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Snakes and Scarves

Keywords:
Purpose: 

In this unit we explore linear patterns using snakes as the context. We examine, construct and record snakes of different patterns. We also put scarves on our snakes and ask others to predict what is hidden.

Achievement Objectives:

Achievement Objective: NA1-6: Create and continue sequential patterns.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  • record patterns on grid paper
  • make predictions about ‘missing’ sections of a pattern
  • use words to describe linear patterns
Description of mathematics: 

The main idea behind this unit is for students to develop basic concepts relating to pattern by exploring simple patterns in a novel situation. So they will use multi-link cubes masquerading as snakes. The snakes have patterned ‘skin’. The students play with a variety of snakes, both inventing their own and investigating other students’. In the process, they should begin to see that (i) patterns are made up of repeating sections of coloured cubes; (ii) they can continue a pattern by adding on more cubes of the right colours; and (ii) they can predict parts of a pattern that are missing.

Pattern is an important idea both in mathematics generally and as a precursor to algebra. For instance, discovering patterns enables us to predict events. By knowing how the tides work we can predict when high tide will be and when will be a good time to go fishing. This pattern concept generalises in secondary school to finding results that work again and again. Pythagoras’ Theorem can be thought of as a pattern. The pattern is that in every right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. More background on patterns can be seen in Algebra InformationBackground.

Required Resource Materials: 
multi-link cubes
pieces of fabric for the scarves
prepared snakes (made with multi-link cubes)
snakes with scarves booklets
strips of cubed paper for recording
crayons or felt pens
Key Vocabulary: 

 pattern, repeat, next, hidden, alike, different, same, similar

Activity: 

Getting Started

Today we investigate snakes with special patterns. We think about what would come next as we increase the length of our snakes. We also think about what happens when we cover part of our snake with a scarf.

  1. This week we are going to investigate patterns. Does anyone know what a pattern is?
    Share ideas about patterns. Encourage the students to look around the classroom for examples of patterns.
  2. I am going to make a snake for you out of these multi-link cubes. Watch carefully to see if you can guess what kind of snake I am making.
    [Make a snake with a blue, red, blue, red, blue pattern.]

snake with blue and red pattern

Who knows what colour comes next in our snake?
How did you know?

  1. Let the students have turns adding cubes to the snake.
  2. Ask if anyone could think of a way of describing the snake to someone who can’t see it. This could be someone who rings to find out what you have been doing in class today.
  3. As a class read the pattern “red, blue, red, blue, red, blue…”
  4. Record the pattern on strips of grid paper one cube wide.
  5. Repeat the process of constructing and examining a snake, finding its pattern and then extending the pattern. This time use a snake that is made of three repeating single colours.

 snake with three repeating colours

Who knows what colour comes next?
How did you know?

  1. Now wrap a scarf around the snake and ask the students to predict what colour cubes are hidden. Make the scarf about 3 cubes wide.

diagram

  1. What cubes are hidden?
  2. How did you know?
  3. Take the scarf off and check.
  4. Continue with this activity until you feel that the students are ready to explore pattern snakes independently.

Exploring

Over the next 2-3 days we examine, construct and record the patterns on our snakes.  We cover parts of our snakes with scarves and play ‘guessing games’ with other students.

  1. Let each child (or pair of students) select a pattern snake from the ‘basket of snakes’. Alternatively you could give each pair of students a collection of prepared snakes. Also give each pair a supply of cubes that they can use to extend the patterns and plain grid paper strips for recording.
  2. As the students examine the snake ask questions that focus on their search for a pattern.
    Can you ‘read’ me your snake?
    What colour cubes is your snake made of?
    Can you see a pattern in your snake?
  3. When the students have discovered the pattern, ask them to extend it using the supply of cubes. Let the students decide on the length of their snakes.
  4. Ask the students to record their completed snakes on the recording strips.
  5. As the snake recordings are completed they could be displayed on a line at the front of the class for others to see.

snake recordings

  1. Alternatively the students could make snakes-in-scarves pages for a class booklet.  These pages have a grid to record the snake and a ‘flap’ to cover part of the snake.

booklet example

  1. The process is repeated as the students select new snakes to investigate.  You may also wish to have a basket for the students to put their snakes in. Other students can then examine them.
  2. At the end of each session look at the snakes displayed and select a couple to put ‘scarves’ on.
    With all the students gathered together ask:
    What cubes do you think are hidden under the scarf?
    How do you know?

Reflecting

We conclude the unit by sharing the pattern snakes that we have made. We look for snakes that are alike.

  1. Give each child one of the recorded snakes from the previous days’ exploration.
  2. Ask one of the students to display their snake to the rest of the class. Together ‘read’ the pattern of the snake.

pattern snake

  1. Ask if anyone else has a snake that has a pattern that is the same as, or similar to, the one being displayed.
  2. How are they alike?
  3. The snakes may be alike in a number of different ways. Accept all the possibilities and then focus the students on the snakes that have exactly the same pattern.
  4. Which snakes have the same pattern as this one?
  5. Sort the snakes on the display line according to patterns

display of snakes

  1. Repeat by asking a child with a different snake to come to the front of the class. Continue to sort the snakes according to their patterns.