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Differentiation
Why is differentiation important for student learning in mathematics?
Student readiness, interests and learning preferences vary greatly within any mathematics classroom. Students will differ in their knowledge and understanding of mathematical concepts and in their use of mathematical skills such as mental math and estimation. Students also vary in their application of the mathematical processes:
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• solving problems in new situations
• reasoning skills including proportional reasoning, algebraic reasoning, and spatial reasoning
• reflecting on and monitoring one’s thinking
• selecting and using a variety of learning tools and computational strategies
• connecting mathematics to real life and to other mathematical ideas
• representing mathematical ideas and relationships concretely, pictorially, numerically, and algebraically
• communicating mathematical thinking orally, visually, and in writing, using everyday language and mathematical vocabulary
Multiply numbers visually
Suppose you want to multiply 22 by 13.
Steps:
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Draw 2 lines slanted upward to the right, and then move downward to the right a short distance and draw another 2 lines upward to the right (see the magenta lines in Figure).
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Then draw 1 line slanted downward to the right, and then move upward to the right a short distance and draw another 3 lines slanted downward to the right (the cyan lines in Figure).
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Now count up the number of intersection points in each corner of the figure.
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The number of intersection points at left (green-shaded region) will be the first digit of the answer.
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Sum the number of intersection points at the top and bottom of the square (in the blue-shaded region); this will be the middle digit of the answer.
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The number of intersection points at right (in the yellow-shaded region) will be the last digit of the answer.
This will work to multiply any two two-digit numbers, but if any of the green, blue, gold sums have 10 or more points in them, be sure to carry the tens digit to the left, just as you would if you were adding.
Mathies Activities
Mathies Activities and The Ontario Educational Resource Bank (OERB) offers a number of digital activities and interactive learning resources Kindergarten to Grade 12 for publicly funded schools. Please click on the picture in the left to go to the website.
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Summaries of the OERB activities are arranged by strand for Kindergarten to Grade 12. Click on a selected grade for the drop down menu to access the summary for a strand or secondary course. All tables feature a description, picture and Resource ID (ex., ELO1414330) for each activity. For easy access, copy the selected activity Resource ID from the summary, enter the OERB site from a new tab and paste in the search prompt.
20 Differentiated Instruction Strategies and Examples
To help create lessons that engage and resonate with a diverse classroom, click on the picture and go to Prodigy website.
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There are 20 differentiated instruction strategies and examples. Available in a condensed and printable list for your desk, you can use 16 in most classes and the last four for math lessons.
Important Note:
Online Tools
The Critical Thinking Consortium**
Ontario Education Resource Bank (OERB)
Username: YRDSBteacher
Password: oerbt
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EduGAINS
Please click on the image. This site is intended to support the facilitator in leading a three-part professional learning series that:
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• Increases teachers’ Content Knowledge for Teaching Mathematics (CKT-M);
• Provides teachers with opportunities to practise selected professional principles related to differentiating instruction;
• Develops awareness of factors that were considered by the teacher in the M.J. Hobbs chapter of the Differentiated Instruction (DI) DVD in differentiating mathematics instruction based on student readiness.