Transcript Document

Doing Mathematics
April 25, 2014
SSOS Central Center of Excellence Team Meeting
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Ability and Math Mindset
Video –
• Jo Boaler, Professor Math Education Stanford University
https://www.youtube.com/watch?v=Ic_fWaomyP0&feature=emshare_video_user
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Standard and Benchmarks
STANDARD 3.1.2 Add and subtract multi-digit whole numbers;
represent multiplication and division in various ways; solve realworld and mathematical problems using arithmetic
• BENCHMARK: 3.1.2.3 Represent Multiplication & Division
Facts: Represent multiplication facts by using a variety of
approaches, such as repeated addition, equal-sized groups,
arrays, area models, equal jumps on a number line and skip
counting. Represent division facts by using a variety of
approaches, such as repeated subtraction, equal sharing and
forming equal groups. Recognize the relationship between
multiplication and division.
• BENCHMARK: 3.1.2.4 Multiplication & Division in the RealWorld: Solve real-world and mathematical problems involving
multiplication and division, including both "how many in each
group" and "how many groups" division problems.
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Big Ideas and Essential Understandings
Standard 3.1.2 Essential Understandings
Students build on previous work with addition and subtraction of 2-digit numbers
to include multi-digit whole number addition and subtraction. They use various
strategies to solve real-world and mathematical problems involving addition and
subtraction. Third grade students begin their formal work with multiplication and
division by representing basic facts in a variety of ways. They represent
multiplication facts in a variety of ways including:
repeated addition, equal groups, arrays, equal jumps on a number line (skip counting)
They represent division facts in a variety of ways including:
repeated subtraction, equal sharing, forming equal groups
Students develop an understanding of the relationship between multiplication
and division which will lead to the development of a variety of strategies for
multiplying and dividing. They will solve real-world and mathematical problems
involving multiplication and division.
Problem solving involving division will include both "how many in each group"
and "how many groups" problems.
Multiplication extends to multiplying a two- or three-digit number by a one-digit
number. Strategies may include mental strategies, partial products, the standard
algorithm, and the commutative, associative and distributive properties. Strategic
thinking when solving problems is the focus, not procedures.
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Learning Objective
Students will be able to write a
situation for a given equation
and be able to represent
division facts using equal
sharing and forming equal
groups.
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We will be working with the
following equation:
48 ÷ 3 = 16
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Write a situation for:
48 ÷ 3 = __
48 ÷ __= 16
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Solve the equation:
48 ÷ 3 = __
48 ÷ __= 16
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Different Standard and
Benchmark
• Now an Algebra Standard (instead of Number and Operation)
STANDARD 3.2.2 Use number sentences involving multiplication
and division basic facts and unknowns to represent and solve
real-world and mathematical problems; create real-world
situations corresponding to number sentences.
3.2.2.2 Use multiplication and division basic facts to represent a
given situation using a number sentence. Use number sense and
multiplication and division basic facts to find values for the
unknowns that make the number sentences true.
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Share Solutions
Share out:
written situation
and
representation
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Discussion
Show the two situations –
•equal sharing (how many in each
group?)
•forming equal groups (how many
groups?)
With partner - discuss
•How are they different?
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Reflect and Connect:
What We Learned about the Two Types
of Division Problems
• Equal Sharing:
• How many in a group?
• Also referred to as Partitive or Distribution Division
• Example: Mrs H has 48 students and needs to split into 3 equal groups. How
many in each group?
Need clarification – - (this link to the equation is where I messed up the first
time):
if the wording says, “split into 16 equal groups” instead of ‘split into 3 equal
groups” ----- does it matter if it is 48/3 = 16 or 48/16 = 3
• Student examples from lesson today
• Forming Equal Groups:
• How many groups?
• Also referred to as Quotative or Measurement Division
• Example: Mrs H needs to form groups of three students. How many groups
can she form if 48 students are in the classroom?
• Student examples from lesson today
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Related Benchmarks
•Multiplication
•Place value benchmarks
•Equal size groups is what
place value is about!!
•We use a base ten system, so
the most common group size
that we see in math is 10
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Other Related Benchmarks
Look at other benchmarks
•in
grade
•in previous grades (K – 2nd)
•in latter grades (4th - 5th)
rd
3
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Solve the following division
problem
1459
18
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Adding on to your thinking
Consider this approach:
18 1459
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