1. Vacaville USD December 4, 2014
SECOND GRADE Session 2
Vacaville USD
December 4, 2014

2. AGENDA Word Problems Number Lines – Adding and Subtracting Time
Problem Solving and Patterns
Math Practice Standards and High Leverage Instructional Practices
Number Talks
Review Addition and Subtractions Strategies
Word Problems
Number Lines – Adding and Subtracting
Time
Data and Graphs

3. Expectations
We are each responsible for our own learning and for the learning of the group.
We respect each others learning styles and work together to make this time successful for everyone.
We value the opinions and
knowledge of all participants.

4. Cubes in a Line
How many face units can you see when cubes are put together?

5. Cubes in a Row
How many face units do you see on 1 cube?

6. Cubes in a Row How many face units do you see on 2 cubes?
How can you keep track of what sides you have counted?

7. Cubes in a Row
You are going to be given 2 strips of paper like this:
_____________ _____________
number of cubes number of face units 7

8. Cubes in a Row What patterns do you see?
How could those patterns help you figure out how many face units there would be?

9. Math Practice Standards
Remember the 8 Standards for Mathematical Practice
Which of those standards would be addressed by using a problem such as this?

10. CCSS Mathematical Practices
REASONING AND EXPLAINING
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Make sense of problems and persevere in solving them
OVERARCHING HABITS OF MIND
Attend to precision
MODELING AND USING TOOLS
Model with mathematics
Use appropriate tools strategically
SEEING STRUCTURE AND GENERALIZING
Look for and make use of structure
Look for and express regularity in repeated reasoning

11. High Leverage Instructional Practices

12. High-Leverage Mathematics Instructional Practices
An instructional emphasis that approaches mathematics learning as problem solving.
Make sense of problems and persevere in solving them.

13. An instructional emphasis on cognitively demanding conceptual tasks that encourages all students to remain engaged in the task without watering down the expectation level (maintaining cognitive demand)
Make sense of problems and persevere in solving them.

14. Instruction that places the highest value on student understanding
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively

15. Instruction that emphasizes the discussion of alternative strategies
Construct viable arguments and critique the reasoning of others

16. Instruction that includes extensive mathematics discussion (math talk) generated through effective teacher questioning
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning

17. Teacher and student explanations to support strategies and conjectures
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others

18. The use of multiple representations
Make sense of problems and persevere in solving them.
Model with mathematics
Use appropriate tools strategically

19. Number Talks

20. What is a Number Talk? Also called Math Talks
A strategy for helping students develop a deeper understanding of mathematics
Learn to reason quantitatively
Develop number sense
Check for reasonableness
Number Talks by Sherry Parrish

21. What is Number Talk?
A pivotal vehicle for developing efficient, flexible, and accurate computation strategies that build upon key foundational ideas of mathematics such as
Composition and decomposition of numbers
Our system of tens
The application of properties

22. Key Components Classroom environment/community Classroom discussions
Teacher’s role
Mental math
Purposeful computation problems

23. Classroom Discussions
What are the benefits of sharing and discussing computation strategies?

24. Students have the opportunity to:
Clarify their own thinking
Consider and test other strategies to see if they are mathematically logical
Investigate and apply mathematical relationships
Build a repertoire of efficient strategies
Make decisions about choosing efficient strategies for specific problems

25. 4 Goals for K-2 Classrooms
Developing number sense
Developing fluency with small numbers
Subitizing
Making tens

26. Clip 2.1 – 2nd Grade Addition: 8 + 6 (using 10-frames)
Before we watch the clip, talk at your tables
What possible student strategies might you see?
How might you record them?

27. What role do the 10-frames play in developing fluency with small numbers?
What questions does the teacher use to build understanding about composing and decomposing numbers?
How does the use of double 10-frames support the goal of K-2 number talks?

28. Clip 2.3 – 2nd Grade Addition: 26 + 27
Before we watch the clip, talk at your tables
What possible student strategies might you see?
How might you record them?

29. How does the teacher record each strategy to provide access for the class?
What strategies are easy for you to follow? Which are difficult or confusing?
What mathematical concepts are being built upon during this number talk?
How does the teacher bring these ideas to the forefront for the class?

30. Possible Number Talk 2.3A
What strategy do you think the teacher was trying to elicit?

31. Possible Number Talk 2.3B
What strategy do you think the teacher was trying to elicit?

32. Clip 3.3 – 3rd Grade Subtraction: 70 – 59
Before we watch the clip, talk at your tables
What possible student strategies might you see?
How might you record them?

33. What strategies seem the most efficient to you? Why?
Would the student strategies work for larger numbers?
How is the open number line used?
How does the teacher use questions to support student thinking?

34. Possible Number Talk 3.3A
70 – 59
70 – 49
70 – 39
70 – 34
What strategy do you think the teacher was trying to elicit?

35. Possible Number Talk 3.3B
70 – 60
70 – 59
70 – 61
70 – 49
What strategy do you think the teacher was trying to elicit?

36. Addition and Subtraction Strategies

37. Strategies Concrete Representational Abstract Alternative algorithms
Traditional algorithms
Mental math

38. Addition: 376 + 248 Concrete Representational Abstract
Alternative algorithms
Traditional algorithms
Mental math

39. Subtraction: 502 – 275 Concrete Representational Abstract
Alternative algorithms
Traditional algorithms
Mental math

40. Solving Word Problems

41. 3 Benefits of Real Life Contents
Engages students in mathematics that is relevant to them
Attaches meaning to numbers
Helps students access the mathematics.

42. On Monday, Mr. Alvarez drove 37 miles to pick up 500 baseballs
On Monday, Mr. Alvarez drove 37 miles to pick up 500 baseballs. On Tuesday, he drove 48 miles to pick up another 300 baseballs. How many total miles did Mr. Alvarez drive?

43. There were 18 more girls than boys in the spelling contest
There were 18 more girls than boys in the spelling contest. If there were 52 girls, how many boys were in the spelling contest?

44. Three friends go apple picking
Three friends go apple picking. They picked a bunch of apples on Saturday but forgot to count how many. Then they picked 23 apples on Sunday. If they end up with a total of 47 apples, how many did they pick on Saturday?

45. Jason’s mom gave him some money to buy pencils
Jason’s mom gave him some money to buy pencils. After he spent 63 on the pencils, he had 28 left. How much money did Jason’s mom give him?

46. Using a Number Line

47. A cricket jumped 7 centimeters forward and then another 5 centimeters forward. How far did the cricket jump?

48. A cricket jumped 14 centimeters forward and then jumped 6 centimeters backward. How far is the cricket from where he started?

49. James and Chloe each have pet snakes
James and Chloe each have pet snakes. James’ snake is 15 centimeters long. Chloe's snake is 9 centimeters long. How much longer is James' snake?

50. Bret and Keisha also have pet snakes
Bret and Keisha also have pet snakes. Bret’s snake is 8 centimeters long. Keisha’s snake is 13 centimeters long. How much shorter is Bret’s snake?

51. Mei’s frog leaped forward 4 centimeters
Mei’s frog leaped forward 4 centimeters. Then it leaped forward some more. In all, it leaped 11 centimeters. How far did Mei’s frog leap the second time?

52. Jose’s frog took 2 jumps forward
Jose’s frog took 2 jumps forward. Jose couldn’t see how long the first jump was but the second jump was 9 cm. If the frog jumped a total of 16 centimeters, how far did Jose’s frog jump the first time?

53. Tyler’s frog started at 0 and jumped forward 14 spaces
Tyler’s frog started at 0 and jumped forward 14 spaces. But then it jumped backward and landed on the 9. How many spaces did the frog jump back?

54. Halle has two ribbons. The blue ribbon is 11 cm long
Halle has two ribbons. The blue ribbon is 11 cm long. The green ribbon is 5 cm shorter than the blue ribbon. How long is the green ribbon?

55. Using a Number Line 2

56. A frog jumped 27 centimeters forward on his first jump and 32 centimeters forward on his second jump. How far did the frog jump?

57. Kris and Sam each have pet snakes. Kris’ snake is 73 centimeters long
Kris and Sam each have pet snakes. Kris’ snake is 73 centimeters long. That is 15 centimeters longer than Sam’s snake. How long is Sam's snake?

58. Bill is 19 inches taller than his baby sister
Bill is 19 inches taller than his baby sister. If his baby sister is 29 inches tall, how tall is Bill?

59. Regan’s frog jumped 43 centimeters. Then it jumped some more
Regan’s frog jumped 43 centimeters. Then it jumped some more. If it jumped a total of 71 centimeters, how far did the frog jump the second time?

60. Courtney’s ribbon is 94 cm long
Courtney’s ribbon is 94 cm long. She cuts off a piece that is 36 cm long to give to Mika. How much ribbon does she have left?

61. Dan buys a bubble gum tape that is 72 inches long
Dan buys a bubble gum tape that is 72 inches long. After giving some of it to his friends, he measures what he has left. If he has 28 inches left, how much did he give to his friends?

62. Using an Open Number Line

63. A cricket jumped 7 centimeters forward and 12 centimeters back then stopped. If the cricket started at 27 on the ruler, where did the cricket stop?

64. James and Chloe each have pet snakes
James and Chloe each have pet snakes. James’ snake is 35 centimeters long. Chloe's snake is 7 centimeters longer than James’. How long is Chloe's snake?

65. Bill throws his baseball 41 feet, which was 14 feet farther than Samantha threw her baseball. How far did Samantha throw her baseball?

66. Mei’s frog leaped forward 34 centimeters
Mei’s frog leaped forward 34 centimeters. Then it leaped forward some more. In all, it leaped 61 centimeters. How far did Mei’s frog leap the second time?

67. Halle has two ribbons. The blue ribbon is 58 cm long
Halle has two ribbons. The blue ribbon is 58 cm long. The green ribbon is 83 cm long. How much longer is the green ribbon?

68. Relate addition and subtraction to length.
2.MD.5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

69. Relate addition and subtraction to length.
2.MD.6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, , and represent whole-number sums and differences within 100 on a number line diagram.

70. Time

71. Number Lines, cont.
What can you tell me about this number line?

72. Number Lines, cont. The number line starts at 0
Each mark represents 1 minute
How many minutes is the arrow showing?

73. Number Lines, cont. The number line starts at 0
Each mark represents 1 minute
How many minutes is the arrow showing?

74. Number Lines, cont.
Minute number line

75. Minutes on a Clock
__:25

76. Minutes on a Clock
__:17

77. Minutes on a Clock
Identify the minutes on each clock

78. Headed to School

79. Hours on a Clock

80. Hours on a Clock
7:__

81. Hours on a Clock
9:__

82. Hours on a Clock
Identify the hour shown on each clock

83. Work with time and money.
2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year). CA

84. Hand Span Measures
Hand span is a measure of distance from the tip of the thumb to the tip of the little finger with the hand fully extended.

85. Hand Span Measures
Place your dominant hand on the edge of a piece of paper with the hand fully extended.
Make a mark at the tip of the thumb and the tip of the little finger. The distance between marks is the length of the hand span.
Measure your hand span to the nearest whole centimeter.
Record your measurement.

86. Represent and interpret data.
2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

87. Hand Span Measures What’s a line plot?
So what info do we need to create a line plot that we can use to show the data?
Smallest hand span
Largest hand span
Collect data!

88. Represent and interpret data.
2.MD.10. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.