More Clothesline Math

I’m having a bit of a hard time shutting work down for the Christmas break, so I thought I would see if I could make up these other primary clothesline cards that I have been pondering.

They are a bit addictive… as I make more cards, I keep thinking about more cards I could make…

This set has benchmarks of 0, 5, 10, 15, 20, and then uses ten frames and dominoes.  I added the numbers from 11-20 with the ten frames and then mixed them up to make addition cards with the ten frames.  I did all the make tens and the doubles and some random other combinations.  The dominoes have all the doubles and all the make tens and then some near doubles and some other random combinations…

Does anyone want to try them out?  I have no printer at home, so can’t test with my own kiddos and we are on holidays until January now (woohoo!).  If you have a chance to try them, I’d love to hear how it goes!  Feedback and suggestions welcome 🙂

See my original post about primary clothesline cards here.

Download the original primary clothesline cards here.

Download the new card set here.

 

 

 

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Investigations with Number Talks

Our last *sniff, sniff* book club meeting was held this week.  We are so appreciative of the teachers who signed up to participate with us.  We are so grateful for the rich and thoughtful conversations and collaborative trouble-shooting that went along with our study of Making Number Talks Matter.  We really believe that professional learning is so much better with colleagues and that setting aside time for professional learning is great for our students, but also helps us (as teachers) stay excited about our work on a day-to-day basis.

This week, we looked at Chapter 9 – Investigations.

We started our meeting with our usual check-in about how Number Talks have been going in the classroom.  It sounds like most people have established a good routine with Number Talks.  Some folks are taking a short break and shifting focus but planning to come back to Number Talks in the New Year.   We did some trouble-shooting discussion about how to deal with students who offer silly answers or make up strange answers that don’t relate to the question posed.  We talked about using phrases that help the student connect their answer with the question (can you explain to me where in the question you got the numbers that you are using in your strategy?).  We also talked about moving on from a student who is having trouble explaining his/her thinking clearly with a statement like: I’m having a hard time understanding your explanation and I would like us both to think about it some more – can I check in with you about your strategy after the number talk is over?

Next, we talked about our BIG IDEAS for the day:

investigations-big-ideas

And outlined how to do an investigation:

investigation-procedure

We then delved into exploring the multiplication strategy of halving and doubling using the general procedure for an investigation.  We started with the question 8 x 26 to try to elicit the strategy of doubling and halving.  Once we looked at all the suggested strategies, we focused in on doubling and halving and talked about the big question of “Does it always work?”  The group split up into partnerships to explore this question – we provided graph paper, colour tiles, rulers, paper and scissors and then circulated to try to see how the investigation went.

It was interesting to note that it is really difficult to be a skeptic in Math – the strategy might make sense to us, but actually thinking about what it takes to PROVE that it works requires much more depth to our thinking.  Many groups got started by discussing WHEN it would be good to use this strategy (ie. what circumstances/numbers make it an efficient strategy).  Some groups explored odd vs. even numbers, some explored big and small numbers, some tried to delve into fractions to see if it worked there.  Some groups worked with the colour tiles to make arrays and others used the graph paper to show the strategy visually.

Then, we wrapped up with a discussion – different groups shared their approaches and it was interesting to note how varied the ideas were.  We looked briefly at the questions offered in the book to guide small group work for this investigation:

  • Will it only work with even numbers?
  • What would happen if, instead of halving, you took a third of one factor?
  • Can you represent this strategy visually/geometrically?
  • What generalizations can you make?
  • Would this work for division?

We had hoped to have time to also have teachers choose another investigation: either the same difference strategy for subtraction or the halving-halving strategy for division, but we ran out of time.  I think participating in an investigation was really valuable.  I enjoyed seeing how much mathematical thinking (curricular competencies) is involved in this type of activity.  Of note – mathematical investigations take time, and it is worth setting aside some time to do activities like this in class.

Once again, a HUGE thank-you to our teachers who participated!  We will be running some more after school PD for intermediate math teachers in the New Year – likely a Mathematical Mindsets book study at some point – so keep an eye on your email in January for information on how to join in.

Number Clothesline Test Run

We (our district’s 2 Intermediate Math Liaisons) are doing a “Getting Started with Number Talks” workshop on our ProD day this upcoming Monday.  This is the last Number Talks workshop we will offer this year, and we have decided to open it to K-10 teachers.  We have been getting quite a few requests for Number Talks in primary and secondary grades, so we thought we would stretch ourselves.

For part of our workshop, we are going to showcase the Number Clothesline as a nice complement for Number Talks.  In the past, we have done this activity with fractions, decimals, and percentage cards (see this post), but we wanted to try to differentiate a bit for our primary and secondary attendees.  I have been intrigued by the idea of using a double clothesline for algebra concepts and so for our secondary extension, we are going to try this activity from Andrew Stadel’s Estimation 180 website.

I was trying to imagine what a beginning clothesline might look like for our early primary students, and so I made up some cards with numbers, dots, ten frames and fingers (after reading this fabulous article by Jo Boaler).  I thought I would do a test run this weekend with my own kiddos (Kindergarten and Grade 2).

We set up the double number line in the living room and this is how it went down…

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We started with the numbers all mixed up and I asked them to help me fix it…
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A standoff…   (My oldest son (blue shirt) doesn’t have dirt all over his face… we forgot it was moustache day at school today to celebrate the end of Mo-vember, so he took it upon himself to draw one on.)
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Using the 5 card to measure out how much space needs to be left for the missing 3 and 4 cards.
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Watching big brother make enough space for the missing cards.
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My little guy was pretty pumped about the hand cards.  Took him a bit to figure out where “neuf” would go on the bottom if there was no “neuf” up top (french immersion is working!).
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A 15!!!!
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Big guy using the 10 card to help him figure out how far over the 15 should go.  Little guy was pretty stumped by the “zero” hand for a while – he couldn’t really tell what number it was supposed to be – kept guessing it was a four.
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A 20!! Not enough room – we’ll put it way over here!
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Another “neuf!”  We already have one!  They decided to start doubling them up.

Overall, a pretty successful test run.  A few thoughts…

  • They both enjoyed the activity, especially the different types of pictures.
  • They were both disappointed that there were no numbers between 10 and 20 for the bottom number line.  I can’t really do that with fingers, but maybe I will make ten frame cards up to 20 and look for domino pictures (at least up to 15’s… do dominos go up to double 20’s?).
  • As usual, I am impressed with how kids solve problems when they are left to themselves to figure out what makes sense.  They didn’t need me to help them with anything – they figured out how to make the right spaces, what to do about missing numbers, what to do about double numbers etc. all on their own.  Another good reminder that sometimes the most powerful teaching is to set the stage carefully, ask good questions and then stand back and let the kids do the thinking!!

If you would like to have these cards for your class, you can download them below.  I will update this file if I manage to make some more ten frame or domino cards, but for now they only have numbers 1-10 in the dots, hands and ten frames.

Downloadable Primary Clothesline Cards