Transcript instructional strategies for teaching quantitative problem solving

GED® MATHEMATICS INSTITUTE
Foundations of
Quantitative
Problem Solving
for Adult Educators
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Quantitative
Reasoning To Solve
Problems Involving
Rational Numbers
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LESSON GOALS
 Perform addition, subtraction, multiplication, and division on
rational numbers. (Q.2.a)
 Perform computations and write numerical expressions with
squares and square roots of positive, rational numbers.
(Q.2.b)
 Perform computations and write numerical expressions with
cubes and cube roots of rational numbers. (Q.2.c)
 Determine when a numerical expression is undefined. (Q.2.d)
 Solve one-step or multi-step arithmetic, real world problems
involving the four operations with rational numbers, including
those involving scientific notation. (Q.2.e)
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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WORKING WITH
THE CONTENT
Think, Pair, Share
Think & Work Alone
Cooperative
Learning In
Small
Groups
Reflect On
Your Own
Learning
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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IN YOUR OWN WORDS…
 Write the definition of a rational number
and give several examples in different
forms.
 Write the definition of an irrational
number and give several examples.
 What would you say that having
“number sense” means?
 Why do you think it is important for us
to have “number sense” and know how
to compute with rational numbers?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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Using the TI-30XS
MultiView Calculator
Calculating with Irrational Numbers
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IS IT POSSIBLE…
 To ever have a fully accurate
answer when calculating with
irrational numbers?
 With repeating decimals?
 With terminating decimals?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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COMPUTING WITH
RATIONAL NUMBERS
Key Concepts
 Factors and Multiples
 Properties of Numbers
 Percents as Decimals
and Fractions
 Order of Operations
and Undefined
Expression
 Percent of a Number
 Exponential Notation
 Discounts
 Rules of Exponents
 Simple Interest
 Percent as a
Proportion
 Scientific Notation
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
FIND THE VALUE OF THE FOLLOWING
ARITHMETIC EXPRESSION.
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8 × 5 ÷ 10 + 50 ÷ 5 × (3 – 1)
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
PRE-INSTITUTE
ASSIGNMENT REVIEW
Identify Your Top 3 Questions
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COMPUTING WITH
SQUARES, SQUARE
ROOTS, CUBES, AND
CUBE ROOTS
What do we need to know?
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GED ASSESSMENT TARGETS
AND KEY CONCEPTS
•
Perform computations and write
numerical expressions with
squares and square roots of
positive, rational numbers. (Q.2.b)
•
Perform computations and write
numerical expressions with cubes
and cube roots of rational
numbers. (Q.2.c)
•
Lesson Key Concepts
 Square Roots and Cube Roots
 Approximating Square and Cube Roots
 Radicals and Rational Exponents
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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CONCEPT BACKGROUND
What are inverse
operations?
What are some
examples of inverse
operations?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
KEY TERMS TO KNOW
 Exponent
 Square
 Square root
 Radical
 Cube
 Cube root
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
USING THE TI-30XS
MULTIVIEW CALCULATOR
Perfect Squares, Cubes,
and their Roots
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PONDER THESE QUESTIONS
EVEN ROOTS
ODD ROOTS
Would a perfect square
ever have more than
one square root?
Would a perfect cube
ever have more than
one cube root?
Rule: If the index is
even, you should
consider both positive
and negative values for
the root.
Rule: if the index is
odd, there is only one
possible value for the
root of a number.
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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CALCULATING
SQUARE & CUBE ROOTS
When would a square or cube
root need to be rounded off?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
YOUR TURN
Calculate these cube roots to the
nearest hundredth.
3√7
≈?
3√32
≈?
3√63
≈?
3√120
≈?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
CALCULATING & SIMPLIFYING
RADICALS
CALCULATING
ROOTS
Calculate the square
root of 90 to the
nearest hundredth.
Answer: √90 ≈ 9.49
SIMPLIFYING ROOTS
Simplify the square
root of 90.
Answer: √90 = √ 9 × 10
= √9 × √10
= 3 × √10
= 3√10
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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WHAT ARE “LIKE”
RADICALS?
Radicals that have the same index are
considered to be like radicals.
ⁿ√a and ⁿ√b are like radicals
Why?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
PROPERTIES FOR LIKE
RADICALS
Multiplication Property for Like Radicals
ⁿ√a x ⁿ√b = ⁿ√ab
Example: √5 x √4 = √20
Division Property for Like Radicals
ⁿ√a ÷ ⁿ√b = ⁿ√a÷b , where b≠0
Example: √20 ÷ √2 = √10
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
YOUR TURN
Simplify and then calculate to the
nearest hundredth.
3√2880
3√60
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
SIMPLIFY THIS EXPRESSION
AND JUSTIFY EACH STEP.
(√9 x 3√729)
(√3 x √27)
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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LET’S TRY WHAT WE
HAVE LEARNED!
25-Minutes to Complete
Assignment
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REFLECTIONS OF
LEARNING
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REFLECTING ON OUR LEARNING …
1. Thinking about this entire lesson, as
well as, the pre-institute assignment, what
key concepts do you feel you still need to
work on?
2. What key concepts do you feel that you
know very well and could explain to your
colleagues?
3. What more could you do to study the
key concepts that you identified in the first
question?
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
ONE OF MY
FAVORITE QUOTES!
INSTRUCTIONAL STRATEGIES FOR TEACHING QUANTITATIVE PROBLEM SOLVING
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