WE ALL NEED……

Want to understand everything they do: Why does it work? What if? Attributes of Geniuses: Want to understand everything they do: Why does it work? What if? 1.) Observe, observe, observe Their brain is constantly sorting, matching, classifying. Making links, re-sorting and linking a different way. Organizing things to look for patterns to explain 2.) Take things apart and put them back together: Number, shapes, equations, expressions, 3.) Compare, Compare, Compare: Look for similarities and differences

A problem-solving activity must ask students to determine a way to get from what is known to what is sought. If students have already been given ways to solve the problem, it is not a problem, but practice. A true problem requires students to use prior learnings in new ways and contexts. Problem solving requires and builds depth of conceptual understanding and student engagement. Alberta Curriculum, 2007, 2014 Thinking101 2014

If it is a problem solving task: You do not know what to do when you first approach it Thinking101 2014

How did you get started? What could you draw, write, diagram to show what you did? Did you explain why you did it? Can we see that you are finished? What’s the math? Did you solve or do you have more more questions? Build, Explain, Represent, Compare

Getting Started: Be a Thinker Can I re-tell the problem? Can I diagram the situation? What do I know for sure?

The history of many cultures includes tales and legends The history of many cultures includes tales and legends. Often there are stories of heroes fighting Giants. In one such story, the Giant is said to be 6 cubits and one span tall. I want you to make a model or representation that allows us to “see” how tall this giant was. Thinking101 2017 Whitecourt

Can I re-tell the problem? Are there facts I need to clarify? Can I diagram the situation? What do I know for sure? Thinking101 2017 Whitecourt

As you work I will ask: 1.) Whatcha doin? 333 As you work I will ask: 1.) Whatcha doin? 2.) What made you decide to do that? What was in the problem got you thinking this wa Did it, is it helping working are you making sense and finding a solution? Thinking101 2017 Whitecourt

As you work I will ask: 1.) Whatcha doin? 2.) What made you decide to do that? What was in the problem got you thinking this way? 3.) Did it, is it helping working are you making sense and finding a solution?

She knows it is a measuring task and that a measuring tool can be used to measure. A measuring tool has number in sequence and hash marks. A measuring tool has numbers in sequence. You start at 0 or 1? She ran out of paper. She knows you are comparing the giant to a person and the giant is taller.

6 what? Where are they? 1 what? Where is it?

Let’s edit to improve the communication here... Communication is key skill. (Math, science, competencies)

Replace big with tall, this task is about tall. “And why”, replace with “The reason that we” If we are sticking with “used” then “was because” Almost, almost Replace “it” with a cubit was almost the length of Elbow Not tallest finger but middle finger (you are assuming is always tallest)

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Focus on Problem yes, but communication is not clear, what is 30? Data Gathered yes, but a diagram or explanation would help, what are you doing with the 30 and why? Thinking about the Data: I see some patterns in this data, but do they help me solve... Can we turn this into a real chart? 30 and 16 seem to be used why? Complete How did 150 become 166 ? 166 what? How tall is the giant? What do I have to do to repeat what you did? I get a different answer when I use 30 as my cubit and 16 as my span.

What we think this student is saying: If 30 cm is your cubit and 16 cm is your span then: 1 cubit 30 2 cubits 60 3 cubits 90 4 cubits 120 5 cubits 150 6 cubits 180 6 cubits plus 1 span 180 + 16 = 196 The giant is 196 cm Do you see a pattern in the data? Can you explain it? Can you explain it with multiplication (Grade 4 and 5)

Grade 4

I measured my cubit. It was 37 cm. I multiplied by 6. 30 x 6 is 180 7 x 6 is 42 so 200 + 22 or 222 cm. Then I measured my span: 14.5 cm Add that on The giant using me, as the measuring tool , is approximately 236.5 cm tall. That would be about 2 and a third meters. He would fit in the room but I would have to look up to see him. This is not really a problem once I start doing the math. But initially I was wondering how much taller than me he was. Then I realized that about 4 of my Cubits fit up my body, so he is more than my waist again as high as me.

How would you explain his strategy? How would you make it more mathematical? How would you communicate it efficiently?

Cubit is 37cm

37cm 74cm 51cm 148cm 173cm 242cm (6 x 37cm) + 19cm = 242 + 19= 261 cm Span 19cm 37cm 74cm 51cm 148cm 173cm 242cm (6 x 37cm) + 19cm = 242 + 19= 261 cm

Thinking101 2014