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West-Orange Cove ISD 2nd Grade Mathematics- 6th Six Weeks 2012 - 2013

Week 1 and 2

Apr 29 – May 3May 6 - 10

Major Concepts:

Fractions

Learning Standards:(3) Number and Operations. The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to: (A) partition objects such as strips, lines, regular polygons, and circles into equal parts and name the parts, including halves, fourths and eighths, using words such as “one-half,” “three-fourths;”(B) explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part;(C) use concrete models to count fractional parts beyond one whole using words such as “one-fourth,” “two-fourths,” “three-fourths,” “four-fourths,” “five-fourths,” or “one and one-fourth,” and recognize how many parts it takes to equal one whole such as four-fourths equals one whole; and(D) identify examples and non-examples of halves, fourths, and eighths.

Processes(1) Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:(A) apply mathematics to problems arising in everyday life, society, and the workplace;(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;(C) select tools, including real objects, manipulatives, paper/pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;(E) create and use representations to organize, record, and communicate mathematical ideas;(F) analyze mathematical relationships to connect and communicate mathematical ideas; and(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Instruction Resources InterventionsExtensions and Stations

Assessment

Key Vocabulary – whole, part, equal, unequal, halves, thirds, fourths, fraction, set, eighths, fractional part

Math background for the teacher: Fractional parts are equal parts of the whole. A fraction compares a part to a whole. A whole can be one object or a group of objects. On a number line the distance from 0 to 1 is the unit. Fractional parts name the parts of the whole. The more fractional parts used to make the whole, the smaller

the parts. Students at this age are able to comprehend sharing equal parts

with friends so use this and build the bridge to fractional parts. The bottom number (denominator) tells how many equal parts

the whole is divided into. The top number (numerator) tells how many equal parts are

indicated.

Begin fractions with sharing tasks: (Van de Walle). Students

enVision Math Topic 10

enVision Math Tools

Fraction circles

Fraction squares

Cuisenaire rods

Fraction Strips

Red/Yellow counters

http://math.rice.edu/~lanius/fractions/frac.html

Math enVision Games

Board games for fractions

Intervention/Extension

Students will work in small group with the teacher using red/yellow counters. The teacher will use the two-sided counters to display and illustrate parts/whole.

enVision Math Assessment

Product/Project

Students will make a foldable or book for fractional parts from 1 whole – 12/12

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should use manipulates to solve the following problems:

NOTE: each solution should be followed by discussion and connection to fraction vocabulary like one half, two-thirds, etc.

Mary and John are sharing one brownie. How much will each one get? (1/2)

Bill is sharing five brownies with a friend. How many brownies will each one get? (2 ½)

Mrs. Smith is sharing 2 brownies between four children. How many brownies will each child get? (1/2)

David is sharing three brownies with himself and 3 friends. How many brownies will each person get? (3/4)

Next have students to use manipulatives to solve the following problems. After solving each have students to record their findings in the form of pictures that they draw in their spiral.

Six pizzas shared with 6 children Four pizzas shared with 6 children Seven pizzas shared with 6 children Five pizzas shared with 3 children

Connect fractional parts to rulers and number lines. For each fractional part in the examples, label it on a number line.

Activity: Make templates for a bowl and “scoops” Students can use different colors of construction paper for different flavors of ice-cream.

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Students label their scoops in terms of fractions. So, if there are 8 scoops altogether, and a student put 3 scoops of mint chocolate chip, she writes "3/8 mint chocolate chip."

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http://www.google.com/imgres?imgurl=http://3.bp.blogspot.com/-9gqurS_3i3U/TevYFmfvGyI/AAAAAAAAARU/4KnVU9OnZAI/s1600/fraction+sundaes+002.jpg&imgrefurl=http://teachingintheearlyyears.blogspot.com/2011/06/fraction-sundaes.html&h=1204&w=1600&sz=183&tbnid=DkyInQibfIrzwM:&tbnh=93&tbnw=124&prev=/search?q=fraction+sundaes&tbm=isch&tbo=u&zoom=1&q=fraction+sundaes&usg=__Du1p-WW4niisXvay9KeDKOk_dt8=&docid=lYyU0STVZxFDmM&hl=en&sa=X&ei=oo3fT-5LhIjoAfif-YML&ved=0CGgQ9QEwAQ&dur=4070


Name Fractional Parts of Whole Objects

Name fractional parts of a whole object when given a concrete representation.

Provide the students with concrete representations of a whole object and prompt the students to identify fractional parts of the whole object.

Example:Ask the students, “What fraction of the square is labeled green?”

Answer: 2 of the 4 equal parts of the square are green, or of the square is green.

Example:Ask the students, “What fraction of the circle is shaded?”

Answer: 8 of the 12 equal parts of the circle are shaded, or of the circle is shaded.

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Example:Ask the students, “What fraction of the octagon is NOT shaded?”

Answer: 5 of the 8 equal parts of the octagon are not shaded, or of the octagon is not shaded.

Represent Fractional Parts of Whole Objects

Create and name fractional parts of a whole object.

Prompt the students to create a representation of a fractional part of a whole.

Example:Prompt the students to create a fractional part of a whole object that

represents 4 out of 12 equal parts or .

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Possible Representation:

Prompt the student to explain their fractional representation:

Possible Answer: “I drew a rectangle with a total of 12 equal parts and I

shaded 4 of the equal parts to represent the 4 out of 12 equal parts or .

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Describing Parts of a Whole

Use concrete models to determine if a fractional part of a whole

is closer to 0, , or 1.Example:Ask the students, “Is the shaded fractional part of the whole closer to

0, , or 1?”

Answer: The shaded fractional part of the whole is closer to 1.

Example:Ask the student, “Which model has a shaded fractional part of the whole

that is closest to ?

Answer :

Name Fractional Parts of a Set of Objects

Name fractional parts of a set of objects when given a concrete representation.

Provide the students with concrete representations of sets of objects and prompt the students to identify fractional parts of the set of objects.

Rethinking Elementary Mathematics for Grades 1-2, “Shake Spill: Fraction Task Card.”

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Example:Ask the students, “Which set is

circles?”

Or

Answer:

Example:Ask the students, “What fractional part of the set of counters is red?”

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Answer: 5 of the 8 parts of the set of counters are red, or of the set of counters are red.

Example:Ask the students, “What fractional part of the set of stickers are NOT moons?”

Answer: 8 of the 12 parts of the set of stickers are not moons, or of the set of stickers are not made up of moons.

Represent Fractional Parts of a Set of Objects

Create and name fractional parts of a set of objects.

Prompt the students to create a representation of a fractional part of a set of objects.

Example:Prompt the students to create a fractional part of a set of objects that

represents 6 out of 10 equal parts or .

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Possible Representation:

Prompt the student to explain their fractional representation:

Possible Answer: “I used 4 circle counters and 6 square counters to create my set of 10 objects. The fractional part I am describing is the

6 out of 10 parts that are square counters or .

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Week 3 and 4

May 13 – 17May 20 - 24

Major Concepts:

Probability

Learning Standards:

Students learn and practice probability in everyday situations.



Assessment

Vocabulary – probability, predict, more likely, less likely, equally likely

Math background for teachers: The outcome of prior trials does not impact the next. The probability of a future event is a number between 0 and 1. A probability of 0 means that it is impossibility and a 1 means that it

is a certainty. Connect outcomes to fractions.

Begin by asking students to judge events as certain, impossible, or possible (it might happen):

It will snow tonight (in Texas in May) It will rain today The cow will jump over the moon You will fly to Alaska tomorrow If I drop a large rock into the river it will sink

Each event should be thoroughly discussed. The events that may occur needs to be discussed and students led to see that although they may

enVision Math Topic 20 (20-5)

enVision Tools

spinners

dice

coins

Probability stations to include: drawing specific items

from a bag Spinning a certain color

or number on the spinner Coin toss Rolling a specific

number or rolling an odd number or an even number

Interventions/ExtensionsStudents will work with a buddy in the stations to help them work through the problems.

Teacher made formal assessment

Product/ProjectStudents will write a probability problem for their partner to solve.

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occur, they are likely not to happen or to happen because of ….

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Probability

Use data to describe events as less likely or more likely.

Prompt the students to use data to describe events as less likely or more likely.

Example:Distribute a bag with 8 green marbles and 2 blue marbles to each pair of students.

Prompt the students to draw a marble from the bag, record its color, and return the marble to the bag. Prompt the students to repeat the procedure 20 times.

Ask the students, “What color marble is less likely to be drawn?”

Answer: Blue

Ask the students, “What color marble is more likely to be drawn?”

Answer: Green

Example:Provide the students with a spinner such as the one shown below.

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Prompt the students to spin the spinner 20 times and record the results of each spin.

Possible Results:Outcome Results

1

2

Ask the students, “If we spin the spinner again, which number is more likely to be spun?”

Answer: 2

Ask the students, “If we spin the spinner again, which number is least likely to be spun?”

Answer: 1

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Week 5 and 6

May 27 - 31Jun 3 - 7

Major Concepts:

Multiplication and division

Learning Standards:

(6) Number and Operations. The student applies mathematical process standards to connect repeated addition and subtraction to multiplication and division situations that involve equal groupings and shares. The student is expected to:(A) model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined; and(B) model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets.(7) Algebraic Reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to: (A) use relationships and objects to determine whether a number up to 40 is even or odd;(B) use relationships to determine the number that is 10 or 100 more or less than a given number up to 1,200; and(C) represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem.



Assessment

Key vocabulary – multiplication, division, equal groups, product, factor, horizontal, vertical, multiply, divide, divided by, input, output

The next two weeks will be focused on multiplication and division. Students will learn to join equivalent set to multiply and separate objects into equal sets to divide.

Math background for teachers: Multiplication may be thought of as repeated addition and involves

joining equal groups. An array involves joining equal groups and is another way to think of

multiplication. Two numbers can be multiplied in any order. Help students make connections to multiplication through skip

counting. Use number lines to solve multiplication problems.

enVision Math Topic 13 and 14

enVision Math Tools

foam tiles (for arrays)

counters

cards

dice

Unifix Cubes

enVision Math games

Interventions/ExtensionsStudents will work with the teacher and do cube-train skip counting (TE 373H)

enVision Math Assessment

Product/Project:Students will make a multiplication book for math facts

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Model, Create, and Describe Multiplication Situations

Model multiplication situations in which equal sets of concrete objects are joined.

Prompt the students to use concrete objects to model multiplication situations.

Example:Hugh wants to give 3 baseballs to each of his 6 friends. What is the total number of baseballs that Hugh will give to his friends?

Answer: 3 each

Ask the students, “How can we model this multiplication situation?”

Answer: 18 baseballs

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Create multiplication situations in which equal sets of concrete objects are joined.

Prompt the students to create multiplication situations in which equal sets of concrete objects are joined.

Possible Answer:There are 3 ponds in the park. In each pond, there are 5 ducks. How many ducks are there in all?

Answer: 15 ducks

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Describe multiplication situations in which equal sets of concrete objects are joined.

Prompt students to describe multiplication situations in which equal sets of concrete objects are joined.

Example:Ask the students, “How can we describe this multiplication situation?”

Possible Answer: “There are 4 groups of 4 frogs. The 4 groups can be added together for a total of 16 frogs.”

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Model, Create, and Describe Division Situations

Model division situations in which a set of concrete objects is separated into equivalent sets.

Prompt the students to use concrete objects to model division situations.

Example:Donna purchased 5 plant stands for her 20 plants. How many plants could she put on each plant stand?

Ask the students, “How can we use counters to model this division situation?”

Possible Answer:

Create division situations in which a set of concrete objects is separated into equivalent sets.

Prompt the students to create a division situation in which a set of concrete objects is separated into equivalent sets.

Example:There were 8 baseball bats equally shared between 2 teams. How many baseball bats did each team receive?

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Answer: 4 baseball bats

Describe division situations in which a set of concrete objects is separated into equivalent sets.

Prompt the students to describe a division situation in which a set of concrete objects is separated into equivalent sets.

Example:Ask the students, “How can we describe this division situation?”

Possible Answer:“There were a total of 12 cookies that were divided into 4 equal groups.

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Each group had 3 cookies.”

Patterns in Whole Numbers

Identify patterns in numbers.

Prompt the students to identify and describe patterns in numbers.

Example:Prompt the students to discuss patterns in a 100s chart.

Ask the students, “What patterns do you see in the numbers that are shaded on the 100s chart?”

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Possible Answer: “The numbers in the columns increase by 10. The shaded numbers are even numbers.”

Example:Prompt the students to skip count by3s and shade those numbers on a hundreds chart.

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Ask the students, “What patterns do you see in the numbers that are shaded on the 100s chart?”

Possible Answer: “The shaded diagonal lines increase by 9. The shaded numbers skip count by 3s.”

Example:Prompt students to identify the pattern created by the numbers and determine the number that is missing from the pattern.

46 42 38 34 26 22

Answer: Subtract 4; 30

Generate Lists of Paired Numbers

Generate a list of paired numbers based on real-life situations.

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Prompt the students to use real-life situations to generate a list of paired numbers.

Example:Prompt the students to describe and list objects that come in two’s, three’s, four’s, five’s and six’s. Prompt the students to record their results.

Possible Answer:Objects that come in 3s:

1. Wheels on a tricycle2. Corners on a triangle

Prompt the students to select one of the objects to generate a table of paired numbers.

Possible Answer:

Number of Tricycles

Number of Wheels

1 3

2 6

3 9

Identify and Extend Patterns in Lists of Related Number Pairs

Identify patterns in related number pairs and extend the pattern.

Prompt the students to identify patterns in a list of related number pairs based on a real-life situation and extend the list.

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Example:Ask the students, “What patterns do you see in this table?”

Number of Cars

Number of Wheels

1 4

2 8

3 12

4 16

5 ?

Possible Answer: “For each car, there are 4 wheels. This means that if we have 2 cars, we have 8 wheels.”

Ask the students, “If there are 5 cars, how many wheels are there?”

Possible Answer: “There are 20 wheels because for each car there are4 wheels, and, if we had 5 cars, there would be 20 wheels.”

Example:Prompt the students to determine the pattern in a list of related number pairs in order to determine the missing information.

Ask the students, “What patterns do you see in this table?”

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Pairs of Shoes

1 2 3 4 5

Number of Shoes

2 4 8 10

Possible Answer: “For each pair of shoes, the number of shoes increases by 2.”

Ask the students, “What number is missing from the table? How do you know?”

Possible Answer: “6. If there are2 shoes for 1 pair of shoes and 4 shoes for 2 pair of shoes, there are 6 shoes for 3 pairs of shoes.”

Identify, Describe, and Extend Patterns

Identify, describe, and extend repeating and additive patterns to make predictions and solve problems.

Prompt the students to identify, describe, and extend patterns to make predictions and solve problems.

Example:Meagan plans to sell lemonade after school on Friday. She makes 10¢ for every cup of lemonade that she sells. How much will Meagan make if she sells 8 cups of lemonade?

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Number of CupsAmount of

Money Made

1 10¢

2 20¢

3 30¢

4 40¢

5 50¢

6 60¢

7

8

Ask the students, “What is the pattern in the table?”

Possible Answer: “For each cup of lemonade Meagan sells, she earns 10¢.”

Ask the students, “How much money will Meagan make if she sells 8 cups of lemonade?”

Answer: 80¢

Describe and use patterns to solve problems.

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Example:William drew the following designs on his paper and recorded the number of tiles used in each design in a table.

1 2 3 4

Design Number Number of Tiles

1 2

2 4

3 6

4 8

5

Ask the students, “What is the pattern in the table?”

Possible Answer: “For each design William draws, he adds 2 tiles.”

Ask the students, “How many tiles will William need for Design 5?”

Answer: 10 tiles

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