Lesson Plan Course: Grade 10 Math Unit 3: Patterns, Relations and Equations

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Lesson PlanCourse Grade 10 MathUnit 3
Patterns, Relations and Equations
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Grade 10 Outcomes Addressed

• C10 describe real-word relationships depicted
  by graphs, tables of values and written
  descriptions
• C8 identify, generalize, and apply patterns
• C1 express problems in terms of equations and
  vice-versa
• C2 model real-world phenomena with linear,
  quadratic, exponential and power equations and
  linear inequalities

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Knowledge and Skills Needed

• Complete a table of values
• Describe patterns in words and translate into
  equations
• Plot points
• Know that the independent variable goes on the
  x-axis and the dependent goes on the y-axis
• Understand how to determine independent and
  dependent variables

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Purpose of the Lesson

• The initial portion of this unit involves
  representing situations in various ways (e.g.
  words, tables, graphs and equations), analyzing
  and interpreting these representations, and using
  them to answer questions, make predictions and/or
  solve problems.
• This lesson aims to activate students prior
  knowledge about the various ways that patterns
  can be represented and allows them to see the
  connections between these representations.
  Throughout the lesson the teacher would be able
  to evaluate areas of strength and need within the
  class and can plan future lessons accordingly.

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Possible Grade 9 Lesson

• The worksheet for this lesson could be used as a
  review or assessment at the end of the Grade 9
  Patterns and Relations unit.

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Grade 9 Outcomes Addressed

• C1 - represent patterns and relationships in a
  variety of formats and use these representations
  to predict and justify unknown values
• C2 - interpret graphs that represent linear and
  non-linear data
• C3 - construct and analyse tables and graphs to
  describe how changes in one quantity affect a
  related quantities
• C5 - explain the connections among different
  representations of pattern and relationships

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Materials Required

• PowerPoint with warm-up questions
• Worksheet
• Cube-links (11 per student or per pair of
  students)

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Warm-Up

• What are the next 3 numbers in this pattern?
• 5, 7, 9, 11, ___, ____ , _____

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• What are the next 2 numbers in this pattern?
• 3 , - 6, 12, - 24, ___, ____

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• Describe any patterns you see in this table of
  values.

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Which graph represents the statement?

• A bicycle valves distance from the ground as a
  boy rides at a constant speed.

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Which graph represents the statement?

• A child swings on a swing, as a parent watches
  from the front.

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Warm-Up

• What are the next 3 numbers in this pattern?
• 5, 7, 9, 11,

13 , 15 , 17 ,
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• What are the next 2 numbers in this pattern?
• 3 , - 6, 12, - 24,

48 , -96 ,
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• Describe any patterns you see in this table of
  values.

As x increases by 1, y increases by 4.
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Which graph represents with statement?

• A bicycle valves distance from the ground as a
  boy rides at a constant speed.

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Which graph represents with statement?

• A child swings on a swing, as a parent watches
  from the front.

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Patterns

• What are some different ways that patterns can be
  represented?
• Graph
• Table of values
• List of numbers/symbols
• Words
• Equations
• Diagrams
• Manipulatives

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Patterns and Relations Activity Using Cube-links
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Activity Directions

• In this activity we are going to be building
  trains out of cube-links and investigating the
  relationship between the number of cars in the
  train and the number of visible faces.
• The faces on the bottom of the train will not be
  included.

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• 1) Build a train, adding one car at a time, until
  it is 6 cars long. As you add each car count the
  visible faces and record in the data table.

5 8 11 14
17 20
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• 2) Describe any patterns that you notice in the
  data table.
• Possible Answers
• Horizontal pattern the number of visible faces
  increases by 3 each time a car is added.
• Vertical pattern each additional car adds three
  more visible faces, and the two faces at either
  end of the train are always visible.

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• 3) If you added 5 more cars to your train, how
  many visible faces do you predict this new train
  will have? After making a prediction, build the
  train and check your answer.
• 35 visible faces (3 added for each car, 5 cars
  added) 20 15 35

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• 4) Complete the following statement
• If you tell me how many cars are in the train,
  I can tell you the number of faces by
  _________________________________________________
  _____________________________
• _______________________________________
• After completing the statement, swap worksheets
  with your partner
• Possible Answer taking the number of cars in the
  train and multiplying by 3 and then adding 2.

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• 5) Use the statement above to predict the number
  of faces in a train with 100 cars. Show the math
  that you did to find your answer.
• Answer
• 3 (100) 2 302
• Swap papers again so that you have your original
  paper

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• 6) Did you get the same answer as your partner?
  If not, discuss with your partner.

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• 7) Describe the pattern in words as you did in
  question 4 but this time use c to represent the
  number of cars in the train and v the number of
  visible faces.
• Possible Answer
• v is equal to three times c plus 2

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• 8) Change your words into mathematical symbols to
  create an equation where v is the number of
  visible faces and c is the number of cars in
  the train.
• Answer
• v 3c 2

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• 9) What is the meaning of the 3 in the equation?
• Every time you add a car you add 3 to the number
  of visible faces.
• 10) Explain the meaning of the 2 in the equation.
  
• The 2 represents the visible faces on the front
  and back of the train.

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• We are now going to graph the table of values.
  Before we begin graphing we need to determine
  which variable goes on the y-axis and which goes
  on the x-axis.

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• 11) Which variable, number of cars c or number
  of visible faces v will go on the x-axis?
  Which will go on the y-axis? How do you
  determine this?

• We must first determine if the number of visible
  faces depends on the number of train cars, or if
  the number of train cars depends on the number of
  visible faces.
• The number of visible faces depends on the number
  of train cars therefore v is dependent and goes
  on the y-axis and c is independent and goes on
  the x-axis.

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A tip for remembering that the dependent variable
goes on the y-axis.

• Think of the y-axis as a flag pole and the x-axis
  as the ground. The flag pole cant stand up
  without the ground, therefore the flag pole
  depends on the ground.

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• 12) Graph the data. Make sure to label the axes
  with a title and scale, and give the graph a
  title.

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• 13) Looking at the graph, where is the 3 from
  the equation? Explain its meaning on the graph,
  and in the context of the train.
• On the graph after moving over one to the right,
  the 3 is the number that you go up to get to
  the next point. Every time you add a car you add
  3 visible faces.

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• 14) Where is the 2 on the graph. Explain its
  meaning on the graph, and in the context of the
  train.
• If we extended the pattern backwards the line
  would cross the y-axis at 2. This represents the
  visible faces on the front and the back of the
  train. On the graph, this would mean for no cars
  there would be two visible faces. This does not
  make sense in this context and that is why there
  is no point plotted at x0.

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• 15) Do you think these point should be connected
  with a straight line? Why or why not?
• Answer No, we should not connect the points with
  a straight line as joining the points would not
  make sense in this context. We could not have
  the number of cars equal to 1.5 or 3.5 as this
  would mean that ½ a car was added to the train.

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Follow up activity or homework assignment

• Students complete a similar activity on their own
  looking at the relationship between perimeter
  (when the trains are observed from the top) and
  the number of cars in the train.

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Questions? Comments?