# Numbers and Operations in Base 10 and Numbers and Operations Fractions

Save this PDF as:

Size: px
Start display at page:

Download "Numbers and Operations in Base 10 and Numbers and Operations Fractions"

## Transcription

1 Numbers and Operations in Base 10 and Numbers As the chart below shows, the Numbers & Operations in Base 10 (NBT) domain of the Common Core State Standards for Mathematics (CCSSM) appears in every grade level for elementary school mathematics. In contrast, the Numbers and Operations Fractions domain begins in grade 3. The highlighted rows indicate the domains we will discuss in this reading. Domain K Counting and Cardinality (CC) Operations and Algebraic Thinking (OA) Numbers and Operations in Base 10 (NBT) Number and Operations Fractions (NF) Measurement and Data (MD) Geometry (G) Let s take a closer look at the Numbers and Operations in Base 10 and the Numbers domains. The table below shows the critical areas and clusters for each grade level (CCSSM, 2010).

2 Numbers and Operations in Base 10 (NBT) Level K CCSSM Critical Areas Representing, relating, and operating on whole numbers, initially with sets of objects Developing understanding of whole number relationships and place value, including grouping in 10s and 1s Extending understanding of base 10 notation Developing understanding of multiplication and division and strategies for multiplication and division within 100 Developing understanding and fluency with multidigit multiplication, and developing understanding of dividing to find quotients involving multidigit dividends Extending division to two-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations Cluster Work with numbers to gain foundations for place value. Extend the counting sequence. Understand place value. Use place value understanding and properties of operations to add and subtract. Understand place value. Use place value understanding and properties of operations to add and subtract. Use place value understanding and properties of operations to perform multidigit arithmetic. Generalize place value understanding for multidigit whole numbers. Use place value understanding and properties of operations to perform multidigit arithmetic. Understand the place value system. Perform operations with multidigit whole numbers and with decimals to hundredths.

3 Numbers (NF) Level CCSSM Critical Areas Developing understanding of fractions, especially unit fractions (fractions with numerator 1) Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) Cluster Develop an understanding of fractions as numbers. Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and compare decimals and fractions. Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Assessing Understanding Regardless of the concept being assessed, the key is to assess the actual skill or practice for which instruction was provided. Different districts have different policies on assessments and grading, but as much as possible, teach the students so that they have a conceptual and procedural understanding of the standards, and then test the students as they were taught. Make sure to spend time making the bridges necessary from the concrete to the representational and from the representational to the abstract.

4 Assessing for Numbers and Operations in Base 10 As previously noted, teachers have numerous assessment strategies at their disposal, which the structure and intent of the CCSSM encourages them to explore. Here are a few things to look for when assessing for understanding of the numbers and operations in base 10 standards: Do students understand the value of each digit rather than looking at the digit in isolation? Can students compose and decompose numbers? Do students see addition and subtraction as inverse operations? Can students verbalize decimal numerals correctly? Can students state the value of a specific digit within a decimal fraction? Assessing for Numbers Here are a few things to look for when assessing for understanding of the Numbers standards: Can students fairly share an area in different ways? Can students divide a variety of shapes or objects accurately? Can students represent fractional parts in nontraditional ways? Do students understand that the denominator represents the number of pieces needed to form the whole? Do they understand that the numerator stands for a specific number of pieces of the unit? Do they understand that when adding or subtracting fractions with like denominators only the numerator changes?

5 Errors and Misconceptions As discussed earlier, while an error can be thought of as a one-off occurrence that doesn t necessary reveal a lack of understanding, misconceptions tend to be frequent and consist. Let s look at a few examples. Common Numbers and Operations in Base 10 Misconceptions Common misconceptions for this domain include the following. Misconception #1 Place Value: Not understanding the value that a digit represents when regrouping or renaming in addition and subtraction problems. This misconception often occurs when students are taught algorithms for adding and subtracting multidigit numbers before they understand the concept of place value and what the digits actually represent. For example, when adding , some students may give the answer 51. They know that 5+6 =11, but since they can only write one digit down for the ones place, they write down only one of the digits and then move on to add 3+2=5. Their final answer then is 51. Another example of this misconception is seen when a student adding gives the incorrect answer of 511. They know that = 11, so they write down 11, and then add = 5 and record a final answer of 511. In both of these examples, the student does not understand the concept of place value; that is, that the 3 and 2 represent 30 and 20.

6 Another example of this misconception is when given a subtraction problem and one of the digits in the bottom number is greater than the digit above it, as shown below Some students, knowing that the smaller number must be subtracted from the larger number will flip 4 6 to be 6 4 and arrive at the incorrect answer of 22 rather than 18. Some possible corrections for this misconception include Introduce the concept of grouping by having students count by 2s, 5s, 10s, or 100s. Use a 100s or 500s chart for addition and subtraction and to look for patterns. Use games in which students bundle groups of objects into 10s and then record the number of bundles of 10s, the number of single objects remaining, and the number it represents. Add bundles of 100s for older students. Have students represent a 2-digit number in as many possible ways as they can using only 10s and 1s. This can be done by modeling, pictures, or symbols. Use 3-digit numbers and 100s for older students. Use partial sums to solve multidigit addition problems. Misconception #2 Multiplication: Treating each digit individually rather than considering its value when multiplying two-digit factors. As covered in the previous reading on Operations and Algebraic Thinking, a common mistake in multiplication is to take the numbers at face value and forget

7 about place value. This tends to occur when students are taught an algorithm without understanding the concept behind the algorithm. For example, a student does the multiplication problem 35 x 23 and gets the incorrect answer of x The student appears to understand that 5 x 3 = 15, so he writes down the 5 and carries the one. He multiplies 3 x 2 = 6 and adds the one that he carried to get 7. What happened? The student appears to understand regrouping, but he is not realizing that in a multiplication problem, every digit in a factor needs to be multiplied by each digit in the other factor. Because the student doesn t understand the concept, he does not realize that his answer does not make sense. Some ideas to reinforce the understanding of multiplication include In addition to teaching multiplication as repeated addition, use the rectangular array (area) model. This can be connected to repeated addition to show students that they are getting the same answer with another model. See the strategy modeled earlier in this reading. Show students how to expand the factors of a given problem and use the partial products strategy, which helps show the connection between the distributive property and multiplication and reinforces place value. This strategy can also be show on a rectangular array model, which will provide a visual of what is happening when performing multiplication with double-digit numbers. 46 x 32 = (40 x 30) + (40 x 2) + (6 x 30) + (6 x 2) = 1, = 1,472

8 Misconception #3 Decimals: Applying whole number concepts to decimal numerals. As students move into studying decimal numerals as a form of fractions, they often try to apply whole number concepts, such as the number with more digits must be larger. This, however, doesn t work with decimals. This leads to difficulties in ordering decimals. Students may also try to align digits, instead of aligning the decimal points, when doing addition and subtraction. Some ideas to reinforce the understanding of decimals include Insist that students read and say decimals correctly. For example, 4.6 should be read as "four and six-tenths," not "four point six." Use models to represent decimal fractions. Base 10 blocks, 10x10 grids, money, and meter sticks offer a good variety and show connections between decimals and real life. Help students understand what moving the decimal point to the right or left means. For example, given the number 6.5, moving the decimal point one place to the right means that the resulting number is 10 times larger than the original one. Conversely, moving the decimal point one place to the left makes the number one-tenth of the original number. Reinforce place value by providing activities that help students name decimal numerals in multiple ways. For example, 52.4 represents five 10s, two 1s, and four tenths OR 52 1s and four tenths OR 524 tenths. Any activities that helps emphasize that the quantity a number represents is the product of its face value and its place value will help correct the misconceptions related to place value. Common Numbers Misconceptions Here are a couple of common misconceptions in the fractions domain.

9 Misconception #1 Equal Parts: Not understanding that fractions are equal parts of a whole. This misconception is displayed when a student says, I want the bigger half! As a result of this misconception, students may try to divide nontraditional shapes into equal parts in the same way that regular shapes, such as circles, squares, and rectangles, are divided. Or they may divide an object or set of objects into equal parts, also known as equipartitioning. This is a critical concept in mathematics and relates to not only fractions but also to multiplication, division, and measurement as well. Some ideas to help correct this misconception include Focusing on fractions as part of a whole or parts of a set in the early grades. Other interpretations of fractions as the result of division, as the ratio of two quantities and as operators, will be covered in middle school and later. Providing opportunities to talk about fractions and to use concrete models to deepen understanding. Varying the shapes that are divided into fractions; that is, use more than the traditional rectangles, squares, and circles/pizzas/pies, when dividing objects into equal parts. Expanding beyond halves, thirds, and fourths. Using grid paper for students to explore different ways of dividing shapes. The grid paper enables a student to confirm that each of the equal pieces of a whole are the same size (same area) even if the shapes are not consistent. Providing opportunities to solve word problems of the area (dividing an area equally) and set (evenly distributing a set of objects) models of fractions. (Bamberger & Oberdorf, 2010)

10 Misconception #2 Whole Numbers: Applying whole number concepts to fractions. There are several ways to identify this kind of misconception about fractions. For example, students may compare 1/4 to 1/3 and choose 1/4 as the larger fraction, because four is the bigger number. Students don t yet understand that larger the denominator, the smaller each of the parts of the whole. Or because they learned to add and subtract all of the digits of whole numbers, they try to add and subtract the numerators and the denominators in fractions. Another example of this misconception is when students think that multiplying two fractions together will always give a bigger number (Bamberger & Oberdorf, 2010). Some ideas to reinforce the understanding of fractions include Using the number line to represent fractions. It can be used to show the magnitude of fractions as well as to add and subtract fractions with like denominators. Giving students the opportunity to visualize and compare fractions. A common cause for these misconceptions is teaching procedures before students have a conceptual understanding of fractions. For example, students are recording fractions on paper with no understanding of what numerators and denominators actually stand for.

### Division with Whole Numbers and Decimals

Grade 5 Mathematics, Quarter 2, Unit 2.1 Division with Whole Numbers and Decimals Overview Number of Instructional Days: 15 (1 day = 45 60 minutes) Content to be Learned Divide multidigit whole numbers

### Understanding Place Value of Whole Numbers and Decimals Including Rounding

Grade 5 Mathematics, Quarter 1, Unit 1.1 Understanding Place Value of Whole Numbers and Decimals Including Rounding Overview Number of instructional days: 14 (1 day = 45 60 minutes) Content to be learned

### In the number 55.55, each digit is 5, but the value of the digits is different because of the placement.

FIFTH GRADE MATHEMATICS UNIT 2 STANDARDS Dear Parents, As we shift to Common Core Standards, we want to make sure that you have an understanding of the mathematics your child will be learning this year.

### Math Content by Strand 1

Math Content by Strand 1 The Base-Ten Number System: Place Value Introduction 2 Learning about whole number computation must be closely connected to learning about the baseten number system. The base-ten

### 5 th Grade Common Core State Standards. Flip Book

5 th Grade Common Core State Standards Flip Book This document is intended to show the connections to the Standards of Mathematical Practices for the content standards and to get detailed information at

### Common Core Standards for Mathematics Grade 4 Operations & Algebraic Thinking Date Taught

Operations & Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35

### Math Common Core Standards Fourth Grade

Operations and Algebraic Thinking (OA) Use the four operations with whole numbers to solve problems. OA.4.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement

### Division of Special Education LAUSD, June Grade 4 Math 156

Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as

### Mathematics Common Core Sample Questions

New York State Testing Program Mathematics Common Core Sample Questions Grade5 The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and

### Vocabulary, Signs, & Symbols product dividend divisor quotient fact family inverse. Assessment. Envision Math Topic 1

1st 9 Weeks Pacing Guide Fourth Grade Math Common Core State Standards Objective/Skill (DOK) I Can Statements (Knowledge & Skills) Curriculum Materials & Resources/Comments 4.OA.1 4.1i Interpret a multiplication

### Bedford Public Schools

Bedford Public Schools Grade 4 Math The fourth grade curriculum builds on and extends the concepts of number and operations, measurement, data and geometry begun in earlier grades. In the area of number

### Grade 5 Math Content 1

Grade 5 Math Content 1 Number and Operations: Whole Numbers Multiplication and Division In Grade 5, students consolidate their understanding of the computational strategies they use for multiplication.

### Just want the standards alone? You can find the standards alone at

5 th Grade Mathematics Unpacked Content This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these

### Progressing toward the standard

Report Card Language: form ordered pairs and graph the coordinates. CCSS: 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form

### COMMON CORE CROSSWALK

COMMON CORE CROSSWALK Grades K - 4 Mathematics Breakout Session January/February 2011 Missouri Department of Elementary and Secondary Education Agenda Common Focus CCSS Search What s common about the Mathematics

### Overview. Essential Questions. Grade 5 Mathematics, Quarter 3, Unit 3.2 Multiplying and Dividing With Decimals

Multiplying and Dividing With Decimals Overview Number of instruction days: 9 11 (1 day = 90 minutes) Content to Be Learned Multiply decimals to hundredths. Divide decimals to hundredths. Use models, drawings,

### Mathematics. Mathematical Practices

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with

### Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade

Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade The fourth-grade standards highlight all four operations, explore fractions in greater detail, and

### Grade 4 Multi-Digit Multiplication and Division with One Divisor Unit of Instruction

Grade 4 Multi-Digit Multiplication and Division with One Divisor Unit of Instruction This is a progressive unit of instruction beginning with students investigating the concrete area model of fraction

### BPS Math Year at a Glance (Adapted from A Story Of Units Curriculum Maps in Mathematics K-5) 1

Grade 4 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Add and subtract within 1,000,000 Module M1:

Common Core Coach Domain Progressions Common Core Coach covers the five domains identified by the CCSS for each grade. Domain Progressions are displayed for each domain, providing a clear visual roadmap

### CCSS-M Critical Areas: Kindergarten

CCSS-M Critical Areas: Kindergarten Critical Area 1: Represent and compare whole numbers Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such

### John Adair Intermediate 4th Grade Math Learning Targets I Can Statements..

John Adair Intermediate 4th Grade Math Learning Targets I Can Statements.. NUMBERS AND OPERATIONS IN BASE TEN 4.NBT Generalize place value understanding for multi-digit whole numbers. Explain how the base

### 4 th Grade Mathematics Unpacked Content

4 th Grade Mathematics Unpacked Content This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these

### Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers

### I have 15 apples to share between four friends and myself. We each get 3. So I have 5 groups of 3 apples. Dina Mendola CCLM^2 Project Summer 2012

Dina Mendola CCLM^2 Project Summer 2012 DRAFT DOCUMENT. This material was developed as part of the Leadership for the Common Core in Mathematics (CCLM^2) project at the University of Wisconsin-Milwaukee.

### Overview. Essential Questions. Grade 5 Mathematics, Quarter 3, Unit 3.1 Adding and Subtracting Decimals

Adding and Subtracting Decimals Overview Number of instruction days: 12 14 (1 day = 90 minutes) Content to Be Learned Add and subtract decimals to the hundredths. Use concrete models, drawings, and strategies

### Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter

Danville District No. 118 Mathematics Fifth Grade Curriculum and Scope and Sequence First Quarter Common Core Operations and Algebraic Thinking (5.OA) Common Core Number and Operations in Base Ten (5.NBT)

### A Correlation of. to the. Common Core State Standards for Mathematics Grade 4

A Correlation of to the Introduction envisionmath2.0 is a comprehensive K-6 mathematics curriculum that provides the focus, coherence, and rigor required by the CCSSM. envisionmath2.0 offers a balanced

### Mathematics Grade 5. Prepublication Version, April 2013 California Department of Education 32

Mathematics In, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions

### Grade 5 Mathematics Performance Level Descriptors

Limited Grade 5 Mathematics Performance Level Descriptors A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 5 Mathematics. A student at this

### AERO/Common Core Alignment 3-5

AERO/Common Core Alignment 3-5 Note: In yellow are the AERO Standards and inconsistencies between AERO and Common Core are noted by the strikethrough ( eeeeee) notation. AERO Common Core Mapping 1 Table

### Fraction Vocabulary. It is important that vocabulary terms are taught to students.

Rational Numbers Fractions Decimals Percents It is important for students to know how these 3 concepts relate to each other and how they can be interchanged. Fraction Vocabulary It is important that vocabulary

### COMMON CORE STATE STANDARDS FOR MATHEMATICS K-5 Overview

COMMON CORE STATE STANDARDS FOR MATHEMATICS K-5 Overview Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Kindergarten Counting and Cardinality Operations and Algebraic Thinking Number

### California Common Core State Standards Comparison- FOURTH GRADE

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics. Standards

### Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

### Grade 5 Common Core State Standard

2.1.5.B.1 Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. M05.A-T.1.1.1 Demonstrate an understanding that 5.NBT.1 Recognize

### Third Grade Common Core Standards & Learning Targets

Third Grade Common Core Standards & Learning Targets CCS Standards: Operations and Algebraic Thinking 3.OA.1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in

### Mathematics K-8 Critical Areas of Focus

Mathematics K-8 Critical Areas of Focus The Common Core State Standards (CCSS) for Mathematics include critical areas for instruction in the introduction for each grade, K-8. The critical areas are designed

### 1 BPS Math Year at a Glance (Adapted from A Story of Units Curriculum Maps in Mathematics P-5)

Grade 5 Key Areas of Focus for Grades 3-5: Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: Multi-digit multiplication Module M1: Whole

### Mathematics K-8 Critical Areas of Focus

Mathematics K-8 Critical Areas of Focus The Common Core State Standards (CCSS) for Mathematics include critical areas for instruction in the introduction for each grade, K-8. The critical areas are designed

### Progressing toward the standard

Report Card Language: add, subtract, multiply, and/or divide to solve multi-step word problems. CCSS: 4.OA.3 Solve multistep work problems posed with whole numbers and having whole-number answers using

### MISSOURI MATHEMATICS CORE ACADEMIC STANDARDS CROSSWALK TO MISSOURI GLES/CLES CONTENT ALIGNMENTS AND SHIFTS Grade 4 DRAFT

CONTENT ALIGNMENTS AND SHIFTS Grade 4 Grade 4 Critical Areas In Grade 4, instructional time should focus on three critical areas: 1. developing understanding and fluency with multi-digit multiplication,

### Fourth Grade Common Core State Standard (CCSS) Math Scope and Sequence

I= Introduced R=Reinforced/Reviewed Fourth Grade Math Standards 1 2 3 4 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 4.0A.1 - Interpret a multiplication

### IA_CCSS_Math Math (2011) Grade 5

IA_CCSS_Math Math (2011) Grade 5 5 In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of

### Grade 5 Math PA Core Standards - CC.2: PA Core: Mathematics. Eligible Content

Grade 5 Math PA Core Standards - CC.2: PA Core: Mathematics Eligible Content Standard Area - CC.2.1: Numbers and Operations Standard - CC.2.1.5.B.1: Apply place value to show an understanding of operations

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 2, Unit 2.1 Multiplying Multi-Digit Whole Numbers

Multiplying Multi-Digit Whole Numbers Overview Number of instruction days: 5 7 (1 day = 90 minutes) Content to Be Learned Use strategies based on place value and properties of operations to multiply a

### Grade 4 Mathematics, Quarter 4, Unit 4.3 Using Place Value to Add and Subtract Whole Numbers to the Millions. Overview

Whole Numbers to the Millions Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Round multi-digit whole numbers using understanding of place value. Recognize that the

### Standards for Mathematical Practice

Common Core State Standards Mathematics Student: Teacher: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively Standards for Mathematical Practice 3. Construct

### COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS

COMMON CORE STATE STANDARDS FOR MATHEMATICS 3-5 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 4, Unit 4.1 Dividing Whole Numbers With Remainders

Dividing Whole Numbers With Remainders Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Solve for whole-number quotients with remainders of up to four-digit dividends

### Robyn Seifert Decker

Robyn Seifert Decker UltraMathPD@gmail.com Place Value Addition Subtraction Problem Solving Fractions If time allows: Multiplication and Division Spiral of change From Prochaska, DiClemente & Norcross,

### SFUSD Mathematics Core Curriculum Development Project

1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own

### 4th Grade Topic 1 - Multiplication and Division: Meanings and Facts

4th Grade Topic 1 - Multiplication and Division: Meanings and Facts Approximately 9 days Standard Objective Notes 1-1 OA1 recognize multiplication as repeated addition G21, G22, G23, G35 1-2 OA5 use patterns

### 4 th Grade. Math Common Core I Can Checklists

4 th Grade Math Common Core I Can Checklists Math Common Core Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. I can interpret a multiplication equation

### DLM Mathematics Year-End Assessment Model Blueprint

DLM Mathematics Year-End Assessment Model 2014-15 Blueprint In this document, the blueprint refers to the range of Essential Elements (s) that will be assessed during the spring 2015 assessment window.

### Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Unit #4 : Division of Whole Numbers and Measurement

Background Information and Research By fifth grade, students should understand that division can mean equal sharing or partitioning of equal groups or arrays. They should also understand that it is the

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### 2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1

2013 Texas Education Agency. All Rights Reserved 2013 Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten Algebra I 1 The materials are copyrighted (c) and trademarked (tm)

### 4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS. Vocabulary. answers using mental computation and estimation strategies including rounding.

4TH GRADE FIRST QUARTER MATHEMATICS STANDARDS Critical Area: Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit

### Common Core State Standards for Math Grades K - 7 2012

correlated to the Grades K - 7 The Common Core State Standards recommend more focused and coherent content that will provide the time for students to discuss, reason with, reflect upon, and practice more

### GRADE 5 Common Core State Standards Critical Areas

GRADE 5 Common Core State Standards Critical Areas In Grade 5, instructional time should focus on three critical areas: (1)developing fluency with addition and subtraction of fractions, and developing

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### Vocabulary Cards and Word Walls Revised: June 2, 2011

Vocabulary Cards and Word Walls Revised: June 2, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

### Just want the standards alone? You can find the standards alone at http://corestandards.org/the-standards

4 th Grade Mathematics Unpacked Content For the new Common Core State Standards that will be effective in all North Carolina schools in the 2012-13 school year. This document is designed to help North

### Progressing toward the standard

Report Card Language: The student can fluently multiply and divide within 100. CCSS: 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and

### Operations and Algebraic Thinking Represent and solve problems involving multiplication and division.

Performance Assessment Task The Answer is 36 Grade 3 The task challenges a student to use knowledge of operations and their inverses to complete number sentences that equal a given quantity. A student

### COURSE OF STUDY UNIT PLANNING GUIDE

COURSE OF STUDY UNIT PLANNING GUIDE FOR: MATHEMATICS GRADE LEVEL: FOURTH GRADE PREPARED BY: TERESA KELLY AND TRACY BUCKLEY B.O.E. ADOPTED AUGUST 20, 2015 REVISED AUGUST 2015 ALIGNED TO THE 2014 NJCCCS

### CORE STANDARDS FOR MATH GRADE 5

5 TH GRADE CORE STANDARDS FOR MATH GRADE 5 2.1 NUMBERS AND OPERATIONS B Numbers and Operations in Base Ten CC.2.1.5.B.1 Apply place-value concepts to show an understanding of operations and rounding as

### Just want the standards alone? You can find the standards alone at

5 th Grade Mathematics Unpacked Content For the new Common Core State Standards that will be effective in all North Carolina schools in the 2012-13 school year. This document is designed to help North

### Georgia Standards of Excellence Grade Level Curriculum Overview. Mathematics. GSE Fifth Grade

Georgia Standards of Excellence Grade Level Curriculum Overview Mathematics GSE Fifth Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

### Overview. Essential Questions. Grade 4 Mathematics, Quarter 1, Unit 1.1 Applying Place Value Up to the 100,000s Place

to the 100,000s Place Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Compare whole numbers within 1,000,000 using >,

### Computation of Fractions

National Center on INTENSIVE INTERVENTION at American Institutes for Research Computation of Fractions 000 Thomas Jefferson Street, NW Washington, DC 0007 E-mail: NCII@air.org While permission to reprint

### Mathematics. Mathematical Practices

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with

### Grade 2. M4: and M:5 Addition and Subtraction of Numbers to 1000. M3: Place Value, Counting, and Comparison of Numbers to 1000

Grade 2 Key Areas of Focus for Grades K-2: Addition and subtraction-concepts, skills and problem solving Expected Fluency: Add and Subtract within 20 Add and Subtract within 100 Module M1: Mastery of Sums

### What Is Singapore Math?

What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has

### Collegium Charter School Grade 5 Math Scope & Sequence. Global Vision. We Use Math in Our Everyday Lives

Collegium Charter School Grade 5 Math Scope & Sequence Global Vision We Use Math in Our Everyday Lives Updated August 2015 Standards of Mathematical Practice (Habits of Mind) in 5th grade: 1. Make sense

September: UNIT 1 Place Value Whole Numbers Fluently multiply multi-digit numbers using the standard algorithm Model long division up to 2 digit divisors Solve real world word problems involving measurement

### Grade 5 Math Curriculum Guide

Grade 5 Math Curriculum Guide Lesson 1 1 st Nine Weeks Unit 1: Number and Operations in Base Ten Understand Place Value 5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents

### CCSS Mathematics Implementation Guide Grade 5 2012 2013. First Nine Weeks

First Nine Weeks s The value of a digit is based on its place value. What changes the value of a digit? 5.NBT.1 RECOGNIZE that in a multi-digit number, a digit in one place represents 10 times as much

### Eureka Math Tips for Parents

Eureka Math Tips for Parents Place Value and Decimal Fractions In this first module of, we will extend 4 th grade place value work to multi-digit numbers with decimals to the thousandths place. Students

### Key Instructional Shifts of the Common Core State Standards for Mathematics

Key Instructional Shifts of the Common Core State Standards for Mathematics Focus strongly where the Standards focus The Standards call for a greater focus in mathematics. Rather than racing to cover topics

### PA Common Core Standards Standards for Mathematical Practice Grade Level Emphasis*

Habits of Mind of a Productive Thinker Make sense of problems and persevere in solving them. Attend to precision. PA Common Core Standards The Pennsylvania Common Core Standards cannot be viewed and addressed

### Correlation to the Common Core State Standards. Math in Focus

Correlation to the Common Core State Standards Math in Focus Correlation to the Common Core State Standards Table of Contents Explanation of Correlation.......................... 1 Grade 1...........................................

### PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION ELEMENTARY MATH GRADE 2 MATH IN FOCUS

PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION ELEMENTARY MATH GRADE 2 MATH IN FOCUS Length of Course: Term Elective / Required: Required Schools: Elementary Student Eligibility:

### Graphic Organizers SAMPLES

This document is designed to assist North Carolina educators in effective instruction of the new Common Core State and/or North Carolina Essential Standards (Standard Course of Study) in order to increase

### Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on.

Year 1 Add with numbers up to 20 Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. +1 +1 +1 Children should: Have access to a wide

### Archdiocese of Newark Catholic Schools. Curriculum Mapping

Curriculum Mapping Curriculum mapping is a process that helps schools and districts/dioceses determine the agreed-upon learning for all students. Curriculum mapping was undertaken in the Archdiocese of

### Unit Descriptions USER GUIDE

LEARNING Unit Descriptions USER GUIDE Pre-K - KINDERGARTEN UNITS Counting Build 1 to 10 Optimally. Students build and identify numbers from static and flashed sets of 1 to 10 objects using the least number

### Parent Packet. HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1

Parent Packet HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1 http://www.hauppauge.k12.ny.us/math 2014 2015 School Year Grade 4 Module 1 Place Value, Rounding, and Algorithms for Addition and Subtraction

### Mathematics Grade 5 Year in Detail (SAMPLE)

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Whole number operations Place value with decimals Add and Subtract Decimals Add and Subtract Fractions Multiply and Divide Decimals

### Mathematics at PS 29. Presented by Molly Dubow, Hana Pardon and Kim Van Duzer

Mathematics at PS 29 Presented by Molly Dubow, Hana Pardon and Kim Van Duzer Agenda Introductions Try Some Math: Convincing a Skeptic Our Beliefs about Teaching Math at PS 29 Our Curriculum and Teaching

### Progressions for the Common Core State Standards in Mathematics (draft)

Progressions for the Common Core State Standards in Mathematics (draft) cthe Common Core Standards Writing Team 2 April 202 K 5, Number and Operations in Base Ten Overview Students work in the base-ten

### UNCOVERING STUDENT THINKING ABOUT MATHEMATICS IN THE COMMON CORE, GRADES 6 8. Estimating Quotients 2.1. Determine the best

28 UNCOVERING STUDENT THINKING ABOUT MATHEMATICS IN THE COMMON CE, GRADES 6 8 1. Determine the best estimate. 22.5 0.54 Estimating Quotients Explain your choice. 2.1 a. Between 4 and 5 b. Between 40 and

### Topic Skill Homework Title Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

Year 1 (Age 5-6) Number and Place Value Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Count up to 10 and back (Age 5-6) Count up to 20 objects (Age 5-6)

### Fourth Grade. Operations & Algebraic Thinking. Use the four operations with whole numbers to solve problems. (4.OA.A)

Operations & Algebraic Thinking Use the four operations with whole numbers to solve problems. (4.OA.A) 4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement