**Week Two of Embolden Your Inner Mathematician**

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

**Course Goals:**

At the end of the semester, teacher-learners should be able to say:

- I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
- I can exercise mathematical flexibility to show what I know in more than one way.
- I can make sense of tasks and persevere in solving them.

**Today’s Goals**

At the end of this session, teacher-learners should be able to say:

- I can use and connect mathematical representations. (#NCTMP2A)
- I can show my work so that a reader understands without have to ask me questions.

From *Principles to Actions: Ensuring Mathematical Success for All: *

**Use and connect mathematical representations:**Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

**Learning Progressions for today’s goals:**

- I can
**use**and connect mathematical representations.

- I can use and
**connect**mathematical representations.

- I can show my work so that a reader understands without have to ask me questions.

**Tasks:**

- Beanie Boos (see slide deck)
- Number Talks
- What do the standards say?

**Addition and Subtraction**

**2nd Grade
**Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

**3rd Grade
**Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

**4th Grade
**Fluently add and subtract multi-digit whole numbers using the standard algorithm.

**Multiplication**

**3rd Grade
**Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

**4th Grade
**Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

**5th Grade
**Fluently multiply multi-digit whole numbers using the standard algorithm.

[Cross posted on Sum it up and Multiply it out]

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” *Experiments in Learning by Doing**or Easing the Hurry Syndrome.*WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Leinwand, Steve. *Principles to Actions: Ensuring Mathematical Success for All*. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

“Number & Operations in Base Ten.” *Number & Operations in Base Ten | Common Core State Standards Initiative*, National Governors Association Center for Best Practices and Council of Chief State School Officers.