# Author: Nova

# Cycle of Measurement & Data

# Dan Finkel, Tiny Polka Dots, & Planning

Interesting Resources:

- Dan Finkel’s TED Talk
- Christina Tondevold’s Build Math Minds Community
- Tiny Polka Dots Game
- YouCubed on YouTube

# #1ProblemChallenge

I have an end of year challenge for you.

**Disclaimer**: there are many ways we can make this challenge higher leverage, involving academic discourse, naming strategies, connections to real-world contexts. I’m keeping it simple, folks. Just see what happens. And then comment and share!!

Rules:

- In one of your upcoming math lessons, only use
**ONE PROBLEM**. One. Uno. Unus. Jeden. Yksi. Moja. 1. **YOU**are**not allowed**to write on the board.*(Ok, you can write the problem on the board if you have to.)*

That’s it! Try it!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Here’s an example of a 3rd grade class who conquered this challenge:

“Best lesson ever! They were so into it. I didn’t have to do anything which was nice, too. I only let one student do each step. Most students contributed. I challenged them by having them show two different strategies and added on an extra question at the end. Thanks!” ~3rd Grade Teacher

# Instructional Materials 3 Act

Look at the graph below.

*Prices may not be accurate. Gathered from http://www3.cde.ca.gov/impricelist/implsearch.aspx on 3/23/17. Please don’t sue me! 😉 *

Our Class Question (pick 1):

1. How bad does an instructional material have to be to be good enough for a school district to adopt it, but bad enough that teachers want it replaced within 4 years?

2. How much money does each company make on a new adoption?

3. What are the benefits for each company to publish a high quality instructional material that can be used for an extended period of time?

What do you notice? What do you wonder? What do you need to know to solve this problem?

Additional Information:

- Prices are based on materials for 1 student
- Prices are based on 3rd grade materials
- Prices are based on CA edition
*Williams vs California*(2004) legally requires each student to have access to instructional materials, meaning each student must have 1 set.

**Show your work. Explain your conclusion using words & pictures. **

# “Broken Lesson”

We think that a lesson means one learning experience for the students.

I’m not asking, I’m stating. We may say we don’t believe that, but nearly all of the lessons I have taught & observed have students engaging in a single learning experience.

Two of the most memorable lessons I’ve seen sent the students to work in small spurts – no longer than 10 minutes at a time – and then brought the class back together multiple times. This happened 2 or 3 times in a lesson. Breaking up the lesson like this seemed to allow students to practice a discrete skill so that when it came time to conceptualize the big idea, they had schema which allowed them to make connections faster.

What are your thoughts? Have you taught a lesson recently where you broke it into a few mini-lessons? Is there a name for this type of lesson? Can I name it the “Broken Lesson” because it is broken up into multiple parts?

Example 1:

In a science lesson, the teacher began by showing a video and connecting to prior learning. Continue reading

# “I pulled my diaper down like undies!”

I adore watching my 3 year old son attend to a task and persevere. This morning he got himself out of bed, announced he had to “go pee pee” and marched into the bathroom by himself. He still wears a nighttime diaper, so he requested help getting the diaper off. I responded, “Try it by yourself, first.” He carefully placed his ball on the counter, plopped himself down, and then tried about 3 different ways to get the diaper off before he was successful. At no point did his tenacity wane, and when he got the diaper off he looked up and said,

## “I take it off like undies!”

Once he was done with the deed, he sat down and put his jammie pants back on. Again, he failed on his first attempt (both feet went down the same leg). So he pulled his foot out and tried another method. This time he stuck his arm down the correct path as if to clear the way. With this, he was successful. Upon further inspection it turns out that along with having on no undies, his pants are also on backwards. Did I tell him to take his pants off and try again? Absolutely not, because he completely the task well enough and he did it independently. When finished, he trudged upstairs to my husband and announced, “I went pee pee. I took my diaper off like undies!” Continue reading

# Math Design Challenge

I was in a 5th grade class today. They were reviewing homework. Not the homework given by the textbook, but homework that the teacher had hand-created the day before. Can I call that “bespoke homework”? It’s not clothing, so probably not, but these kids were certainly trying on something new…

The teacher asked students to discuss their strategies with their group, de-emphasizing the answer. “What strategies did you use? Did you use the order of operations? How did you see the problem?” It quickly became clear that there were 2 understandings:

2.3+6×2²

AND

2×3+6×2²

What a great discussion! “How do we know which problem to solve? Does it matter? What is the right way to write this equation? What’s a different way to write this equation so that it is clearer? Why do we have the order of operations? Why are there different symbols for multiplication? Why isn’t there a symbol for multiplication that doesn’t have two meanings!?”

The teacher could have told one group that they clearly misunderstood and to redo their work, but instead she validated them and asked them to justify their answer no matter how they saw it.

And then I threw in, “Why don’t you have a design challenge where everyone creates a new multiplication sign and we vote on which new sign to use! It can be the new international multiplication sign!” (The teacher was really pleased with me for throwing that one out there.)

So I challenge you! In the comments or tweet #multiplicationsign, what new sign do you think we should use!?

# Find Regularity in Repeated Reasoning

I have a question…

- We look for regularity in multiplication in many ways. And one way we learn multiplication is repeated addition.

- Additionally, we learn how to add together strings of 3 addends (we rarely ask students to add more than 3 addends, unless we’re working on mastery of 2.NBT.6).

It seems like you could develop a lesson that incorporates the 2. I’m thinking of building a lesson based on something like: Continue reading

# Busy Bee Summer Resources

Updated 6/24/16

Resources I will be using throughout the summer:

Jo Boaler’s latest work about finger discrimination and having a math mindset.

–> Interested in Jo Boaler’s work? Take her online course (MOOC)! She has a Kid’s version which is free and totally adult-friendly, or you can pay for the full version for Parents & Teachers.

The research about finger discrimination.

California Infant/Toddler Curriculum Framework

The subitizing article I shared is from NCTM and is member’s only. But you can find more subitizing resources & activities on Pinterest.