- Los Angeles Unified School District
- Secondary Math Toolsets
Toolsets
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Toolsets are one of the components of Local District West's Framework for Ambitious Math Teaching. Toolsets are a suite of high leverage math activities that promote the use of effective teaching practices and the use of the student math practices.
Number Sense Routines
Math Instructional Activity (IA)
Description
PtA Effective Math Teaching Practices (MTP) Contained within IA
Equity-Based Math Teaching Practices (EB-MTP)
Common Core Student Math Practices (SMP)
Which One Doesn’t Belong
Resources:
Students are presented four items in a grid and are asked to select one that doesn't belong and explain why.
MTPs 1, 2, 4 ,5 ,8
EB-MTPs 1, 2
SMPs 2, 3, 6, 7
Error Analysis
Resources:
Students find the error, describe the nature of the error and the faulty reasoning, and then explain the correct solution path. It can be used to address common errors, misconceptions, and as a reflection piece after an assessment
MTPs 1, 2, 4, 5, 6, 7, 8
EB-MTPs 1, 2, 3, 4
SMPs 1, 2, 3, 6
Number Talks
Resources:
Students share their solution method to a mental math problem. Number talks help students develop number sense by learning how to flexibly de-compose and re-compose numbers and develop number sense.
MTPs 1, 2, 3, 4, 5, 6, 8
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EB-MTPs 1, 2, 3, 4, 5
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SMPs 1, 3, 6, 7 Always, Sometimes, Never.
Resources:
Students decide whether a statement is always sometimes or never true. The teacher prompts students to provide supporting evidence and facilitates a discussion of the responses.
MTPs 1, 2, 4, 5, 6, 8
EB-MTP 1, 2, 3
SMPs 1, 2, 3, 6, 7
Visual Patterns
Resource:
Students are provided with the first few figures in a pattern and are asked to describe what the nth figure would be like. Visual patterns call on students to recognize, describe, and generalize patterns using multiple algebraic representations
MTPs 1, 2, 3, 4, 5, 6, 7, 8
EB-MTP 1, 2, 3, 4, 5
SMPs 2, 3 ,4 ,6 ,7, 8
Open Middle
Resource:
Open middle problems have the following characteristics:
they have a “closed beginning” meaning that they all start with the same initial problem.
they have a “closed end” meaning that they all end with the same answer.
they have an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.
Open middle problems require a higher depth of knowledge than most problems that assess procedural and conceptual understanding. They provide students with opportunities for discussing their thinking.
MTPs 1, 2, 3, 4, 5, 6, 7, 8
EB-MTPs 1, 2, 3, 4, 5
SMPs 1, 2, 3, 4, 5, 6, 7, 8
Problem Based Lessons
Math Instructional Activity (IA)
Description
PtA Effective Math Teaching Practices (MTP) Contained within IA
Equity-Based Math Teaching Practices (EB-MTP)
Common Core Math Practices (SMP)
MARS Formative Assessment Lessons
Resource:
A lesson cycle consisting of
a short mini-assessment to assess the current level of understanding
followed by a problem solving task, with a teacher-facilitated discussion
followed by a mini-post assessment to help determine growth.
MTPs 1, 2, 3, 4, 5, 6, 7, 8
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EB-MTPs 1, 2, 3, 4, 5
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SMPs 1, 2, 3, 4, 5, 6, 7, 8
Three Act Tasks
Resource:
Act One
Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible.
Act Two
The student overcomes obstacles, looks for resources, and develops new tools.
Act Three
Resolve the conflict and set up a sequel/extension.
MTPs 1, 2, 3, 4, 5, 6, 7, 8
EB-MTP 1, 2, 3, 4, 5
SMP 1, 2, 3, 4, 5, 6, 7, 8
Low Floor High Ceiling Problem Solving Tasks
Resources:
the tasks and more section of Jo Boaler's Youcubed.org
Open-ended tasks with multiple access points and multiple solution paths. A teacher led discussion can help students develop understanding of math concepts and make connections. Teachers would use the Thinking Through A Lesson Protocol (TTLP) to plan these lessons.
MTPs 1, 2, 3, 4, 5, 6, 7, 8
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EB-MTPs 1, 2, 3, 4, 5
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SMPs 1, 2, 3, 4, 5, 6, 7, 8
Desmos Classroom Activities
Resources:
Pre-made calculator activities that address all 3 aspects of rigor: conceptual understanding, application, and fluency.
MTPs 1, 2, 3, 4, 5, 6, 7, 8
EB-MTPs 1, 2, 3, 4
SMPs 1, 2, 3, 4, 5, 6, 7, 8
