Stage 2 - number and algebra -number patterns

Use the 'think aloud' strategy; build, describe and record number patterns using a variety of strategies; describe number patterns in words

Strategy

Students can:

  • use the ‘think aloud’ strategy
  • build, describe and record number patterns using a variety of strategies
  • describe number patterns in words

Activities to support the strategy

At this stage, students need to be able express their ideas and understanding by communicating and providing reasons for their thinking. Students are required to be able to generate number patterns, describe and record the patterns using diagrams, words or symbols.

The mathematical language required needs to be modelled by the teacher and students need to be provided with opportunities to talk through their thinking. For example, 3, 6, 9, 12… students describing this pattern may say, “It goes up by threes”, or, “It looks like the three times tables”, we would encourage students in Stage 2 to refer to this pattern as showing the “multiples of threes”. This wider classification will help students when they are required to find solutions to problems involving finding higher terms, e.g. the 10th term in a pattern.

Playing games like ‘guess my rule’ e.g. 1, 4, 7…what is my rule? Will provide students with the chance to talk about patterns and to apply their knowledge. We also want students to make connections between the patterns they are creating and describing with addition and multiplication facts.

Teaching strategy – think aloud

This teaching strategy focuses on the teacher explaining the thinking process while completing a task. The teacher models the thinking process by talking through the steps. The Think Aloud strategy can be used when applying any problem solving process or procedure. It is best to pre-plan exactly what is to be said so that all steps are correctly sequenced and explicit.

Implementation of this strategy reflects best practice in instructional intervention. Critical factors are:

  • Control of task difficulty
  • Small group instruction ensuring full participation
  • Questioning procedures that promote "thinking aloud"

1. Use a 'think aloud' strategy to explicitly teach students the steps to identify the next number in a pattern. This strategy focuses on the teacher explaining the thinking process while completing a task. The teacher models the thinking process for a subtraction number pattern by talking through these steps.

  • Say: Look at this pattern. Can you see what has happened to get the next number in the pattern?

Are the numbers getting bigger? 58, 52, 46,40

  • Are the numbers getting bigger? No. If the numbers are getting smaller, the pattern might be to take away a number.
  • I need to find the difference between two numbers in the pattern.
    Two of the numbers are 46 and 40. The difference is 6. Is the difference between 58 and 52, 6? Yes.
  • The pattern is going down by 6 each time.

  • Click here to use the number grid to investigate patterns on the hundreds chart.

2. Say: This question asks about a pattern. Can you see what has happened to get the next number in the pattern?

What number can replace the ?

Are these numbers getting bigger? 3426 ? 2446 2456 2466 illustrated

  • Are the numbers getting bigger? Yes. If the numbers are getting bigger the pattern might be to add a number. I need to find the difference between two numbers in the pattern.

  • What is the difference between 3466 and 3456? The 3000 is the same and the 400 is the same. There are two numbers left to compare, 66 and 56. 56 is 10 less than 66.

  • Does 10 less work with the next number? Let's see. 3456 and 3446. 3000 is the same, 400 is the same, then I have 56 and 46. 46 is 10 less than 56. Yes the pattern looks like 10 less.

The teacher continues to work through the ‘think aloud’ strategy with the class to find the missing number.

10 less than 46 is 36 and the next number in the pattern is 26, which is 10 less than 36. Therefore the pattern is subtract 10 and the missing number is 3436.

10 less than 46 is 36 and the next number in the pattern is 26, which is 10 less than 36. Therefore the pattern is subtract 10 and the missing number is 3436.

3. Students could work in pairs and demonstrate how to use the ‘think aloud’ strategy to find a missing number in this four-digit number pattern involving counting back by 100s.

4. Provide lots of different examples leading students through the ‘think aloud’ strategy until they can verbalise the process independently.

5. Students use the Exploring Patterns Learning Object to explore patterns. This interactive resource generates random number patterns for students to explore, interpret and continue. Instant feedback enables students to correct errors. Included are print activities, solutions and a video which explores patterns in dance.

6. Number Patterns- Activities from  Mathematics K6 Programming support

Generating and investigating multiples sequences

Students use a variety of materials such as pop sticks, hundreds charts and the constant function on a calculator to investigate and record patterns for threes, fours, sixes, sevens, eights and nines. See Patterns and Algebra - Number Patterns

Exploring patterns with pattern blocks

Students use pattern blocks to explore patterns for threes (triangles), fours (squares) and sixes (hexagons). Ask questions such as:

  • If I had 80 popsticks, how many rhombuses could I make?

Investigating sequences of multiples

Look for patterns in sequences of multiples. See Patterns and Algebra - Number Patterns

References

Australian curriculum reference

ACMNA060: Describe, continue, and create number patterns resulting from performing addition or subtraction.

NSW syllabus reference: MA2-8NA

Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values.

NSW numeracy continuum reference:

Aspect 3: Pattern and number Structure – Number properties.

NSW literacy continuum reference: VOCC10M1:

Vocabulary knowledge, Cluster 10, Marker 1: Demonstrates understanding that words can have different meanings in different contexts.

Other literacy continuum markers: SPEC9M4

Aspects of speaking, Cluster 9, Marker 4: Contributes relevant ideas to discussions, asks questions and re-phrases to clarify meaning.  WRIC9M4: Aspects of writing, Cluster 9, Marker 4: Structures texts using paragraphs composed of logically grouped sentences that deal with a particular aspect of a topic.

Teacher resources

Student resources

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