Math CAMPPP 2012 Balancing Assessment K-4 Breakout Five 1 <Welcome participants.> K-4 Breakout Five 1

Participant Learning Goals: Participants will: investigate portfolio assessment deepen their understanding of Balanced Assessment become aware of important understandings and misconceptions and how to assess for understanding in the learning of fractions.

Minds on: Inside/Outside Circle 4 Discussions:

Discussion #1 Describe any experience you have had with portfolio assessment?

Discussion #2 What is one thing from Chris’ presentation that you don’t think would work in K-4? How could this be tweaked for K-4?

Discussion #3 Describe one criterion that you would like to see represented in a student portfolio? Explain.

Discussion #4 Describe an idea about assessment that you would like to learn more about?

Sharing Our Stories

Action: Myth Busting Myth: Fractional parts of a set must look exactly the same.

The Fruity Set Problem In groups of 4 (mixed grade), work together to solve the following problem. (you may use materials/manipulatives) Record your solution on chart paper. Post your solution.

The Fruity Set Problem A basket of fruit, containing mangos, blueberries, apples and cherries was delivered to the palace. The king took one sixth of all the fruit. From what was left, the queen took one fifth of the fruit. From what was left, the princess took one fourth of the fruit. From what was left, the prince took one third of the fruit.. From what was left, the duchess took one half of the fruit.. This left only 2 blueberries and 1 mango in the bowl for the servant. How many pieces of fruit were originally in the basket?

Gallery Walk What are the big ideas and misconceptions about fractions that this problem may address/expose? Write these on stickies and post them on the learning wall.

Guess and Check Pick a multiple of 6 - let’s say 60. One sixth of 60 is 10 which leaves 50. One fifth of 50 is 10 One fourth of 40 is 10 One third of 30 is 10 One half of 20 is 10 10 left over is too high Try a lower multiple of 6.

Draw a Diagram King removes one sixth of fruit Queen removes one fifth of remainder Princess removes one fourth of remainder Prince removes one third of remainder Duchess removes one half of remainder 2 blueberries and a mango left

Another Diagram 3 + 3 + 3 + 3 + 3 + 3 = 18 3 King Queen Princess Prince Duchess Servant 3 3 + 3 + 3 + 3 + 3 + 3 = 18

Working Backwards Servant receives 3 pieces. Duchess (took one half) so 3 is half of 6 Prince (took one third) so 6 is two thirds of 9 Princess (took one fourth) so 9 is three fourths of 12 Queen (took one fifth) so 12 is four fifths of 15 King (took one sixth) so 1 is five sixxths of 18

Algebraic Solution

Finding a Pattern Start with 24 Choose a lower number One sixth of 24 equals 4 One fifth of 20 equals 4 One fourth of 16 equals 4 Choose a lower number One sixth of 18 equals 3 One fifth of 15 equals 3 3 blueberries is what was left so 6 people times 3 equals 18 pieces of fruit.

Myth: fractional parts of an area need to look exactly the same (size and shape) Re-organize into homogeneous grade groups of 4 to 6. Consider the following problem.

Is one fourth of the square in the picture shaded? (P61 A Focus on Fractions)

Maria’s Response p62

William’s Response p63

Placemat What do you know about each student‘s understanding?” “What are you unsure of?” “What would you ask each next?”

Group Placemat What I am sure about Maria`s understanding: What I would ask Maria next: What I am sure about William`s understanding: What I would ask William next: Informed Practice:

William`s Follow-up p63 William took 4 marbles out of his desk . He said that even though the marbles were not the same size, one of the marbles was one fourth of his set of four marbles – the shaded portion of the square is one piece out of four pieces , so it is one fourth of the square

Maria`s Follow-up pg 64 Mrs. Armstrong asked Maria if each of the figures below showed one fourth of the figure shaded. “No, one fourth is not shaded because Square 1 is not divided into 4 equal parts and Square 2 is divided into 2 unequal parts not 4 parts.”

Placemat Part 2 Add to your group’s placemat any new information you have about Maria or William’s understanding. Complete the circle in middle: How can this follow-up student work inform teaching/practice?

Reflection – Your Choice What is your A-HA moment from today? Record for your treasure box. Comment on the following quote: “A fine glass vase goes from treasure to trash, the moment it is broken. Fortunately, something else happens to you and me. Pick up your pieces. Then, help me gather mine.” ― Vera Nazarian,

Home Activity Problem: Find as many different ways to show one half a geoboard and record each way on the grid square handout.