Real-life Algebra Lesson Plan – Looking at Patterns in Paving Stones

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Summary of Lesson Plan:

In this lesson plan, students apply algebraic patterning concepts to describe, continue and repeat number patterns. They apply these understandings in the real life context of problem solving the cost of paving stones. Students use virtual manipulative to explore their ideas and an excel document to record their findings.

Australian Curriculum Links:

Year 3 Mathematics:
  • Describe, continue, and create number patterns resulting from performing addition or subtraction(ACMNA060)

Year 4 Mathematics:

  • Explore and describe number patterns resulting from performing multiplication (ACMNA081)

Lesson Plan Sequence:

Mathematical Prior Learning:

Students have experience investigating and solving number patters that increase. They are able to identify missing elements in simple number patterns and have experience with finding unknown quantities in basic number problems ie. 5 + _ = 17. Student also have an understanding of variation in that as one number increases, as will another by the same factor. Students are able to
complete addition and substation using at least two digit numbers and have experience solving multiplication problems using written and mental strategies. They have also begun understanding the measurement concept of ‘area’ and square metres.

Rationale:

In primary school students should be supported to develop pre-algebraic thinking in order to encourage a deeper understanding of number and number operations, providing strong links to algebra in the secondary years. Patterning plays a crucial role in the development of the understanding of algebra concepts so considerable practice is required. Providing visual representations and the use of manipulatives largely supports the development of mathematical fluency in patterning as students have the opportunity to work with symbolic materials to develop abstract ideas. Lastly this experience can be adapted and connected with other projects students are undertaking to it provide an opportunity for students to experience how algebraic concepts can be applied in real life situations, ensuring the lesson is meaningful and relevant to the students.

Objectives:

For students to:

  • Build, describe and continue the sequence of a number pattern
  • Generate and record a number pattern using a table
  • Describe a pattern in more than one way
  • Solve a variety of equations relating to the number of stones needed in a garden project

Lesson:

Students are told they are in the process of each designing a garden (or other relevant context). Students need to calculate how many paving stones they each require to order for their designs. Students are provided with the choice to pick from the following stones:
  • Stone A: 4 paving stones cover 1 m2;
  • Stone B: 8 paving stones cover 1 m2 ;
  • Stone C: 10 paving stones cover 1 m2.
Students are to use the virtual manipulatives to model the task. They are then required to use an excel spread sheet to record their findings up to 6 m2 ie. For Stone A:
Paving Area Table
Students are to identify the patterns between each numbers (working both vertically and horizontally). Students then choose four other sized areas to extend the pattern to. They are asked to describe and write down their patterning rules in more than one way. Next, students delete the numbers in six cells and swap with a peer. Students play Guess My Rule and work out their peer’s pattern.

Questioning to extend Working Mathematical focus:

  • Can you describe the pattern to me? Is there another way this pattern could be described? (Reasoning)
  • Can you work out how many stones you would need if the area was 40 meters square? How could you work this out? (Problem Solving/Reasoning)
  • If I used 320 stones, how many meters square could I cover? (Problem solving)
  • How can you check your answers? (Reasoning)

Integration of Technology:

Virtual manipulatives provide a symbolic tool for students to develop abstract about the pattern. Using the Excel document to create a table provides an introduction into using Excel to algebra equations.

Assessment:

Informally through conversations between peers and interview questions, assessment of language, strategies and reasoning provided. Analysis of work sample – spread sheet of record keeping.

Resources:

 

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Feature image source: http://pad2.whstatic.com/images/thumb/b/b7/Install-Pavers-Step-10.jpg/550px-Install-Pavers-Step-10.jpg

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