Lesson 6 - hand2mind · COMMON CORE MATHEMATICS CURRICULUM 2•Lesson 9 Lesson 9: Concrete to abstract: measure the lengths of string using measurement tools; represent length with

Lesson 6 COMMON CORE MATHEMATICS CURRICULUM K•2

Lesson 6: Find and describe solid shapes using informal language without naming. 7/3/13

2.B.3Date:

© 2013 Common Core, Inc. All rights reserv ed. commoncore.org

Lesson 6

Objective: Find and describe solid shapes using informal language without naming.

Suggested Lesson Structure

Fluency Practice (12 minutes)

Application Problem (5 minutes)

Concept Development (25 minutes)

Student Debrief (8 minutes)

Total Time (50 minutes)


Beep Number K.CC.4a (4 minutes)

Hide and See 5 K.OA.2 (4 minutes)

Take Apart Groups of Circles K.OA.1 (4 minutes)

Beep Number (4 minutes)

Note: This ensures that students gain flexibility with number order in both directions of the number line.

Conduct as outlined in GK–M1–Lesson 15, but now intermingle counting up and counting down sequences, for example, 5, beep, 7 and 7, beep, 5.

Hide and See 5 (4 minutes)

Materials: (S) 5 linking cubes, personals white boards

Note: In this activity, students’ understanding of conservation of a number develops into part to whole thinking at the concrete level, anticipating the work of Module 4 (number bonds, addition, and subtraction).

Conduct as described in GK–M1–Lesson 11, but now have students write the expressions on their personal white boards. Challenge students to list all possible combinations.

Take Apart Groups of Circles (4 minutes)

Materials: (S) Personal white boards

Note: In order to meet the goal of adding and subtracting fluently within 5, students will need to begin

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Lesson 1 COMMON CORE MATHEMATICS CURRICULUM 1•2

Lesson 1: Solve word problems with three addends, two of which make ten. Date: 7/3/13 2.A.5

© 2013 Common Core, Inc. All rights reserved. commoncore.org

Equal Number Pairs for Ten (5 minutes)

Materials: (S) 5-group cards (1 “=” card and 2 “+” cards) per set of partners

Note: This activity builds fluency with partners to ten and promotes an understanding of equality. The 5-group cards can be accessed and printed from G1─M1─Lesson 5.

Assign students partners of equal ability. Students arrange 5-group cards from 0 to 10, including the extra 5, and place the “=” card between them. Write 4 numbers on the white board (e.g., 5, 9, 1, or 5). Partners take the 5-group cards that match the numbers written to make two equivalent expressions (e.g., 9 + 1 = 5 + 5).

Suggested sequence: 5, 9, 1, 5; 0, 1, 9, 10; 2, 5, 5, 8; 2, 3, 7, 8; 4, 1, 9, 6; 3, 4, 6, 7.


John, Emma, and Alice each had 10 raisins. John ate 3 raisins, Emma ate 4 raisins, and Alice ate 5 raisins. How many raisins do they each have now? Write a number bond and a number sentence for each.

Note: This problem was chosen as an application of the culminating subtraction work from Module 1. All three subtraction sentences and number bonds focus on partners to ten, which are foundational to the first lesson of Module 2.


Materials: (T) Bin, three different kinds of blocks/pattern blocks, string (S) Three different kinds of pattern blocks (10 of each shape, e.g., trapezoid, triangle, and square blocks), personal white boards

Have students sit in a semicircle at the meeting area with their personal white boards.

T: The first grade classrooms each have these special bins with different types of blocks in them. Let’s figure out how many we have! (Lay out 9 triangle blocks in a 5-group configuration.) How many triangle blocks do we have?

S: 9 triangle blocks!

T: (Lay out 1 square block and 4 trapezoid blocks. Ask students to state the quantity of each group.) We need to figure out how many there are altogether. Help me write the number sentence.





Lesson 9: Concrete to abstract: measure the lengths of string using measurement tools; represent length with tape diagrams to represent and compare the lengths.6/26/13

2.D.15Date:


Lesson 9

Objective: Concrete to abstract: measure lengths of string using

measurement tools; represent length with tape diagrams to represent and

compare the lengths.



Application Problems (6 minutes)





Adding Multiples of 10 to Numbers 2.NBT.5 (6 minutes)

Happy Counting by Centimeters 2.NBT.2 (4 minutes)

Meter Strip Addition: Adding Multiples of 10 to Numbers (6 minutes)

Materials: (S) Meter strips (as pictured)

Note: Students apply knowledge of using the ruler as a number line to fluently add multiples of ten. The meter strip solidifies the process for visual and tactile learners, and creates the groundwork for students to make tape diagrams in the lesson.

T: (Each student has a meter strip.) Put your finger on 0 to start. I’ll say the whole measurement. Slide up to that number. Add 10 centimeters and tell me how many centimeters your finger is from 0.

T: Let’s try one. Fingers at 0 centimeters! (Pause) 30 centimeters.

S: (Students slide their fingers to 30.)

T: Remember to add 10. (Pause.) How far is your finger from 0?

S: 40 centimeters.

Continue with the following possible sequence: 45 cm, 51 cm, 63 cm, 76 cm, 87 cm, and 98 cm. As your students show mastery, advance to adding 20 centimeters.




Lesson 12 COMMON CORE MATHEMATICS CURRICULUM 3

Lesson 12: Round two-digit measurements to the nearest ten on the vertical number line.

Date: 7/4/13 2.C.3


NOTES ON

LESSON STRUCTURE:

This lesson does not include an

Application Problem, but rather uses

an extended amount of time for the

Problem Set. The Problem Set provides

an opportunity for students to apply

their newly acquired rounding skills to

measurement.

Lesson 12 Objective: Round two-digit measurements to the nearest ten on the

vertical number line.







Rename the Tens 3.NBT.3 (4 minutes)

Halfway on the Number Line 3.NBT.1 (5 minutes)

Rename the Tens (4 minutes)


Note: This activity anticipates rounding in Lessons 13 and 14 by reviewing unit form.

T: (Write 9 tens = ____.) Say the number.

S: 90.

Continue with the following possible sequence: 10 tens, 12 tens, 17 tens, 27 tens, 37 tens, 87 tens, 84 tens, 79 tens.

Halfway on the Number Line (5 minutes)


Note: This activity prepares students to round to the nearest ten in this lesson.

T: (Project a vertical line with ends labeled 10 and 20.) What number is halfway between 1 ten and 2 tens?

S: 15.

T: (Write 15, halfway between 10 and 20.)

Repeat process with ends labeled 30 and 40.

T: Draw a vertical number line on your personal boards and make tick marks at each end.





Lesson 2: Express metric mass measurements in terms of a smaller unit; model and solve addition and subtraction word problems involving metric mass.7/3/13

2.A.19 Date:

© 2013 Common Core, Inc. All rights reserv ed. commoncore.org

NOTES ON

TERMINOLOGY:

Mass is a fundamental measure of the amount of matter in an object. While weight is a measurement that depends upon the force of gravity (one would weigh less on the moon than one does on earth), mass does not depend upon the force of gravity. We do use both words here, but it is not important for students to recognize the distinction at this time.


The distance from school to Zoie’s house is 3 kilometers 469 meters. Camie’s house is 4 kilometers 301 meters farther away. How far is it from Camie’s house to school? Solve using simplifying strategies or an algorithm.

Note: This Application Problem reviews G4–M2–Lesson 1. Students will express a metric measurement in a larger unit in terms of a smaller unit and model and solve an addition word problem involving kilometers and meters. Be sure to discuss why 7,770 m and 7 km 770 m are the same.


Materials: (T) 1-liter water bottle, small paper clips, dollar bill, dictionary, balance scale or weights (S) Personal white boards

Problem 1

Convert kilograms to grams.

Display the words weight and mass.

T: (Hold up a 1-liter bottle of water.) This bottle of water weighs 1 kilogram. We can also say that it has a mass of 1 kilogram. This is what a scientist would say.

T: This dictionary weighs about 1 kilogram.

T: The mass of this small paperclip is about 1 gram. A dollar bill weighs about 1 gram, too.

T: (Write on the board: 1 kilogram = 1,000 grams.) If the mass of this dictionary is about 1 kilogram, about how many small paperclips will be just as heavy as this dictionary?

S: 1,000.

Take one minute to balance 1 dictionary and 1,000 small paperclips on a scale. Alternatively, use a 1-kilogram mass weight. Also balance 1 small paperclip and a 1-gram weight.

T: Let’s use a chart to show the relationship between kilograms and grams.




Lesson 3 COMMON CORE MATHEMATICS CURRICULUM 5

3.B.4


Lesson 3: Add fractions with unlike units using the strategy of creating equivalent fractions.

Date: 8/7/13

NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION:

Students performing above grade level enjoy the challenge of a bonus problem. If time permits have one of the students draw the bonus problem model on the board and share his/her solution with the class.

Fractions as Division (1 minute)


T: When I show a fraction, you write it as a division statement. T: (Write 3/4.) S: (Write 3 ÷ 4 = 3/4.) T: (Write 5/2.) S: (Write 5 ÷ 2 = 5/2.)

Continue with fractions that are less than and greater than one. Possible sequence: 1/3, 7/4, 5/8, 9/5, 3/10, 13/6.


Alex squeezed 2 liters of juice for breakfast. If he pours the juice equally into 5 glasses, how many liters of juice will be in each glass? (Bonus: How many milliliters are in each glass?)

T: Let’s read the problem together. S: (Students read chorally.) T: What is our whole? S: 2 liters. T: How many parts are we breaking 2 liters into? S: 5. T: Say your division sentence. S: 2 liters divided by 5 equals 2/5 liter. T: Is that less or more than one whole liter? How do you know?

Tell your partner. S: Less than a whole because 5 ÷ 5 is 1. 2 is less than 5 so

you are definitely going to get less than 1. I agree because if you share 2 things with 5 people, each one is going to get a part. There isn’t enough for each person to get one whole. Less than a whole because the numerator is less than the denominator.

T: Was anyone able to do the bonus question? How many milliliters are in 2 liters?

S: 2,000. T: What is 2,000 divided by 5? S: 400. T: Say a sentence for how many milliliters are in each glass. S: 400 mL of juice will be in each glass.




Lesson 4: Summarizing Deviations from the Mean Date: 8/15/13 42


COMMON CORE MATHEMATICS CURRICULUM M2 Lesson 4

ALGEBRA I

Lesson 4: Summarizing Deviations from the Mean

Student Outcomes

Students calculate the deviations from the mean for two symmetrical data sets that have the same means.

Students interpret deviations that are generally larger as identifying distributions that have a greater spread orvariability than a distribution in which the deviations are generally smaller.

Lesson Notes

The lesson prepares students for a future understanding of the standard deviation of a data set, focusing on the role of

the deviations from the mean. Students practice calculating deviations from the mean and generalize their calculations

by relating them to the expression 𝑥 − �̅�. Students reflect on the relationship between the sizes of the deviations from

the mean and the spread (variability) of the distribution.

Classwork

Exercises 1–4 (15 minutes)

Discuss Exercises 1–4 as a class.

Exercises 1–4

A consumers’ organization is planning a study of the various brands of batteries that are available. As part of its planning,

it measures lifetime (how long a battery can be used before it must be replaced) for each of six batteries of Brand A and

eight batteries of Brand B. Dot plots showing the battery lives for each brand are shown below.

1. Does one brand of battery tend to last longer, or are they roughly the same? What calculations could you do in

order to compare the battery lives of the two brands?

It should be clear from the dot plot that the two brands are roughly the same in terms of expected battery life. One

way of making this comparison would be to calculate the means for the two brands. The means are 101 hours for

Brand A and 100.5 hours for Brand B, so there is very little difference between the two.

2. Do the battery lives tend to differ more from battery to battery for Brand A or for Brand B?

The dot plot shows that the variability in battery life is greater for Brand B than for Brand A.

3. Would you prefer a battery brand that has battery lives that do not vary much from battery to battery? Why or why

not?

We prefer a brand with small variability in lifespan because these batteries will be more consistent and more

predictable.




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Lesson 6 - hand2mind · COMMON CORE MATHEMATICS CURRICULUM 2•Lesson 9 Lesson 9: Concrete to abstract: measure the lengths of string using measurement tools; represent length with