K-2 Common Core Fractions and Geometry January 2012…Elementary Math Facilitators

What does research say about early learning of fractions? What happens in the early grades to “cause” later confusion with fractions? Where did fractions of a set go?

If the whole square is equal to 1, label each part with the appropriate fraction

What did you start with?

Fractions in K-2 In Gr 3-5 there is a Fraction strand In Gr K-2 there isn’t a Fraction strand… are they off the hook? Where are they? What do they look like?

Take a card Groups of 4; take one card and read it to yourself Determine the “big idea” Read your card aloud and say “The big idea in – grade…” Then lay all cards down

Digging Deeper Now look at all standards and unpacking Complete the chart

Where is Kindergarten? 2G2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

What does this even mean???

Let’s Partition With your partner, fold your plate so each of you gets the same amount. Did you get equal amounts? How do you know? Prove it! If students do this, have they met the standard? What else is needed?

Fold and fold again! Now you and your partner find another pair. Fold your plate so each person in your group (4) gets a fair share. Did you get equal amounts? How do you know? Prove it! If students do this with rectangles and circles, have they met the standard? What else is needed? How does the process of folding in halves different than folding in fourths?

Discussion THE big idea in 1 st grade- What does ‘understand’ mean exactly?

Understand (from NCDPI) Revised Bloom’s Taxonomy – Equal to “comprehend” – Level 2 of 6 in terms of difficulty Common Core – Understand means students can Apply (Level 4 of Bloom’s), Explain and make connections

Look at this a different way, What is NOT included in the standard?

PARTITION How will you ensure students understand and use these words? Attend to precision-

1 st Grade Planning In planning, a teacher shares a sheet she is going to use with her students. It looks like this:

Students need to Partition unmarked regions (no lines already drawn). Why?

Pre-partitioned regions lead to a common misconception: ¼ 1/3 1/3

1 st Grade CMS unit Where are the Pearson lessons? – Partition a clock vs. Partition a circle Why only 2 lessons?

Heads-Up phrases in planning Well I’m going to ____ because my kids can get it How can students think about fractions if they are not writing them?

Sharing the Paper You have a rectangular piece of paper. Cut your paper so you can share an equal piece with your friend.

Sharing the Paper Cut the paper so that you and three friends get an equal section.

Dividing the Room You want to share the space in your school closet between yourself and 3 other facilitators. On grid paper, draw three congruent 6x4 rectangles to represent the closet. Label your rectangles a. b. and c. Divide the closets so that: a) 2 sections are rectangles and 2 sections are different shaped rectangles b) 2 sections are rectangles and 2 sections are triangles c) You have 4 different shaped regions

How do we make fourths? “Half of a half” concept

Discussion Time! Have groups share their pieces and ask… What do you notice about these fourths? Are they equal? Prove it! A big idea in second grade…

How do students think about this? Read the Dialogue Box When done discuss: – Evidence of student understanding – Teacher moves to check for understanding

How is this different from what is expected in 1 st grade?

What’s NOT included in the standard? Page 65 second grade unit

DO’S AND DON’TS What DID we do? -Partitioned- drew, cut, folded rectangles and circles -Reasoned about the size of the pieces -Reasoned about how to use a half to make a fourth -Vocab: -Used the word partition -Used “half of, a fourth of, quarters, etc. -Used “one- fourth, one-half, etc. - What DIDN’T we do? -Write fractions -Find a fraction of a set -“If there are 2 green cubes and 3 blue cubes, what fraction of the cubes is green?” -Find equivalent fractions -Compare and order fractions

You are in 2 nd grade planning Where are fractions of a set? Should we teach them anyway? There are 8 cookies that you want to share between 2 people. How many cookies does each person get? What is the “action” in the problem above?

You are in 2 nd grade planning There are 8 cookies that you want to share between 2 people. How many cookies does each person get? What is the “action” in the problem above? 8 divided into 2 groups if 4. What grade do we start to teach division? Why do we not divide in Grade 2?

How will you help your 1 st – 2 nd grade teachers get ready to teach this content ? 1 st Grade 2 nd Grade