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Agenda Thoughts/Concerns
Warm Up
Share Session
Six Shifts in Mathematics
Break
Task Analysis
Math Meeting # 3
Please share your thoughts or concerns
You are not the only one feeling overwhelmed!
CCLS CONTENT AND MATHEMATICAL PRACTICES: AREAS OF FOCUS
5
GRADE BAND DOMAIN OF FOCUS
PreK-K Operations and Algebraic Thinking
1-2 Number and Operations in Base Ten
3 Operations and Algebraic Thinking
4-5 Number and Operations—Fractions
6-7Ratios and Proportional Relationships
8 Expressions and Equations
PLUS…
Targeted Standards of Mathematical
Practice:
MP. 3
Construct Viable Arguments and
Critique the Reasoning of
Others
and/or
MP. 4
Model with Mathematics
WARM UP64 = 65
•Start with an 8 x 8 square with an area of 64 units2
•Make 3 cuts.•Form a 13 x 5 rectangle with an area of 65 units2
• Does 64 = 65? Justify your response.
What mathematical practices did we use in this example?
Watch Video
Networking
Each participant shares what they brought with them in a round robin format
Each table will share 2 things that will benefit the entire group
Common Core Shifts in MathShift Topic
Shift 1 Focus – focus on the math that matters most
Shift 2 Coherence – What you learned in each grade, builds on what you learned the grade before.
Shift 3 Fluency – Insist on developing fluencies, ex. Simple addition and
subtraction, multiplication tables
Shift 4 Deep Understanding – By truly understanding the core
math, they can apply concepts to something they haven’t seen before.
Shift 5 Application - Ability to apply math in different situations even
when you are not prompted to do so.
Shift 6 Dual Intensity - Fluency and Application of understanding.
Practices vs. a few rich problems.
Mathematics Shift 1: FocusWhat the Student Does… What the Teacher Does…
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Mathematics Shift 1: FocusWhat the Student Does… What the Teacher Does…
•Spend more time thinking and working on fewer concepts.
•Being able to understand concepts as well as processes (algorithms).
•Make conscious decisions about what to excise from the curriculum and what to focus on.
•Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic.
•Think about how the concepts connect to one another.
•Build knowledge, fluency and understanding of why and how we do certain math concepts.
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Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding
K–2 Addition and subtraction, measurement using whole number quantities
3–5 Multiplication and division of whole numbers and fractions
6 Ratios and proportional reasoning; early expressions and equations
7 Ratios and proportional reasoning; arithmetic of rational numbers
8 Linear algebra
Priorities in Math
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Instructional Shifts in Math
Which Instructional Shifts are the most urgent for your own work?
Which shifts are the more urgent to achieve the citywide expectations?
How are those priorities similar or different
than the urgent shifts for our own work?
Take a Break
Task Analysis Guide How do we know that our tasks are
meeting the new CCLS demands?
Take a look at the Task Analysis Guide (TAG)
Activity
Study & Compare the sample tasks Turn and Talk
What do you notice about the differences between the examples and non-examples?
Based on the sample tasks and your experiences with assessment tasks, what would you say are the characteristics of effective assessment tasks?
Group Share
Comparing Two Mathematical Tasks ~ Grade 3
How are the following two tasks the same and how are they different?
Find the product for each problem.
Follow the procedure shown below.
16 32 56 56
x 8 x 8 x 2 x 8
128
Use grid paper to find the solution to 8 x 4 and 8 x 8. Write your solution in equation form.
Continue to use 8x4 and 8x8 to help you find the solutions to 8x16 and 8x32. Show your work. Write your solutions in equation form.
Write about the relationship that you notice among the equations.
8 x 4
8 x 8
8 x 16
8 x 32Adapted from the Institute for Learning professional development session October 2011 – Supporting Teachers in Planning, Teaching, and Reflecting on
Mathematics Instruction
Activity
Tasks A – DAt your table, determine where these 4
tasks fall within the Task Analysis GuidePlease justify your responses in the right
column
Group Share
Task ACounting Coins
Imad collects quarters, dimes, nickels and pennies. This morning he took $1.80 from his collection. He counted the coins and found that he had twice as many nickels as dimes. What coins could Imad have? Explain with words and pictures how you figured out your answer. Remember to show all your work.
Task B
Explain what the equal sign means in this number sentence
14 - 3 = 8 + 3
Task C
Gabe has a rectangular garden.The area of his garden is 117 square meters. It is 13 meters long.Find the width.
Use words and diagrams to explain how you can find the width of the garden.
Write an equation that explains how you solved the problem.
Task DHenry’s Secret Numbers
I’m thinking of some numbers.Each number is less than 40- I land on these numbers when I count by 2- I land on these numbers when I count by 3- I do not land on these numbers when I
count by 4What is Henry’s smallest secret number? Use words or an equation to show that your choice of number is Henry’s smallest secret number.
