evaluate which symmetry applies.

This week’s

Follow-up

Lesson

learning

focus

Introduce a conceptual understanding of line symmetry and rotational symmetry.

Develop a deeper conceptual understanding of line symmetry and introduce rotational symmetry.

Broaden experience from the identification of line and rotational symmetry to creating designs with such features.

This week’s

Follow-up

Lesson

activity

focus

Practise in identifying symmetrical images and lines of symmetry. Experience in drawing multiple lines of symmetry.

Practise in rotating shapes to identify rotational symmetry. Experience in completing and creating shapes and designs with line symmetry.

Experience in completing creating shapes with line and rotational symmetry.

Cog. Skills Knowing Applying Reasoning

Strategies Visualising Visualising Visualising

Preparation

Materials

Copy of Questions for each student

Red Group Worksheet

Shapes cut out from the Red group –Symmetry Sheet

Copy of Questions for each student

Yellow Group Worksheet

Shapes cut out from the Yellow group –Symmetry Sheet

Copy of Questions for each student

Green Group Worksheet

Cognitive Area Reasoning

Cognitive Skill Analyse

Strand Measurement and Geometry

Content Area Geometry

TIMSS Topic Use elementary properties, including line and rotational symmetry, to describe, compare, and create common two-dimensional shapes.

T2 Week 3_Mathematics_G4_Symmetry

Follow-up Lesson (15-20 minutes) 1. Introduction (whole class):

a) Introduce the focus of the Lesson: ‘Interpreting Pictographs’ and remind students that the

Question-a-Day questions they did over the last week were about how to read and interpret

pictographs.

a) Go through the Vocabulary and explain the

meaning of all words listed.

b) Go through the Problem Solving Checklist points

and remind students of what they need to do

when solving problems.

2. Suggested Activities (in colour groups):

Red (score 0 or 1) Yellow (score 2 or 3) Green (score 4 or 5)

1. Using a cut out rectangle from the red group symmetry sheet, introduce/reinforce the concept of line symmetry by showing how a rectangle can be folded in half, with the edges lining up exactly, in two ways. Demonstrate that, when folded diagonally, the edges do not line up. Therefore the diagonal line is not a line of symmetry. 2. Introduce the concept of rotational symmetry. Using the cut out square and the triangle from the red group symmetry sheet, demonstrate how, when a square is turned, it looks the same. However, when the triangle is turned, it cannot look the same.

1. Read through ‘Wednesday’ question. Invite students to explain why each of the incorrect responses are wrong.

2. Students complete ‘Green Group Worksheet’. In question 1, encourage

students to visualise folding the grid along the red line to develop an understanding of how to complete the drawing.

1. Read through ‘Sunday’ question. Have students visualise folding each of the shapes to see if each of the edges match exactly.

2. Students complete ‘Red Group Worksheet’. In question 1, encourage

students to visualise the fold to predict if it is a line of symmetry and then to check by folding.

1. Read through ‘Tuesday’ question. Ask students to share how they could use visualisation to get the answer.

2. Students complete ‘Yellow Group Worksheet’. In question 2, encourage

students to visualise folding the grid along the red line to develop an understanding of how to complete the drawing.

Problem Solving Checklist Understand the problem

Plan a strategy

Solve the problem

Check your answer

Visualisation Visualisation requires the learner to picture the problem in their mind.

Vocabulary Line symmetry A shape has line symmetry when

one half of an image is the exact reflection of the other.

Rotational Symmetry A shape has rotational symmetry when it still looks the same after a rotation

T2 Week 3_Mathematics_G4_Symmetry

3. Explicit instruction in solving the QaD ‘Thursday’ question (whole class): The following provides a suggested step-by-step approach to solving Thursday’s

question.

Read the Thursday question out aloud to all students. Then use a question-answer

approach to go through the problem.

It would be useful for pairs of students to have each of the shapes from the question cut

out and available for use.

Teacher: ‘Let’s understand the problem first. What do we know about line

symmetry and rotational symmetry?’

Students: (We know that a shape has line symmetry if, when folded in half, the

edges match exactly. A shape has rotational symmetry if it looks the

same after being rotated)

Teacher: ‘OK. So what do we need to do for this question? What do we need to

work out?’

Students: (We need to work out what type of symmetry each shape has.)

Teacher: ‘OK. Let’s all look at/pick up the triangle. See if you can work out if it

has line, rotational or both types of symmetry)

Students: (It has line symmetry. When we fold it in half, the edges match exactly.

It also has rotational symmetry. When we rotate it a third of a turn, it

looks the same again. So this triangle has both line and rotational

symmetry’)

Teacher: ‘Great. So it goes in the third column. OK. Let’s all look at/pick up the

next shape. See if you can work out if it has line, rotational or both

types of symmetry.)

Students: (It has both line and rotational. When we fold it in half, the edges

match exactly. It has rotational symmetry because when we turn it a

half turn it looks the same.)

Teacher: ‘Yes. So it goes in the last column. OK. Let’s all look at/pick up the

diamond shape. See if you can work out if it has line, rotational or

both types of symmetry.)

Students: (It has both line and rotational. When we fold it in half, the edges

match exactly. It has rotational symmetry because when we turn it a

half turn it looks the same.)

T2 Week 3_Mathematics_G4_Symmetry

Teacher: ‘That’s right. So it goes in the last column. OK. Let’s all look at/pick up

the trapezium shape. See if you can work out if it has line, rotational

or both types of symmetry.)

Students: (It has line symmetry only. When we fold it in half, the edges match

exactly. However it does not have rotational symmetry because it has

to do a full rotation before it looks the same again.)

Teacher: ‘Great. So it goes in the first column. OK. Let’s all look at/pick up the

last shape. See if you can work out if it has line, rotational or both

types of symmetry.)

Students: (It has rotational symmetry only. When we fold it in half, the edges do

not match exactly. However it does have rotational symmetry because

when we turn it, it looks the same.)

Teacher: ‘That’s great! So it goes in the middle column.’

T2 Week 3_Mathematics_G4_Symmetry

Answers to ‘Red Group Worksheet’ 1.

2.

Answers to ‘Yellow Group Worksheet’ 1.

2.

3. Look at students’ individual designs to evaluate their understanding of line symmetry.

T2 Week 3_Mathematics_G4_Symmetry

Answers to ‘Green Group Worksheet’ 1.

2 and 3. Look at students’ individual designs to evaluate their understanding of line and rotational

symmetry.

T2 Week 3_Mathematics_G4_Symmetry

Red Group Activity:

1. Cut out the shapes on the ‘Line Symmetry’ sheet. Fold each shape in half to see if it has

line symmetry. Paste the shape in the correct column. For the symmetrical shapes, draw

on the lines of symmetry.

Has line symmetry Does not have line symmetry

2. Cut out the shape from the ‘Rotational Symmetry’ sheet. Place it on the outline of the

shape drawn below. Then, rotate the shape half of a turn and trace around it in the first box. Repeat for the second box.

T2 Week 3_Mathematics_G4_Symmetry

Red group –Symmetry Sheet

Please note there are TWO copies of the sheet per page.

1. Line symmetry. Cut out the shapes and complete question 1.

2. Rotational Symmetry. Cut out the shape and complete question 2.

1. Line symmetry. Cut out the shapes and complete question 1.

2. Rotational Symmetry. Cut out the shape and complete question two.

3

3

T2 Week 3_Mathematics_G4_Symmetry

Yellow Group Activity:

1. Cut out the shape from the ‘Rotational Symmetry’ sheet. Place it on the outline of the

shape drawn below. Then, rotate the shape half of a turn and trace around it in the first box. Repeat for the second box.

2. Finish each of the shapes below so that the red line is a line of symmetry.

a)

3. Create your own design that has line symmetry. Draw on all of the lines of symmetry.

Example:

b)

T2 Week 3_Mathematics_G4_Symmetry

Yellow group – Rotational Symmetry Sheet

Please note there are TWELVE copies of the sheet per page.

1. Rotational Symmetry. Cut out the shape and complete question two.

T2 Week 3_Mathematics_G4_Symmetry

Green Group Activity:

1. Finish each of the shapes below so that the red line is a line of symmetry.

a)

2. Create your own design that has line symmetry. Draw on all of the lines of symmetry.

Example:

3. Create your own design that has rotational symmetry.

b)