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Summer Camp–so far

Five days. Five days to spend with about 50 educators thinking, reading, talking, exploring, investigating all things math. IMG_8098

6 grade levels, kindergarten through grade 5

5 days of community and conversation with people who care about how kids learn, who are willing to really think about what needs to happen in classrooms to meet kids where they are in their understanding and move them forward, and who share the joy that comes from figuring something out

4 structures: daily reading selections, math work stations, number routines (counting circles, choral counting, number talks, number strings, strategies from Intentional Talk), and math tasks

3 resources: Intentional Talk by Elham Kazemi and Allison Hintz, Number Talks by Sherry Parrish, and Math Work Stations by Debbie Diller


2 things I noticed: People really like learning, including being challenged and pushed a bit. Enthusiasm for learning is contagious.

1 great friend who gave up 5 days of her summer to spend with me and a fabulous group of educators

Day 2 of Summer Math Camp

Day 2 of Summer Math Camp was fabulous. It was fabulous because the 26 people with whom I spent the day are fabulous. They walked in the door with an I love math and teaching so much that I am spending day 3 of my summer vacation working on math tasks, reading and talking about teaching and learning, and thinking about my classroom room and what I want it to be for next year’s students. With all of that amazing energy how can you have anything except a fabulous day!


We started out our day by reading an article and thinking about its content using the sentence-phrase-word protocol, courtesy of posts written by Jill Gough on her blog Experiments in Learning.


Then, we worked on four tasks from the Young Mathematicians at Work series written by Cathy Fosnot. We are considering using some of the units on multiplication and division next school year and wanted teachers to have a chance to investigate the materials, The tasks are nicely constructed, very versatile, and work for a wide range of learners and in a variety of instructional settings.


After we discussed the content students explore and the instructional moves we might use when working on the four tasks, we talked about how the big ideas of multiplication relate to grade level standards, and how students’ thinking, reasoning, and understanding develops across the grade levels. The final component of the morning session was the construction of a concept map that organized the big ideas, strategies, and models of multiplication, as well as, the teacher moves that support students building their understanding of multiplication.

After lunch, we spent some time talking about division before moving into math work stations.


The day ended with a bit of reflection.


Quote of the day:  I can do more than I think I can.

Thank you one and all for sharing two days of your summer, your thoughts, ideas, questions, and your care for the children who are fortunate to spend their days with you.

Day 1 of Summer Math Camp

Today was awesome. I spent the day with 25 educators investigating, exploring, discussing, and grappling with ideas that comprise a big idea in elementary mathematics instruction: multiplication.

The day started with a video from The Math Forum of Max sharing a set of gum balls among a number of people. We spent some time thinking about what kinds of questions the video prompted us to want to investigate. Some of the questions that people were thinking about are as follows:

  • If each person gets 1/2, do they all get the same amount of gum balls?
  • What would each person’s share of the gum balls be, written as a fraction and as a percent?
  • How many gum balls does each person get?
  • What does 1/2 mean?
  • Is there something here with exponents:  1/2 of a 1/2 of a 1/2?

The actual questions we started our exploration with were:

  • How many gum balls does Jaysen get?
  • How many gum balls does Marinda get?
  • How many gum balls does Zack get?

In addition to the notes each person made, the table groups were asked to represent their solutions using Unifix cubes. It was really interesting to hear and see the different connections that were made when ideas and solutions were described using Unifix cubes. When we went back and looked at the questions we had listed after watching the video, we could answer all of them!! The a-ha moment we had was if we had started with some or most of them, we might not have persevered. However, starting with the three question we did allowed us to take on the questions the group had generated. It was for us, a nice fit of a low floor and taller ceiling kind of task.

We then worked our way through a variety of multiplication algorithms, based on the work of Cathy Fosnot. The teachers explored the strategies of doubling, doubling and halving, and partial products, and how the strategies can be represented using arrays and area models. There was lots of great conversation focused around how the strategies and the models are connected.

After lunch, we worked on a number string, again based on the work of Cathy Fosnot.

10 x 13

2 x 13

12 x 13

20 x 13

22 x 13

29 x 13

Some offered to be in the group that participated in the number string. The rest of the group focused on the instructional moves used when facilitating a number string. The strategies and models we worked on in the morning were put to use in the afternoon: doubling, area and array models, and partial products all made an appearance at some point during the number string and the debrief that followed.

The last part of our day was spent engaging in a different tasks, games, and activities involving multiplication. These were set up in math work stations.

Our closing reflection was a 3-2-1: three ideas that resonated with you or you are considering in some way to include in your work with students, two a-ha moments from the day, and one question you are still pondering.

The best comment of the day: What do we have for homework?

How much for the race car?

A few weeks ago, you figured out that 258 twelve-packs of soda were used to build the race car.


The other night when we stopped at the store, we noticed that the grocery store had posted this sign in front of the display.


So it made us wonder a whole bunch of things as we walked through the store:

  • How much would it cost to buy the twelve-packs of soda necessary to build the race car?
  • How much would it cost to buy the twelve-packs to build the race car when they are not on sale?
  • How much would money do you save when you buy the twelve-packs on sale?
  • How much will you pay in CRV fees, at $0.05 per can?

What other questions do you have?

American Flag

The coke soda guy has been at it again. Check out the current display.

Screen Shot 2015-06-05 at 10.44.00 AM
How many cans of soda does it take to create the display of the American flag?

How many 12-packs did he use to make the display?

How did you figure it out?

Here’s what we did:

We think that the flag is 12 twelve-packs across and 13 twelve-packs high. So, we figured out that he used a total of 156 twelve-packs used to make the display. We know that 12 rows of 12 twelve-packs is 144 twelve-packs, and one more row of twelve-packs means that there are 156 twelve-packs. Then, we multiplied the 156 twelve-packs by 12 since there are 12 cans per twelve-pack. (That’s a rather obvious statement, isn’t it.) Our total is 1872 cans of soda.