Grade 1st Six... · Web view2018-09-25 · are available in a separate file titled Curriculum Documents. Ten Frame Mat. Place Value Mat. Number of the Day. Remember to write the

West-Orange Cove ISD 2nd Grade Mathematics – 1st Six Weeks 2012 - 2013

Week 1

August 27 - 31

Major Concepts:

Review from 2nd GradeTeach expectations, routines, procedures

Learning Standards:

Expectations, routines, procedures

Processes

Expectations, routines, procedures

Instruction Resources InterventionsExtensions and Stations

Assessment

This year second grade students will be taught using the new math standards. This will prepare them for the new standards next year that they will be taught in 3rd grade.

In Grade 2, instructional time should focus on three critical areas: making comparisons within the base-10 numeration system; solving problems with addition and subtraction within 100; and building foundations for multiplication.

(A) Students develop an understanding of the base-10 numeration system and place value concepts. Their understanding of base-10 numeration includes ideas of counting in units and multiples of thousands, hundreds, tens, and ones, and a grasp of number relationships, which they demonstrate in a variety of ways.

(B) Students identify situations in which addition and subtraction are useful to solve problems. Students develop a variety of strategies to use efficient, accurate, and generalizable methods to add and subtract multidigit whole numbers.

(C) Students use the relationship between skip counting and equal groups of objects to represent the addition or subtraction of equivalent sets. This builds a strong foundation for multiplication and division.

(4) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.

Math literature

Base 10 blocks

Pre-Assessment

enVision Math Textbook

enVision Math Tools

manila papercrayons

enVision eTools

Stations:Model each math station prior to implementing each station such as :

Exploration of Manipulatives

Interactive Math Story

Number sense addition and subtraction timed drills and computation

Use a place value chart to order numbers and identify

Number Lines

Number patterns

Read a book from the Math Start collection

Interventions/Extensions Based on student needsMeeting Individual Needs

Pre-Assessment:

Products/Projects:

Math Posters

Journal Entry

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Below are the process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

(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.

In conjunction with the new standards, the first six weeks will be focused on:o Place Value

Standard form, expanded form Read and write numbers from 0 to 1,200 Greater than, less than (using symbols) Base ten blocks to show various ways to express #s

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(ex: 545)o Number lineso Hundreds number charto Patternso Skip counting (starting at various points…ex:24)o Problem Solving throughout

Math Essentials: (Daily Routine) Ten minutes of basic fact fluency (District program – Creative

Math by Kim Sutton) Ten minutes of spiral review and vocabulary – this may be a

math station Problem of the Day - this may be a math station Close each math lesson with a math journal entry (invented

spelling is acceptable) encourage complete sentences. As they apply to the topics read the books in the Math Start

collection and then allow the students to read them (accordingly).

The first week of school the teacher will: Read your favorite literature book connected to math or The

Math Curse to students. Follow up by discussing how they use math in their everyday life from the time they wake up until they go to bed. Students can make posters that demonstrate how they use math every day. Share posters.

Teach students the daily routine. The daily routine consists of basic facts fluency, inquiry, problem solving, Math Stations, small group instruction with the teacher, journal reflection/writing, and number fluency through the “Number of the Week.”

Teach the West Orange Problem Solving Model. Practice this model with several problems daily the first week to ensure students are familiar with the process and expectations.

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Conduct a Pre-Assessment

Profile Pre-Assessment with students. Graph the results in whole class and display. Review results with each student pointing out their strengths and weaknesses. Develop an IEP with the student and use it as a guide to structure small groups, homework, and interventions.

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Week 2 and 3

Sept 4 – 7Sept 10 -

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Major Concepts:

Base-Ten Numeration System

Place Value

Learning Standards:(2) Number and Operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:(A) use concrete and pictorial models to compose and decompose numbers up to 1,200 as a sum of so many thousands, hundreds, tens, and ones, in more than one way;(B) use standard, word, and expanded forms to represent numbers up to 1,200.

Processes Use of manipulatives to explore the concepts of mathematics Apply problem solving strategies such as acting it out, talking it

out, drawing it out, etc. Understand the relationships and patterns that exist among

numbers Express whole numbers (through 1200) in standard form and

expanded form Use a place value chart to name the value of digits in whole

numbers. The position of digits in a number determines what they represent

– the value The groupings of ones, tens, hundreds, thousands can be taken

apart in different ways (356 = 3 hundreds, five tens, 6 ones or 2 hundreds, 15 tens, 6 ones, etc.

Instruction Resources Math Stations AssessmentKey Vocabulary: ones, tens, hundreds, thousands, digits, number, expanded form, standard form, before, after between, pattern, skip counting

Quick Note: It is important to spend two weeks with this concept and providing students with the opportunity to work with base 10 blocks and work mats. DO NOT SKIP THIS – STUDENTS MUST HAVE THIS REPETITION TO FULLY UNDERSTAND THE MATHEMATICS AND LANGUAGE OF PLACE VALUE AND THE GROUPING BY TEN. Do not move directly to the abstract before they have mastered the concrete.

Math Background for the teacher:

Students must understand the difference between a digit and a number before they can

enVision Topic 4 and Topic 11

enVision Math Tools

http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html

Manipulatives –Base 10Craft SticksBeansToothpicksUnfix Connecting CubesPlace Value Work Mat (attached)

Basic Facts – songs, timers for drills

Measurement – rulers, balance, and an assortment of items to measure and weigh

Place Value – work mats and manipulatives (provide challenging numbers for students to represent with base 10 or other counters

Interactive Math Story (enVision Math)

Game – Model 10s and Ones (modify board to include 100s) (enVision Math)

Interventions/Extensions

Informal based on observations

Formal – understanding of base 10 system- standard, word, expanded form

Journal Entry

Projects/Products:

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begin to understand place value.

Numeration System is our system for naming numbers. It uses 10 digits – 0 – 9.

The position of a digit in the number tells its value.

Each position to the left is 10 times more than the one to its right.

Sets of ten and (tens of tens) can be perceived as single entities. These sets can be counted and used as a means of describing quantities. (Van de Walle)

The Base-Ten System is based on the positions of digits in numbers to determine what they represent.

There are patterns to the way that numbers are formed

The groupings of ones, tens, and hundreds can be taken apart in different ways. (composing and decomposing numbers)

Begin with Topic 4 which focuses on numbers to 99. When students grasp the concept with smaller numbers, move to Topic 11 and work with larger numbers.

There are several manipulatives and work mats that may be used to facilitate students understanding of place value. These templates are available in a separate file titled

Students will work in small group with teacher to practice skills.

Have students create their own set of vocabulary flash cards with visuals

Students will model and write as many representations of a specific number.

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Curriculum Documents.

Ten Frame Mat Place Value Mat Number of the Day

Remember to write the numbers in word form and expanded form as well as standard form throughout your modeling so students connect different ways of seeing numbers.

Use concrete models to represent whole numbers 0-1,200.

Before beginning the lesson, distribute base 10 blocks and a work mat to every student. Students should use their base 10 blocks and work mats to make the numbers in the examples. If students are not accustomed to using work mats and base ten blocks, model this process for them several times using smaller two digit numbers before moving to larger two digit numbers as well as three and four digit numbers.

Example:Prompt the students to use concrete models, such as base ten blocks, torepresent the number 57.

Possible Answers:5 tens 7 ones

or 4 tens 17 ones

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If a student makes this representation, ask the student “Is there a way to trade some of the ones so that you are using fewer base ten blocks?”

Possible Answer: I could trade 10 ones for a ten. I would have 5 tens and 7 ones.

Read , Write, and Describe Whole Numbers 0-1,200

Example:

Write the number 39 on the board. Ask the students, “How can you read this number?”

Possible Verbal Answers: “The number is 39.” “It is three tens and nine ones.” or “3 tens and 9 ones.”

Possible Written Answer: “The number is 39 or thirty-nine.”

Example: Ask the students, “How can you write 6 tens and 7 ones?”Answer: 67

Example:Ask the students, “How can the number 74 be described?”

Answer: 7 tens and 4 ones or 70 + 4

Activity: Counting in Groups – put a 125

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buttons in a baggie. Ask the students, “How could we count our buttons in a way that would be easier than counting by ones?” Try several of their suggestions. If no one suggests counting by tens, suggest it. Next connect this to the way students at this level usually count is by ones. Demonstrate how you get the same answer and why it is “faster” to count by tens.

Activity: Groups of 10 – (Do this first with two digit numbers then do it with three digit numbers when students are ready.) Set up 5 or 6 stations in the room. At each station provide a container of objects such as counters, beans, toothpicks, or other items. Provide each student with a recording sheet. Groups move from station to station and complete their record sheets. Assess students as they move through the stations. Do they make one group of ten the n start with one again? Do they make groups of ten as they count? If not, help them make the transition to do this because this demonstrates their understanding of the base 10 structure.

Station

Word Form

Tens Ones

Expanded Form

BeansButto

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nsCrayonsPaper Clipspasta

Station Word Form

Hundreds Tens Ones

Expanded Form

BeansButtonsCrayonsPaper Clipspasta

After completing this activity, ask students what is another way to make ----- number from the bean station, etc.

Remember: Throughout the lessons you are consistently asking students what other way can I make ---- number. It is important for students to understand this concept of composing and decomposing numbers. Make it a race to see who can come up with the most ways to make in developing their mathematical understanding of place value.

Once students have mastered two digit numbers move to three and four digit numbers (Topic 11) and continue the questioning. Topic 11 only goes to 999 you must incorporate through 1200 on your own. Continue providing work mats and base 10 blocks for students to use as a concrete

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method of grasping place value.

By the middle of week 2 of this lesson, students should be able to move to paper and pencil. They can then use the work mat and draw the base 10 on the mat to represent numbers before moving to simply writing the numbers.

Week 4 & 5

Sept 17 – 21Sept 24 - 28

Major Concepts:

A number line is a geometric graphic designed to simplify the size of numbers by emphasizing

Learning Standards:(2) Number and Operations. The student applies mathematical process standards to understand how to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:(C) generate a number that is greater than or less than a given whole number up

Processes

Use a place value chart to name the value of digits in whole numbers

Use place value to compare whole numbers Compare whole numbers on a number line

and use greater than, less than, and equal to

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the distances between them Problem solving involves

the active use of knowledge, analysis, and application

to 1,200;(D) use place value to compare whole numbers to 1,200 using comparative language, numbers, and symbols (>, <, or =); (E)locate the position of a given whole number on an open number line;(F) name the whole number that corresponds to a specific point on a number line; and(G) order whole numbers to 1,200 using place value and open number lines.(4) Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve addition and subtraction problems with efficiency and accuracy. The student is expected to:(D) generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 100.

symbols to express comparison Order whole numbers through 1,200 Implement the West Orange Problem

Solving Model when solving story problems Apply problem solving strategies such as

guess and check, drawing a picture, acting it out, etc.

Instruction Resources InterventionsExtensions and Stations

Assessment

Key Vocabulary: pattern, number line, greater than, less than, equal to, before, after between least, greatest, pattern, skip counting, problem solving, justify, reasonable

The next two weeks the focus is on patterns, number lines, and comparing numbers. Problem solving will also be introduced and students will solve one digit addition and subtraction problems. They may use a number line or a hundreds chart to help them if needed.

Math Background for the Teacher:

Pattern relations and functions- relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in a predictable way. Counting and place value patterns can be seen on a hundreds chart. In addition to the standard hundreds chart (1 – 100) provide students with other charts such as (51 – 150), (251 – 350), (1000 – 1150), etc.

Activities in which students are asked to find numbers that are between, before, or after a specific number will help them

enVision Math Topic 16 – Number Lines enVision Topic 4, 11, 12- comparing numbers, patterns

enVision Math Tools

Hundreds charts

Crayons/dry erase markers/sock (for erasing)

Number Lines

http://www.ixl.com/math/grade-2/hundreds-chart

http://www.ixl.com/math/grade-2/counting-patterns-up-to-1000

http://nlvm.usu.edu/en/nav/

Basic Facts – songs, timers for drills

Measurement – rulers, balance, and an assortment of items to measure and weigh


Interventions/ExtensionsPlace Value – work mats and manipulatives

Number line

enVision Math Assessment

(use data to form small groups and math interventions/extensions)

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http://nlvm.usu.edu/en/nav/frames_asid_156_g_1_t_1.html?open=activities&from=category_g_1_t_1.html






understand the relative size and order of numbers.

Each whole number can be associated with a unique point on the number line.

Patterns can be used to skip count on the number line.

Students can compare and order numbers on a number line.

Patterns in charts:Activity: Brainstorm patterns they see on a standard hundreds chart. Answers may include: “The numbers in a column all end with the same number,

which is the same as the number at the top. In a row, one number “counts” (the ones digit goes 1, 2, 3, 9, 0); the “second” number goes up by ones, but the first number (tens digit) stays the same.

In a column, the first number (tens digit) “counts” or goes up by ones

You can count by tens going down the right-hand column. If you count by fives, you get two columns, the last column

and the 5 column.” (Van de Walle) Odd numbers Even numbers Introduce skip counting. Begin with what students already

know and that is to skip count by 2, 5, and 10. Next have students to skip count by 3, 4, 6, 7, 8, 9, 25, 30, etc. Remember you are also providing other charts for students to use so select skip counting activities accordingly.

o Students should color in the skip counting patterns. Discuss the patterns in the numbers. Which counts only make column patterns? Diagonal patterns?

Activity: Missing Numbers – Students fill in the missing number(s) on the chart. Remember students must now be able to count and order numbers up to 1,200.

frames_asid_156_g_1_t_1.html?open=activities&from=category_g_1_t_1.html

activitiesHundreds Charts Activities


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More and Less on Hundreds Chart:Begin with a blank hundreds chart. Put a target number on the chart. Place a circle where the numbers on each side of the target number as well as the number above and below the target number is. (See example below). Students must provide the missing numbers. Ask for patterns and what they notice about the neighbors of the target number. For example the neighbors on either side will be one less and one more; the numbers above and below will be 10 less and 10 more. Provide many opportunities for students to practice this skill.

56

Have students to make a chart from 1 – 1200 by using 12 blank “Hundreds Charts”. Students can divide this task up and each pair can create a specific part of the chart. Tape all the charts together. Laminate and display. Use daily to identify numbers, patterns, compose and decompose numbers, write a specific number in expanded form, count forward, count backward, one more, ten more, etc.

After students have used several hundreds and thousands charts transition to a number line.

Activity: Brainstorm a comparison of a hundreds chart and a number line.

Activity: Provide students with a blank number line that has been laminated. Students will use a dry erase marker and locate and number points on a number line.

Activity: Use the number line to skip count by 2, 3, 4, 5,6,10,

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20, 50, 100s, etc.

Activity: Generate a number that is greater than or less than a number up to 1,200

Activity: Provide students with a number line that has some number missing. Students must determine what number goes to a particular point.

Activity: Use the number line to compare and order numbers. Introduce comparison symbols <,>, =.

Compare and order numbers using symbols up to 1,200:

Example:

Tens Ones8 69 2

Ask the students, “Which number is greater?”

Answer: 92

Ask the students, “Which number is smaller?”

Answer: 86

Example:

Tens Ones6 87 8

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Prompt the students to use the symbols < and > to compare the numbers.

Answer: 68 is less than 78, or 68 < 7878 is greater than 68, or 78 > 68.

Example:

Tens Ones7 36 78 9

Prompt the students to put the numbers in order from greatest to least and/or from least to greatest.

Answer: Least to greatest: 67, 73, 89 and greatest to least: 89, 73, 67.

Example:Use an instructional strategy, such as a place value chart, to compare whole numbers from 0-99.

Prompt the students to look at the greater place value (tens) to see which number has a greater value.

Tens Ones6 96 5

If the digits are the same, prompt the students look at the next larger place value (ones) to see which number has a greater value.

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Tens Ones6 96 5

Prompt the student to compare the digits in the ones place to determine which number has the greatest value.

Answer:69 is greater than 65;65 is less than 69.

Example:Prompt the students to place the following numbers in order from least to greatest and/or greatest to least.

86, 70, 84

Prompt the students to look at the greatest place value (tens) to see which number has a greater value.

Tens Ones8 67 08 4

If the digits are the same, prompt the students to look at the next largest place value (ones) to see which number has the greatest value.

Tens Ones8 67 08 4

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Prompt the student to compare the digits in the ones place to determine which number has the greatest value.

Answer:Least to greatest: 70, 84, 86Greatest to least: 86, 84, 70

Example:Prompt students to place the following numbers in order from least to greatest and/or greatest to least.

421, 612, 432

Hundreds Tens Ones

4 2 1

6 1 2

4 3 2

Least to greatest: 421, 432, 612Greatest to least: 612, 432, 421

Example: Prompt students to place the following numbers in order from least to greatest and/or greatest to least.

1,198, 985, 1889Thousands Hundreds Tens Ones

1 1 9 8

9 8 5

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1 8 8 9

Continue to provide examples to students. You may also put several examples in a station for students to practice.

Problem Solving:Teach student the problem solving process. You may want to make a poster or chart and display it in your room for students to use as a reference.

Step 1: Read and understand What am I trying to find out?

o Tell what the question is asking. What do I know?

o Tell the problem in my own words.o Identify key facts and details.

Step 2: Plan and Solve What strategy or strategies should I try? Can I show the problem?

o Try drawing a pictureo Try making a list, table, or grapho Try acting it out or using objects.

How will I solve the problem? What is the answer?

o Tell the answer in a complete sentence.o

Step 3: Look Back and Check Did I check my work?

o Compare my work to the information in the problem.

o Be sure all calculations are correct. Is my answer reasonable?

o Estimate to see if my answer makes sense.o Make sure the question was answered.

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Problem Solving Strategies: (Make a poster of these for the classroom so students can use them as a reference.)

Show what you knowo Draw a pictureo Make an Organized Listo Make a tableo Make a Grapho Act it Out/Use Objects

Look for a pattern Try, Check, Revise Write a number sentence Use reasoning Work backward Solve a simpler problem

Provide students with a variety of problems to solve using single digit addition and subtraction.

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