Teaching Math thru Big Ideas Focusing on Differentiation. Marian Small April 2017 San Diego, CA

Transcription

1 Teaching Math thru Big Ideas Focusing on Differentiation Marian Small April 2017 San Diego, CA

2 Our focus today Differentiation by focusing on big ideas Formative assessment/feedback Planning lessons/units

3 Number and Operations in Base Ten Representing a number in different ways tells different things about that number.

4 So I might ask Represent the number 225 in lots of ways. Which of those ways

5 So I might ask helps you see that 225 is a multiple of 25? is more than 200? is about ¼ of 1000? is closer to 200 than 300?

6 Number and Operations in Base Ten The place value system standardizes how numbers are decomposed. This makes comparison and computation easier.

7 So I might ask What numbers can you represent with exactly 20 base ten blocks?

8 Or I might ask I add a number I can model with 8 base ten blocks to one that I can model with 5 blocks. Why might I only need 4 blocks to show the sum?

9 Number and Operations in Base Ten Benchmarks are useful for relating numbers and estimating amounts.

10 So I might ask What could the two numbers be? 3000

11 Number and Operations -Fractions Representing a number in different ways tells different things about that number.

12 So I might ask Show 2/3 in a bunch of different ways. Which of your ways.

13 So I might ask made it easy to see that 2/3 is more than ½? two sets of 1/3 is not easy to show as a decimal

14 So I might ask always shows 1/3 at the same time is closer to ¾ than 1/2

15 Or I might ask When would it be useful to represent 0.25 as ¼? When would it be less useful?

16 Number and Operations- Fractions When a fraction or decimal is used to describe part of a whole, the whole must be known.

17 So I might ask Could 1/5 be a lot? Explain.

18 Number and Operations- Fractions There are various strategies for comparing fractions.

19 So I might ask Fill in the blanks so that the first fraction is MUCH bigger than the second; then MUCH smaller; then close. []/8 and []/2

20 Operations and Algebraic Thinking Using properties and looking for generalizations that apply to numbers allow us to calculate more fluently and to gain greater insight into numbers.

21 So I might ask Jane said that you can divide by 5 by doubling the number you are dividing and dividing by 10. Do you agree? Always? Use a picture to explain.

22 So I might ask e.g. 20 5

23 So I might ask e.g = 40 10

24 Or I might ask You add three numbers in a row (like 10, 11, and 12). List some possible NON-answers more than 100.

25 Operations and Algebraic Thinking It is important to recognize when each operation is appropriate to use.

26 So I might ask Give me a problem that you would solve by figuring out

27 Operations and Algebraic Thinking All patterns are based on pattern rules. Without a rule, you cannot be sure how to continue a pattern.

28 So I might ask Think of 3 ways to continue 4, 7,10, to make a pattern. Tell why each way is a pattern.

29 Operations and Algebraic Thinking Patterns can be compared in many ways, including how they grow.

30 So I might ask Two patterns include the number 50, but not at the start. One grows much faster than the other. What could the patterns be? Which grows faster? Why?

31 Operations and Algebraic Thinking Patterns can be represented visually to make them easier to see.

32 Operations and Algebraic Thinking Equations involving unknowns are solved using properties of numbers and meanings of operations.

33 So I might ask What equation do you see? What do you know about the weight of each red box compared to the blue one?

34 So I might ask

35 Measurement and Data A measurement is a comparison of the size of one object with the size of another, often a benchmark.

36 So I might ask How could you decide if the amount of text on a web page was more or less area than the amount of image?

37 Measurement and Data The numerical value attached to a measurement is relative to the measurement unit.

38 So I might ask Anna and Joachim measured the area of the same table. Anna said it was about 150 squares big. Joachim said it was 40 squares big. Show possible units to scale.

39 Measurement and Data Sometimes measurements of a shape are related; knowing one or more measures might reveal the value of others.

40 So I might ask I know the perimeter of a rectangle is barely more than double its length. What else do I know about the rectangle?

41 Measurement and Data Graphs are powerful data displays because they quickly reveal a great deal of information.

42 So I might ask

43 Geometry Different attributes of shapes and figures can be used to sort and classify these shapes in different ways.

44 So I can ask Why might someone say these shapes are similar? Why different?

45 Geometry Different systems can be used to describe the location of objects.

46 So I could ask Draw a quadrilateral that is not a rectangle on a coordinate grid. Name the vertices with ordered pairs.

47 Some interesting problems to try

48 McNuggets In some places, they sell McNuggets only in packs of 6, 9 and 20.

49 McNuggets Name some total amounts of McNuggets you could buy and some total amounts you could NOT buy.

50 Half a Rectangle You make a rectangle with square tiles. You cut it in half on a line of symmetry.

51 Half a Rectangle

52 Half a Rectangle

53 Half a Rectangle What fraction of the old perimeter might the new perimeter be? Find a few options.

54 Modelling multiplication You can model 3 x 15 with 18 base ten blocks.

55 Modelling multiplication

56 Modelling multiplication What other multiplications can you model with 18 blocks?

57 Remainders You share some cookies among some people. If you give them the same amount, there is one cookie left.

58 Remainders How many cookies and how many sharers might there be?

59 Close to 1 Two fractions are both close to 1. But one of them is closer than the other. What might the fractions be?

60 Denominator 15 You add two fractions. The result is []/15. What could the original denominators have been?

61 Three times The perimeter of a rectangle is about 3 times the length. What could the length and width be?

62 Lines and angles A shape has six sides and two 90 angles. What could it look like?

63 Lines and angles

64 How do you create more open questions?

65 Start with an answer Instead of: What is 13 x 12? Ask: You use an operation with two numbers. The result is 156. What numbers? What operation?

66 Start with an answer Instead of: What is 3/5 + 2/3? Ask: You use an operation with two fractions. The result is 19/15. What fractions? What operation?

67 Use wiggle room words Instead of: What is the third angle in a triangle where two angles are 85 and 15? Ask: Two angles in a triangle are pretty close together in size. The other angle is pretty small. What could the angles be?

68 You try Think of a big idea to focus on. Create an open ended question to address it that allows for differentiation.

69

70 Looking at work Let s look at some of the work you brought it. Let s work in groups of 3. Trade work.

71 Looking at work Discuss what feedback you would give. Discuss whether or not you would evaluate.

72 Backwards design Suppose I am designing a lesson. My learning goal should not just restate a standard. I should focus on a big idea.

73 For example In a lesson about how numbers are read, you can focus on the patterns in how numbers are read.

74 My problem Give examples of numbers that take different numbers of words to say. Do greater numbers usually take more words or not?

75 To consolidate What is the least number of words you can say? When?

76 To consolidate Do you use the same number of words for numbers with the same number of digits?

77 To consolidate Could a big number take not many words? Could a small number take a lot?

78 To consolidate If you rearrange the digits in a number, does it change how many words you say?

79 Now Now you work on a lesson that uses big ideas to help you shape goals; That uses an open question; That consolidates ideas and not just answers.

80 Download at: SanDiego3-5