Maori Weaving

Fold or weave each piece as illustrated by the arrow until the piece is lying in the position illustrated by the next picture. When you have completed each step, repeat steps 3 to 6 again and again.

Assessment Tasks

Task 1: Turning

Equipment: a large teddy bear from the teddy bear kit, soft toy or doll. A thin strip of paper folded near the middle to form an angle tester.

Implementation

Stand the teddy bear in front of the child facing the same way as the child.

  • Stand up and turn around slowly looking at what is in the room
  • Now sit down again.
  • I am going to turn the teddy bear.

Turn the bear a half turn clockwise.

  • Without turning your head, what would you see if you turned the same amount as teddy.

Probe. If the student cannot answer let them turn and look.

  • Without turning your head, turn teddy to look at the ...... (select something like a door that is in line with a 90 anticlockwise turn. It does not matter if the child moves teddy in the opposite direction through 270)
  • Here is a strip of paper that can be opened. (Quickly open and close the strip of bent paper.)
  • Can you show me how much teddy turned with the strip of paper.

Probe: If the student cannot do it, put the bend of the angle tester next to teddy with two arms together facing the original direction and say

Try opening one part so the turn is made.

Angles Assessment - Task 1 - Turning

Emerging Strategies

Makes a complete turn and names something that is not in front

Perceptual Strategies

Turns around physically to answer the question, may check they are the same as teddy bear.

Turns own body as well as teddy to look at the object

Pictorial Imagery Strategies

Can name object behind without turning and moves the teddy without looking to check.

Opens the angle tester satisfactorily when helped in the probe

Pattern and Dynamic Imagery Strategies

Opens the strip of paper after putting it against teddy to check

Efficient Strategies

Opens the strip of paper without putting it against the teddy to check

Task 2: Ordering Angles on Shapes

Equipment: Set of the seven-piece tangram with right-angled isosceles triangle, square, and parallelogram. Quadrilateral cut out with no angles matching those on the tangram pieces. Angles drawn on paper.

Implementation:

Places the pieces in front of the student.

  • Point to all the angles on the shapes. Show with your finger the lines that mark the angle.

Probe: Show the student how to mark an angle's lines. This can be done with opening the thumb and forefinger around the angle. Show the child how to overlay one angle on top of another to decide if one is bigger than the other.

  • Select the angle that is biggest
  • Show why it is bigger than another angle
  • Make a new angle using those you are given.
  • Without touching the pieces, which angles are nearly the same as in the drawings.

Angle Assessment - Task 2: Ordering Angles

Emerging Strategies

Points to all the angles on the shapes

May select a large piece for a large angle

Perceptual Strategies

After being shown, student can overlay angles and point to the gap to show which is larger. Points to lines bounding the angles.

Can select drawn angles only if the pieces are placed on the angles and checked first

Pictorial Imagery Strategies

Selects without checking the largest angle. Can then overlay against others to illustrate why it is larger or illustrates amount of turning.

Can select all the given angles that match the drawn angles.

Can make a larger angle by trials.

Pattern and Dynamic Imagery Strategies

Selects two angles to join to make a new angle. Shows by marking the two lines edging the angle.

Efficient Imagery Strategies

Selects, in different ways, angles to make a straight angle which is recognised in the crossing of lines.

S1 Lesson 1 - Silence

Description

Without making a sound, students in groups of six, try to complete a regular shape. Students will need to use their observation and imagery skills to discriminate between similar shapes.

Purpose

Students need to imagine what shape is needed to complete a shape. They may need to turn the shape around. This activity develops pictorial imagery and beginning dynamic (turning or flipping) imagery of 2D shapes.

Outcomes

SGS1.2 Manipulates, sorts, represents, describes and explores various two-dimensional shapes

Knowledge and skills
Students learn about / Working mathematically
Students learn to
  • making representations of two-dimensional shapes in different orientations, using drawings and a variety of materials
  • identifying the arms and vertex of the angle in a corner
/
  • identifying shapes that will complete a shape in an arrangement of shapes or in a design (Applying strategies)

Key ideas

Identify and name parallel, vertical and horizontal lines

Compare angles by placing one angle on top of another

Expected learning strategies

The student attends to spatial features and is beginning to make comparisons, relying on what she/he can see or do. The student:

  • recognises shapes in different orientations and proportions, checking by physical manipulation
  • describes similarities and differences and processes of change as they use materials

The student is developing mental images associated with concepts. She/he demonstrates an increasing use of standard language. The student:

  • generates images of shapes in a variety of orientations and with different features
  • discusses shapes, their parts, and actions when the shape is not present

Materials

Each group of six students will need a set of six squares. (See blackline masters on the next few pages.) If circles are used, each circle can be cut into three pieces and marked on one side to provide cues for the students when first playing this game.



S1 Lesson 1 - Silence

Activities / Teaching Points and Questions
Introduction (whole class)
  • Write the rules of the game on the chalkboard.
  • Read the rules to the students emphasising the SILENCE rule and the NO TAKE rule.
  • Show the students the how the shapes have been cut into three pieces.
  • Select three students to participate in the demonstration game.
  • Sit on the floor with the three students. The rest of the class stand behind, watching (in silence)
  • The cards are shuffled and handed out to the players ( three pieces to each player)
  • Play the game
/ THE GAME
The game must be played in total silence
You must not take, you only give
You can only have three pieces at a time.
The game ends when every person in the group has a complete shape.
All players must look closely at the pieces they have in front of them and also the pieces in front of the other players.
Player number one tries to identify a piece in front of them that they think one of the other players needs. This piece is handed to that player. The player receiving the piece must then pass over one of their pieces. Players can only have three pieces at a time.
The next player then has a turn.
The game continues until all players have completed their shape.
Activity (pairs)
  • Each group is given a set of shapes
  • The game is played as described in the Introduction.
  • The game is played a number of times
/ Groups of six give the best interaction. The smaller the group the more direct swapping and the easier the task. If the class is playing in smaller groups remember to remove some of the shapes from the sets.
Emphasise cooperation.
Conclusion (whole Class)
Discuss the different strategies that students used to work out which pieces the other players needed. / What did you like about the game?
What strategies did you use to play the game?
What things did you learn?
Additional Activities
  • Play the game using other regular shapes. (triangles, circles, rectangles)
  • Cut the shapes using straight or curved lines and with fewer visual cues.
(Lovitt, C. & Clarke, D. (1989). The Mathematics Curriculum and Teaching Program, Activity Bank.Melbourne: Curriculum Corporation)

S1 Lesson 2 - Making Pictures With Tangram Pieces, With Lines Marked

Description

Students are given the tangram pieces and copies of the pictures to make.

Purpose

Making the picture requires students to disembed the parts. It will also involve orientation and motion in turning the pieces to fit. Difficulty can be increased by having no lines and by making the pictures small so students make the picture beside the picture rather than on top of it. Students enjoy making pictures.

Outcomes

SGS1.2 Manipulates, sorts, represents, describes and explores various two-dimensional shapes

Knowledge and skills
Students learn about / Working mathematically
Students learn to
  • joining and separating an arrangement of shapes to form new shapes
  • deciding on angles that match
  • visualising where shapes will fit when turned or flipped
/
  • visualise, make and describe recently seen shapes (Applying strategies, Communicating)
  • identify shapes that are embedded in an arrangement of shapes or in a design (Applying strategies)

Key ideas

Compare angles by placing one angle on top of another

Expected strategies for learning

The student is developing mental images associated with concepts. She/he demonstrates an increasing use of standard language. The student:

  • completes a partially represented shape or simple design
  • discusses shapes, their parts, and actions when the shape is not present.

Materials

A seven piece tangram set per pair of students. Copies of pictures for the levels of difficulty expected.

It is possible to make tangrams from cardboard. Other tangram sets can also be used. Most commercial sets have accompanying booklets of pictures. Students can also make background scenes for the pictures that they make.

Extra paper and paste for displays. Coloured pencils to create backgrounds. Coloured paper, pencils, and scissors if pieces are to be traced, cut out and pasted to make a display.

S1 Lesson 2 - Making Pictures With Tangram Pieces, With Lines Marked

Activities / Teaching Points and Questions
Introduction(whole class)
  • Place a picture and the pieces on the board (e.g. with blu-tak).
  • Discuss with students what shapes they might select for different parts of the picture and how they know why it might fit.
  • Discuss how angles might be made up of two pieces.
  • Remind students about cooperating and telling each other why you think different pieces should be tried before taking away one that has already been put in place by your partner.
/ Where will we start? Why?
Who can select a piece for this section of the picture?
Why do you think it might fit?
Most angles will be recognised as a right angle, pointy or blunt. Angle size and length of sides will give clues in most cases. However, some angles can be made up of two smaller angles and pieces can be joined to make longer lines.
How do you move the piece to make it fit?
Activities(pairs of students)
  • Distribute a tangram set to each pair.
  • Let students select a picture to make from a group of a suitable difficulty.
  • Increase difficulty as appropriate
  • Students may not go on to the next part of the lesson because it is good to have lots of experience with the pieces and not just create a display.
  • Students can create the background and place the picture on it if appropriate.
  • Students can trace the pieces on coloured paper to cut out and remake the picture.
  • Students put their pictures on display.
/ Help students to select a piece that might look the same if turned.
Help students to match right angles or other angles to get started.
Which piece does this part look like?
Which piece has an angle (corner) like this one? What other piece might fit if it doesn't work?
How might you use two angles to make this angle?
Which piece has a side length like this one?
Conclusion(whole class)
  • Select some pictures for discussions.
  • Have two students come to the front to share a question and answer session. One student can ask the other how they knew which piece to choose.
  • This might be repeated with other students.
/ Why did you select this piece for here?
What is the same about this piece and this part of the picture?
Why was this part tricky? How did you decide what to put there?
Who would like to ask someone about their picture pieces?
Extension
  • Some students will be able to make pictures when the lines are not marked
/ Working without lines requires mental imagery. Students can make some shapes like triangles and squares with 2 to 3 pieces without much trouble but it is much harder for them to work with more shapes or with pictures that do not have lines marked.

S2 Lesson 3 – Exploring Pattern Blocks

Description

Students explore the angles of the pattern block pieces by marking and overlaying the blocks to compare them.

Purpose

The angles of the pattern blocks are designed so that similar angles on different shapes can be seen and some angles are conveniently double or triple others. This provides a space-number interlink.

Outcomes

SGS2.2b Identifies, compares and describes angles in practical situations

Knowledge and skills
Students learn about / Working mathematically
Students learn to
  • identifying angles with two arms in practical situations, e.g. corners
  • comparing angles using informal means such as an angle tester
  • drawing angles of various sizes by tracing along the adjacent sides of shapes and describing the angle drawn
/
  • identify examples of angles in the environment

Key ideas

Compare and describe special groups of quadrilaterals

Describe angles using everyday language and the term ‘right’

Compare angles using informal means

Expected strategies for learning

The student uses pattern and movement in her/his mental imagery and is developing conceptual relationships. The student:

  • develops and uses a pattern of shapes or relationship between parts of shapes
  • discusses patterns and movements associated with combinations of shapes and relationships between shapes.

Materials

Each pair of students take at least 3 narrow rhombuses, and 2 of each of the other shapes. Paper and pencil for recording.

Hint

Tracing around the angle might help students to see it apart from the whole shape.

Doubling and tripling decades like thirty is a good skill for mental calculation problems.

S2 Lesson 3 – Exploring Pattern Blocks

Activities / Teaching Points and Questions
Introduction(whole class)
  • Revise the ways used to compare the angles of the seven-piece tangram set. Revise how the angles were compared and their sizes considered.
  • Take some of the pattern block pieces and overlay them to show how they can be compared, joined and compared.
  • Set the two problems
(i)order the angles from smallest to largest.
(ii) how big is the smallest angle if compared to the right angle. / How might we compare the angles on these pieces?
Which angle is the smallest?
What angle is found on both the tangram pieces and the pattern blocks?
Do you think one of the pattern blocks has an angle smaller than the one on the tangram pieces?
Does the size of the shape decide the size of the angle?
Does the length of the side matter?
Activities(pairs)
  • Each pair of students take at least 3 narrow rhombuses, and 2 of each of the other shapes.
  • Students put the pattern blocks so the angles are ordered from smallest to largest.
  • Students can trace around the angles in order.
  • Students find out how many of the small angle make a square angle. By placing the angles onto a square angle,they calculate the size by knowing a rightangle is 90º
  • Students can then work out the 60º angle and then the other angles.
/ Why do you think this is the smallest angle/ largest angle?
Can you see any angles that are double others?
How can you check how many angles you need to make the other angles?
Conclusion(whole class)
  • Class as a whole make the summary from their small pair findings.
/ Which angle will we trace as the smallest?
How big is it? How did you do that?
What is the next sized angle? What shapes have this angle?
What is next?
Next? What size is it? How can you find out that? Is there another way of deciding the size of the angles? For example, by making a full revolution which is 4 right angles.

S3 Lesson 4 – Dynamic Triangles

Description

Students work in pairs to change triangular shapes to decide how the triangles vary and make decisions about what might be all possibilities.

Purpose

Students can first imagine what the triangles might look like and then they can see how they are changing. Students may see a pattern in how the triangles change.

Outcomes

SG3.2a Manipulates, classifies and draws two-dimensional shapes and describes side and angle properties

Knowledge and skills
Students learn about / Working mathematically
Students learn to
  • manipulating, identifying and naming right-angled, isosceles, equilateral and scalene triangles
  • comparing and describing side properties of isosceles, equilateral and scalene triangles
/
  • describe side and angle properties of two-dimensional shapes (Communicating)
  • explain classifications of two-dimensional shapes (Communicating)
  • [extension: construct a shape using computer drawing tools, from a description of its side and angle properties (Applying strategies )]

Key ideas