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NUMBERS AND OPERATIONS

By Carl Hart,2014-06-16 01:20
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NUMBERS AND OPERATIONSand

    NUMBERS AND OPERATIONS

    Grade K

    BIG IDEA (1): Understand numbers, ways of representing numbers, relationships among numbers and number systems

CONCEPT EXPECTATION EXAMPLE

    Read, write *Rote count to 100 Problem: A

    and compare and recognize Have students stand in a circle and count by ones from 1 to 10 in unison. Then, call numbers numbers up to 31 on students to do this in pairs or individually. Follow the same procedure for counting

    by ones from 1 to 20, then to 30, to 40, to 50…and eventually to 100.

    Or, give the students a starting number between 2 and 20 and have them count by

    ones from that number to a designated number. Repeat the process using a starting

    number between 11 and 20.

    Have the students count in unison before asking them to count in pairs or

    individually.

    Problem:

    Give each student a copy of a blank calendar for the month. Begin each school day

    by having students write in their calendar the number that represents the day of the

    month as you record it on the classroom calendar.

    Ask students to use the classroom calendar to answer questions you ask them

    about the calendar that require specific number answers

    Problem:

    Provide students with daily experiences with the calendar. Refer to numbers on the

    calendar in connection with special events, field trips, birthdays, parties, Fridays,

    Mondays, assemblies, etc. Always draw attention to the calendar numeral by writing

    it on the board, counting it out with concrete objects, writing it in the air, and having

    the students write it.

    NUMBERS AND OPERATIONS Kindergarten DRAFT 1

TEACHER NOTES:

    As students go beyond rote counting, they should be learning to count small collections of objects, keeping track of what they have already counted. Gradually, they should learn to count larger groups of objects by correctly keeping track of what they have already counted. Opportunities to count things should be natural situations within the classroom, such as counting how many snacks are at a table, how many snacks are needed at a table, etc.

Students should also begin to establish a system of tagging (one number to one

    object) as they move or touch objects when counting a collection.

    Students learn to rote count through repeated experiences with counting and listening to the counting sequence. One way to give this practice meaning is to offer students one row at a time of the 100s chart. As the students master counting 1 to 10 (in various venues), the next row can be added so that they learn to count 1 to 20, but they also focus on the bridge numbers (910, 1920, 2930, etc.) and

    visually see how the tens continue to grow: 10203040…

    Evidence of mastery is the student counting 1 to 100 without hesitation at the bridge numbers.

    Teachers may want to highlight the bridge numbers on the 100s chart.

    Differentiation: They may want to challenge some students by asking them to begin

    counting at a number other than ―1‖ to check for understanding.

Students should be able to recognize the numerals when dealing with the calendar.

In order for children to work with and understand the function of the calendar as a

    tool that we use to measure or keep track of time, students need to be able to recognize numerals up to 31 at least.

Students learn to recognize numerals through a number-rich classroom.

    NUMBERS AND OPERATIONS Kindergarten DRAFT 2

CONCEPT EXPECTATION EXAMPLE

    Represent and *Recognize ? a Problem: B

    use rational shape Prepare several sheets of paper each with a line drawn that separate the sheet into numbers equal or unequal regions. Ask students to respond with a ―thumbs up‖ for those that

    show equal (same size) regions and ―thumbs down‖ for those that show unequal

    regions.

    Problem:

    Prepare several sheets of paper that have been cut into two equal parts. Show ? of

    one of the sheets and ask the students to identify the other halve of the sheet.

    Another way to do this activity would be to give each student ? of a sheet of paper

    that has been cut apart and ask them to find the person who have the other half of

    their sheet of paper.

    NUMBERS AND OPERATIONS Kindergarten DRAFT 3

    CONCEPT EXPECTATION EXAMPLE Compose and *Use concrete Problem: C

    decompose objects to compose Use various objects arranged different ways to represent the same number.

    numbers and decompose For example:

    values up to 10 1. 5 buttons

    2. 5 triangles

    3. plastic numbers 4 and 1

    4. 5 pieces of candy

    NUMBERS AND OPERATIONS Kindergarten DRAFT 4

    BIG IDEA (3): Compute fluently and make reasonable estimates

CONCEPT EXPECTATION EXAMPLE

    Develop and *Connect number Problem: B

    demonstrate words (orally) and Have students sit in a semicircle facing you. Each of you has a mat (blank

    fluency quantities they sheet of paper) and 10 counting pieces. Read the story ―Mr. Vet‘s Dogs.‖ Say

    represent to the students, ―For every dog named in the story, we will place a counting

    piece on our mat to represent that dog.‖

    ―Mr. Vet has a black dog with one brown spot.‖

    (Pause. Put one counting piece on your mat to stand for the black dog with

    one brown spot.)

    ―Mr. Vet has one white dog.‖

    (Pause. Put one counting piece on your mat to stand for the white dog.)

    ―Mr. Vet has one dog with long, brown hair.‖

    (Pause. Put one counting piece on your mat to stand for the dog with long,

    brown hair.)

    ―Mr. Vet has one gray dog with short hair.‖

    (Pause. Put one counting piece on your mat to stand for the gray dog with

    short ―Mr. Vet has one gray dog with short hair.‖

    (Pause. Put one counting piece on your mat to stand for the gray dog with

    short hair.)

    ―Mr. Vet has one dog that is four different colors.‖

    (Pause. Put one counting piece on your mat to stand for the dog that is four

    different colors.)

    ―How many dogs does Mr. Vet have altogether?‖

    (Pause. Let the students counts the chips on their mat to tell how many

    dogs Mr. Vet has.)

    Answer: 5

    NUMBERS AND OPERATIONS Kindergarten DRAFT 5

Problem:

    Students count the crayons in their supply box on their desk (610 items).

    Have them start counting with a different color each time. They count the same

    set of crayons several times, getting the same answer, no matter what the sequence of the colors.

    Check to see that each student understands the ordinal sequence of numbers, as well as the cardinal meaning of the numbers. Being able to count accurately using

    the ordinal sequence is not the same as knowing that the ending number of a sequence tells the quantity of the things we have counted.

Problem:

    Display different numbers of items and have student count them. Ask questions such as:

    ~ ―How many Unifix cubes are on the table?‖

    ~ ―How many blue color tiles are in your pattern?‖

    ~ ―How many students are here today?‖

    ~ ―How many snacks or milk do you need at your table?‖

    ~ ―Can you show me five fingers?‖

TEACHER NOTES:

    Students can count from 1 to 100 and still not have the skills and the understanding of one-to-one correspondence necessary to connect number to quantity. Some students can connect number to quantity but still not truly understand the difference between ordinal and cardinal numbers.

    Students should be learning to count small collections of objects, keeping track of what‘s been counted, and gradually learning to count larger groups of objects by correctly keeping track of what they have already counted. Opportunities to count things should be natural situations within the classroom, such as situations identified in the problem above.

    Students should establish a system of tagging (one number to one object) as they touch or move objects while they are counting. This counting and tagging should

    follow the rote number sequence of counting.

    NUMBERS AND OPERATIONS Kindergarten DRAFT 6

    NUMBERS AND OPERATIONS

    Grade 1

    BIG IDEA (1): Understand numbers, ways of representing numbers, relationships among numbers and number systems

CONCEPT EXPECTATION EXAMPLE

    Read, write *Read, write and Problem: A

    and compare compare whole Provide each student with a card with a number less than 100 written on it. Ask numbers numbers less than each one to find someone with a number on their card that has something in