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Accessible Mathematics Day 3. Shifts 3, 4, and 5. Review Shifts 6-9 & Discuss the Homework. Instructional Shift 3. Use multiple representations of mathematical entities. Fractional parts of wholes vs. Fractional parts of sets. In your mind’s eye….

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accessible mathematics day 3

Accessible MathematicsDay 3

Shifts 3, 4, and 5

instructional shift 3
Instructional Shift 3

Use multiple representations of mathematical entities.

draw a picture use a number line ask them what it looks like
“Draw a picture!” “Use a number line!” “Ask them what it looks like!”

Solve the following problems:

1. 2.

How would you explain the difference between the following 2 expressions: and ?

singapore math
Singapore Math
  • Refer to the following website:

Thinking Blocks Modeling Tool

so what should we see in an effective mathematics classroom
So what should we see in an effective mathematics classroom?
  • Frequent use of pictorial representations to help students visualize the mathematics they are learning.
  • Frequent use of the number line and bar models to represent numbers and word problems.
  • Frequent opportunities for students to draw or show and then describe what is drawn or shown.
instructional shift 4
Instructional Shift 4

Create language-rich classroom routines.

“…one of the simplest and easiest ways to take the students who are just below proficient and move them to proficient is to attend to the fact that they just may not have known five mathematical terms.”
so what should we see in an effective mathematics classroom1
So what should we see in an effective mathematics classroom?
  • An ongoing emphasis on the use and meaning of mathematical terms, including their definitions and their connections to real-world entities and/or pictures.
  • Student and teacher explanations that make frequent and precise use of mathematics terms, vocabulary, and notation.
  • An extensive use of word walls that capture the key terms and vocabulary with pictures when appropriate and in English as well as Spanish when appropriate.
instructional shift 6
Instructional Shift 6

Take every opportunity to support the development of number sense.

what is number sense
According to Mr. Leinwand, “a comfort with numbers that includes estimation, mental math, numerical equivalents, a use of referents like ½ and 50%, a sense of order and magnitude, and a well-developed understanding of place value…”What is Number Sense?
so what should we see in an effective mathematics classroom2
So what should we see in an effective mathematics classroom?
  • An unrelenting focus on estimation and justifying estimates to computations and to the solution of problems.
  • An unrelenting focus on a mature sense of place value.
  • Frequent discussion and modeling about how to use number sense to “outsmart” the problem.
  • Frequent opportunities to put the calculator aside and estimate or compute mentally when appropriate.
homework for next time
Homework for next time:
  • Read Chapters 2, 3, and 11.
  • Review the Singapore Math website and find a way to incorporate the bar model in one of your lessons. Bring this with you next time.