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Non-Curricular Tasks

Spend the first 5 classes on NCT to…

build confidence, work on collaboration & perseverance skills, and to foster a “thinking” classroom.

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Thinking tasks create the conditions where students:

  • get stuck
  • experiment
  • might fail
  • apply knowledge in new ways (non-routine tasks)
  • engage in a cross section of mathematics (or other curricular thinking)

Characteristics of a Thinking Task

Effective thinking tasks should have:

  • Highly engaging problems
  • Easy entry points (low floor)
  • Evolving complexity (high ceiling)
  • Open middle structure - multiple ways of arriving at an answer

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  • Begin the class (within the first 5 minutes) with a thinking tasks

  • The first three to five thinking tasks you use should be non-curricular, and highly engaging �
  • After that shift to scripted curriculum thinking tasks

  • Script curricular tasks such that you:
    • Begin by asking a question about prior knowledge,
    • Then ask a question that is an extension of that prior knowledge, and
    • Then ask students to do something without telling them how

Giving a Thinking Task

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FIRST Week:

  • Each day ask them to define what a mathematician is… By the end of the week, they will be saying thinker, problem solver, etc.

First Month:

  • Learning names while at the VNPs! When students go to the boards, ask them to write their names on the boards: “Write your name on the top left if you are a morning person, etc…”

  • Have them make a Venn Diagram and then given them one minute to find as many things they have in common with each other!

Building Community

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Venn Diagram

Name 1

Name 2

Name 3

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Wolves and Sheep

M

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Task: Wolves and Sheep

Teacher Note: Verbally Introduce the task

Use the script to verbally explain and practice the rules with students already in their random groups of 3 and the vertical boards. (Use two color post-it notes, or have them use Ws and Ss.) Start with a 4x4 grid and then work up to 5x5, or even a 6x6 when groups are ready and ask for the the challenge!

The rules are simple:

you want to place the sheep on the board so that the wolves can’t eat them. A wolf can eat a sheep if it has a direct path to it – or is in same row, column, or diagonal as that sheep.

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The Candy Corn Puzzle

Place 8 candy corns on the grid so that no two candy corn pieces are in the same row, column, or diagonal.

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Cups and String Challenge

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Tallest Tower

Materials: raw spaghetti noodles, mini marshmallows and

Task:

1. Your group will first have 5 minutes to discuss a plan for building the tallest tower!

2. Next, you will have 10 minutes to BUILD the tallest tower!

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Which One Doesn’t Belong

Here are 3 possible task examples

You could use …

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Villains Scenario:

You are now a movie critic giving a presentation on fictional villains. You must rate each character and justify your rating with 2-3 supporting reasons.

5

Pure Evil

4

Mostly Evil

3

Evil

2

Somewhat Evil

1

A Little Bit Evil

0

Not Evil At All

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Ultimate

Tic Tac Toe

You must win each small box to claim the big box!

What will your strategy be?....

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3D Tic Tac Toe

Can you win?... What does it take?...

Is there a strategy?...

Play until you come up with a winning strategy!

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Task: Alice came across a lion and a unicorn in a forest of forgetfulness. Those two are strange beings. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, however the other days of the week he speaks the truth.

Lion: Yesterday I was lying.

Unicorn: So was I.

On which day did they say that?

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TEACHER NOTE:

Do not show the table below at first… See if any of the groups use an organizational strategy. If not, do a mini huddle and ask how they might organize a lot of information…

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What’s the message?

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11

19

92

27

75

53

61

1

58

29

78

65

74

46

33

36

15

6

67

2

3

4

71

51

56

68

28

64

17

10

42

73

25

20

79

7

35

23

8

76

52

9

50

44

48

40

59

39

13

30

18

12

16

24

80

72

32

60

47

69

81

34

57

5

21

70

38

41

54

77

49

66

22

14

43

63

37

45

26

62

55

31

82

83

84

85

86

87

88

89

90

91

93

94

95

96

97

98

99

100

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If you only have a 5 gallon and and 3 gallon jug…

How do you make exactly 4 gallons?

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Mr. Noah wants his Ark to sail along on an even keel. The ark is divided down the middle, and on each deck the animals on the left exactly balance those on the right – all but the third deck.

Can you figure out how many SEALS are needed in place of the question mark so that they (and the bear) will exactly balance the six zebras?

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Opening problem slide

How many squares are on a standard 8x8 chessboard?

How many rectangles?

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Hank Aaron traveled 11 miles more around the bases on his hits than any other batter in major league history.

I said ELEVEN MILES.

TASK: How many FEET is that?

…inches? ... cm?

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Bridge to Camp

Four campers need to cross a rickety rope bridge at night to get back to their camp. They only have one torch and the bridge is too dangerous to cross without a torch. The bridge can support only two people at a time.

All the people don’t take the same time to cross the bridge. Time for each person: 1 min, 2 mins, 7 mins, and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

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Teacher Tips:

1. Have colored chips, or coins for students to use as they problem solve.

2. Use the handout as your thin-sliced progression, and as your huddle questions.

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Eagle Airplane Sadness Bus Breeze Lion Joy Dolphin Bicycle Anger Thunder Elephant Fear Sunshine Car Kangaroo

Rain Excitement Snowflake Train

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The Four Fours Challenge

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Start with a collection of paychecks, from $1 to $12. You can choose any paycheck to keep. Once you choose, the tax collector gets all paychecks remaining that are factors of the number you chose. The tax collector must receive payment after every move. If you have no moves that give the tax collector a paycheck, then the game is over and the tax collector gets all the remaining paychecks. The goal is to beat the tax collector.

The Tax Collector: Give these directions verbally!

I have seen this problem done in elementary AND a high school calculus class! :)

The pre-knowledge is to verbally begin with is to make sure everyone understands what a factor is… and a good time to also discuss a multiple.

First: discuss what a factor is; Second: share the problem; Third: do a few examples so they can see what to do; Fourth: Set the loose to explore! Use the link in the notes to see the extension for groups who need it. Here is a teacher script you can use…

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Use these dominoes to make this square so that each side has eight dots.

DOMINO SQUARE

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Print & cut these out for partners as a tool to solve the Domino Square

DOMINO SQUARE (dominoes)

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Lots of Dots (LINK)

There are 16 dot cards in each game. Each group member will receive their own set of 4 dot cards. Each card has one or more duplicates, but there is one card that has NO duplicates; it does not have a match. Your job as a group is to find the one dot card that doesn’t have a match.

Here are the rules:

● You may only look at YOUR cards.

● You cannot show your cards to another group member.

● You cannot draw pictures or diagrams of the designs.

● The number at the bottom of each card is irrelevant, and should not be considered as part of the dot card.

● You may talk any way you choose.

If your group thinks they have identified the one card without a match, call me over to confirm.

The task ends whether or not you are correct, so make sure your group is confident before

calling.

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Cows Crossing A Bridge

Bob has four cows that he wants to take across a bridge, but he only has one yoke, which can hold up to two cows side by side that are tied to the yoke. The yoke is too heavy for him to carry across the bridge, but he can tie (and untie) cows to it in no time at all. Of his four cows, Maxie can across the bridge in 2 minutes, Daisy can cross in 4 minutes, Crazy can cross it in 10 minutes, and Lazy can cross it in 20 minutes. Of course, when when two cows are tied to the yoke, they must go at the speed of the slower cow. What is the shortest time that Bob needs to get all the cows across the bridge?

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What is the area of the orange square--in terms of x--sitting inside the unit square?

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SPLIT 25

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Numeracy Based Non-Curricular Tasks Collection from the book Building Thinking Classrooms

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Resources for NCTs

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What is the milk to espresso ratio in a pumpkin spice latte?

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The Pumpkin Sale

At a pumpkin patch, small pumpkins are sold for $3, medium pumpkins are sold for $7, and large pumpkins are sold for $12. Ms. Jones is in charge of the decorations for the town’s fall festival and purchased 16 pumpkins from the pumpkin patch including at least one of each size. She spent a total of $109. How many of each size pumpkin did she buy?

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Cylinders

PROMPT: If each cylinder has a fixed perimeter on the rectangular part of the net, predict which cylinder will have the greatest volume? Explain your reasoning.

Time permitting…

Think of how you could defend all three cylinders.

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The NET of a cylinder is what it looks like flat

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Penny Task Instructions

Consider a collection of pennies with the following constraints:

When the pennies are put in groups of 2 there is one penny left over. When they are put in groups of three, five or six there is also one penny left over. But when they are put in groups of seven there are no pennies left over. How many pennies could there be?

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Teachers:

LINK to PDF and solutions

Groups will select ONE card Task at a time.

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BIN-PACKING

How can you pack the bins (rectangles on the right) using the packages shown such that you use the least amount of bins?

Note: Each bin is 1 x 10

SLIDESMANIA.COM

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BIN-PACKING

Is it possible to use all the pieces and use only 3 bins?

2 bins?

1 bin?

Note: Each bin is 4 x 8

SLIDESMANIA.COM

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KNAPSACK

Who can package the items in such a way that they get the most value?

Red = $7, Blue = $10, Orange = $12, yellow = $6

Note: The knapsack is

6 x 8

SLIDESMANIA.COM

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SLIDESMANIA.COM