# ©Marian Small, 2010 Big Ideas K-3 Session 1 Marian Small.

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©Marian Small, 2010 Big Ideas K-3 Session 1 Marian Small

©Marian Small, 2010 Try this You are going to write a number the “regular” way, e.g. 34 or 2 or 619, etc. When you read the number, some of the words you say are: hundred, three, fifty What could the number be? Record some possibilities in the chat box.

©Marian Small, 2010 Possible answers 350 351 (or 352 or…. or 359) 153 (or 253 or 353 or… or 953)

©Marian Small, 2010 What are big ideas anyway? Which of these do you think is a big idea? A: Writing a number less than 100 in words B: Place Value C: Recognizing that different representations of a number give you different understandings about it D: Recording the hundreds, tens, and ones digit of a number

©Marian Small, 2010 Big ideas are meant to… Help you as a teacher see what you are really going for.

©Marian Small, 2010 Big ideas are meant to… Help you as a teacher see what you are really going for. Provide you with a teaching framework- to see how outcomes are connected.

©Marian Small, 2010 Big ideas are meant to… Help you as a teacher see what you are really going for. Provide you with a teaching framework- to see how outcomes are connected. Give purpose to the activities you do

©Marian Small, 2010 Big ideas are meant to… Help students build connections

©Marian Small, 2010 Big ideas are meant to… Help students build connections Help students see the forest for the trees

©Marian Small, 2010 The three sessions Session 1- A focus on number Session 2- A focus on pattern and data Session 3- A focus on geometry and measurement

©Marian Small, 2010 The big ideas in number Early number and operation

©Marian Small, 2010 The big ideas in number

©Marian Small, 2010 So how do we bring these out? Let’s look at the first one. How do we make kids see this? Maybe– which of these do you need to count to know how many? Why?

But…. Does a number always tell how many? Give me an example when it doesn’t. Raise your hand.

©Marian Small, 2010 BIEN 2 You are hopping on a number line and just saying the numbers you land on. You can start wherever you want. What numbers might you say right before 12 if you land on 12? Could it be: A: 11 or 10 B: 11 or 10 or 9 C: 11 or 10 or 9 or 8D: anything < 12

©Marian Small, 2010 BIEN 2 You are hopping on a number line and just saying the numbers you land on. You can start wherever you want. What numbers might you say right before 12 if you land on 12? Raise your hand.

©Marian Small, 2010 BIEN 3 You need to represent the number 7 in a lot of different ways. Be ready to draw your pictures on the white board.

For example 5 + 2 4 + 3 Seven VII XXXXX XX

©Marian Small, 2010 Which ones…. are most alike?

©Marian Small, 2010 BIEN 4 How can you tell whether my name has more letters in it than yours if you could NOT count the letters? How could you tell if you could count? Raise your hand.

©Marian Small, 2010 Related… Why is this a not-so-good bar graph? Vanilla Chocolate Respond on the board.

©Marian Small, 2010 BIEN 5 How do you know FOR SURE that 13 is more than 9? What other numbers would be easy to compare the same way?

BIGWN 1 Which of these would you find easier to count? Why? Choose A for the first group and B for the second.

B

Related How does this big idea relate to using tally marks? Raise your hand to talk.

©Marian Small, 2010 BIGWN 2 Have you seen a question that brings this out?

©Marian Small, 2010 Maybe… You can show a number with 12 base ten blocks. What could it be? 93 847566574839 12 2130 Circle the numbers right on the board.

©Marian Small, 2010 BIGWN 3 How could you represent 175 to show that: It is 7 groups of 25? Raise hands.

©Marian Small, 2010 BIGWN 3 How could you represent 175 to show that: It is 25 short of 200? Raise hands.

©Marian Small, 2010 BIGWN 3 How could you represent 175 to show that: It is 17 tens and 5 more? Raise hands.

©Marian Small, 2010 BIGWN 4 How does thinking of 138 and 173 in terms of 150 help you decide which is greater?

©Marian Small, 2010 BIGWN 5 A number is about 300. What might it be? A: 295B: 278C: 328D: all of the above What do you think it couldn’t be?

©Marian Small, 2010 Suppose… I asked students how to solve 15 ÷ 3 using multiplication, then addition, then subtraction. What big idea might I be drawing out? Raise hands.

Suppose… I asked students for three different ways to solve 100 – 28. What might they be? What big idea might I be drawing out? Be ready to draw on white board.

©Marian Small, 2010 100 - 28

©Marian Small, 2010 Did you know???? One way to solve 100 – 28 is to solve 99 – 28 and then add 1. Why is it a good idea? Why does it work?

©Marian Small, 2010 Suppose… I asked students for three situations to which 50 – 28 applied, but they all had to sound really different. What might they be? Raise hands. What big idea might I be drawing out?

©Marian Small, 2010 Suppose… I asked students for three different sums that were close to, but not exactly, 90. What big idea might I be drawing out?

©Marian Small, 2010 Suppose… I asked students why this picture actually shows three fractions. What might they say? Raise hands. What big idea might I be drawing out?

©Marian Small, 2010 Suppose… I asked : How could 2/3 be less than 1/2? What might they say? What big idea might I be drawing out?

©Marian Small, 2010 Would you be willing to…. Try out either one of the questions we discussed or, even better, your own question to bring out a big idea in number. We’ll talk about the results next time.