High School Algebra: Where is it and what do we do about it

1
High School Algebra Where is it and what do we
do about it?

• MK Math PD Session
• November 22, 2005

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Agenda for the day

• 900 Introduction and outline day
• 910 Problem-solving activity to get our brains
  working
• 930 Session 1 Addressing the Gaps
• 1030 break
• 1045 Session 2 Grade 10 Algebra
• 1200 Lunch
• 1245 Afternoon Warm-up Problem
• 100 Session 3 Quadratics
• 200 Session 4 Exponentials and Logs

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A problem to start your brains!

• The Wooly Sheep
• Two brothers sold a herd of sheep. For each
  sheep they received as many dollars as the number
  of sheep in the original herd (i.e. if there are
  15 sheep they sell each for 15). The money was
  divided as follows the older brother took 10,
  then the younger brother took 10, and so on. At
  the end of the division, the younger brother,
  whose turn it was, found that there was less than
  10 left for him. He took what remained. In
  order to even things up the older brother gave
  him some of his money. How much money did the
  older brother give him?

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Addressing the Gaps

• Exploring the Algebra from grades 7 to 9

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What algebra should students know when they leave
grade 9?

• Students should be exposed to extensive algebra
  in middle school
• Concrete, pictorial, verbal, contextual, and
  symbolic representations are emphasized
• Understand the meaning of a variable
• Recognize like and unlike terms and be able to
  determine when terms can and cannot be combined
  (added) or separated (subtracted)
• Can solve simple single variable equations

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What algebra should students know when they leave
grade 9?

• Multiply a monomial by a monomial, and a
  polynomial, and multiply two binomials
• Simple factoring and dividing a polynomial by a
  monomial (using area models/ arrays)
• Understand operations on algebraic terms
  correlate to operations on numerical values
• Have an understanding of simple inequalities
• Understand and apply properties associative,
  commutative, distributive

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But what if its not a perfect world?

• Although students are expected to come to grade
  10 with these algebraic skills often times this
  is not the reality
• Math 10 Plus and Math 10 Foundations Plus is
  designed to address these gaps while teaching the
  grade 10 curriculum
• We need to address these gaps throughout
• Exploring some activities (see Smart Board file)

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An Overview of Grade 10 Algebra

• Linear, quadratic, and exponential functions

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Grade 10 Algebra

• Analyzing and describing patters is a theme
  throughout grade 10 mathematics
• Students explore patterns to determine if they
  are linear, quadratic, or exponential and then
  describe these patterns using algebraic
  expressions, which they use to make predictions
• The primary algebraic focus is on linear and
  quadratic functions although they also work with
  developing and manipulating formulas

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Grade 10 Algebra

• Linear relations are not new to students so the
  goal this year is to develop fluency with linear
  relations by exploring their properties in detail
  as well as exploring alternate forms for the
  functions
• Quadratic functions are somewhat familiar to
  students but they will explore them in much
  greater detail this year, key ideas include
  graphing from the transformational form and
  connecting the roots and the factors.
• Solving linear systems
• Explore smart board activities

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Afternoon Warm-up

• Using your phone number put the first three
  digits on one side of an equal sign and the last
  four digits on the other side
• Use operations (,-,,/) to make the equation
  true, for example

7 5 6 2 3 9 6
(7 5) x 6 2 / 3 x 9 6
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Quadratic Functions

• Exploring more advanced concepts

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Exploring Quadratic Functions

• Different forms of the function
• General f(x) ax² bx c
• Standard f(x) a(x - h)² k
• Transformational 1/a (y - k) (x - h)²
• Students must be able to move from any one of
  these forms to one of the others with fluency
• Factoring and expanding
• Completing the square

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Exploring Quadratic Functions

• Analysis of properties
• Describe Transformations
• Interpret Values of a, b, c, h, k
• Examine the differences in the table of values
• Symmetry and vertex
• Develop fluency with finding and analysing roots
• Connecting factors and roots
• Develop and interpret the quadratic formula
• Smart Board Activities

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Exponential and Logarithmic Functions

• Exploring their properties for greater
  understanding

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Exponential and Logarithmic Functions

• Analysing exponential and log functions
• their tables, graphs, and equations
• Understand the connection between the two
  functions
• Solving equations involving both types of
  functions
• Understand and Apply laws of exponents and laws
  of logs