Differentiating math
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Differentiating Math. Using Assessments and Extension Menus to compact, accelerate, and differentiate math instruction. . What is today’s objective?. To share with you a strategy for differentiating instruction in Math using pre-assessments and extension menus We will be showing you:

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Differentiating math l.jpg

Differentiating Math

Using Assessments and Extension Menus

to compact, accelerate, and differentiate math instruction.

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What is today’s objective?

To share with you a strategy for differentiating instruction in Math using pre-assessments and extension menus

We will be showing you:

Hardest 5 quizzes

Math Extension Menus

Ideas for Classroom Management and Environment

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What is the Hardest 5 quiz?

Pre-assessment tool used to check a student’s mastery of a Math concept

5 most challenging questions from the lesson

5-minute quiz time (more time-consuming concepts such as long division or multiplication with greater numbers may require another 1 or 2 minutes)

To test-out, students must earn 100%

Two forms: one Hardest 5 quiz given daily or a set of Hardest 5 quizzes on the next week’s lessons

Can be made to be projected on a screen or as a paper quiz to be distributed

Students permitted to study ahead of time

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How do I use the Hardest 5 Quiz?

  • The Hardest 5 quiz is used to assess prior knowledge of students.

  • Students who show mastery on a math concept can “test out” for the day and work on math extension activities.

  • If a whole class passes the hardest 5, this data can be used to compact or accelerate a lesson (by simply doing a quick review, for example.)

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Give the Hardest 5 Quiz that covers the lessons you will be teaching the following week.


Before the lesson:

Give the Hardest 5 Quiz that covers the lesson you will be teaching that day.

After the Lesson:

Give the Hardest 5 Quiz that covers the lesson you will be teaching the following day.

When do I give the Hardest 5 ?

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What does a daily lesson look like?

  • Lesson

    • Teach math lesson to class

    • All students must listen and take notes

  • Structured Practice/Guided Practice

    • Students who have tested out will at this time be excused to work on their Scholar Menu

    • Students that have not tested out will continue with the practice phase of direct instruction.

      • Expect classroom transition here!

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  • Independent Practice

    • Students that struggled with the guided practice will meet with the teacher in small groups for additional support with the lesson.

    • Students who understood the lesson will move on to independent practice.

    • If students finish independent practice quickly they can move on to Challenge problems that have been assigned.

    • Hardest 5 students will continue to work on their Scholar Menu in their small groups.

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What are Extension Activities?

  • The purpose of Extension Activities is to provide students who have shown mastery on a math concept with opportunities to:

  • Extend Their Learning

  • Apply Mathematical Knowledge Beyond Procedures

  • To Connect Mathematical Knowledge to the Real World.

    Extension Activities are presented on Extension Menus, which provide an activity for every lesson in a Unit, as well as optional activities for student choice.

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How do I make Extension Menus?

  • Look for challenge questions / pages in your text book.

  • Supplemental Challenge activities with your math program.

  • Differentiating Instruction with Menus - Math by Laurie E. Westphal

  • Find real world applications for the math concept.

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21.2 Multiply Fractions and Whole Numbers

Think Like a Top Chef!

Find or create a recipe that contains at least 3 fractions, no mixed numbers.

Create 3 recipe cards:

First, triple the recipe (multiply every ingredient by 3). Remember, this will triple the amount of people that the recipe will serve.

Second, rewrite the recipe for a party by multiplying everything by 8.

Third, rewrite the recipe for a banquet by multiplying everything by 24.

What are some sample activities?

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Lines and Angles Map It!

Create a road map for a fictional city. Your map should include examples of each of the following geometric concepts:

o Point o Line

o Ray o Line segment

o Plane o Right angle

o Acute angle o Obtuse angle

o Parallel line o Intersecting line

o Perpendicular line

Create a legend to explain where each geometric concept can be found on your map.

Your town should be named, colored, locations should be clearly labeled, and your map should include color where appropriate.

What are some sample activities?

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How do I assess Extension Activities?

  • Rubrics can be created to assess for:

    • Mathematical Understanding

      • Does the assignment show correct understanding of the math concept?

    • Content

      • Does the assignment follow all directions completely and include all necessary information?

    • Creativity and Effort

      • Is the assignment neat, attractive, creative, and show effort and scholarly pride?

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Classroom Environment

How can I organize my classroom to make Hardest 5 run smoothly?

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Where do I keep a list of Math Groups?

Math Groups labeled and listed on a classroom Math board (e.g. Team 1/ Team 2 with students numbers listed under the appropriate title)

Location suggestions: whiteboard, sheet protector with a white paper, pocket chart

Other option: Math groups do not have to be displayed; lists can written down and kept by the teacher only

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Where do I put Math Extension Menus?

Pocket files on the Math board or standing file folder that the students have access to

Menu activity resources should be in the same location

Other option: Distribute the Menu to all the students at the beginning of the week; students keep it in a Math folder until the end of the Unit

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Where do the students who tested out work while I am teaching the lesson?

Work areas should be designated in the classroom

Suggestions: classroom library, small group table, computer table

Move students in the classroom so table groups can be made into Extension Group work areas

Students understand they are to be working quietly during your instruction

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Troubleshooting! How can I ensure that Differentiation is a Success?

  • Model expectations for Hardest 5 group

  • Preview Scholar Menu at beginning of unit or on Monday when test out students are posted

  • Transitions - provide time (when test out students are excused and students move to empty seats)

  • High standards for Extension Menu

    • Set expectations at the beginning

    • Create a rubric for scholarly work

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Presented by: Success?