# Millburn Math Curriculum Focus Points

**Orange School District**

Mathematics

Grades 3-5

**Curriculum Guide **

2010 Edition

**APPROVED ON:______**

## BOARD OF EDUCATION

Patricia A. ArthurPresident

Arthur Griffa

Vice-President

Members

Stephanie Brown / Rev. Reginald T. Jackson / Maxine G. Johnson

Eunice Y. Mitchell / David Wright

**SUPERINTENDENT OF SCHOOLS**

Ronald Lee

DEPUTY

SUPERINTENDENT /

**ADMINISTRATIVE ASSISTANT**

**TO THE SUPERINTENDENT**

Dr. Paula Howard

### Curriculum and Instructional Services

/ Belinda Scott-Smiley### Operations/Human Resources

**BUSINESS ADMINISTRATOR**

DIRECTORS

Barbara L. Clark, Special Services

Candace Goldstein, Special Programs

Candace Wallace, Curriculum & Testing

**Curriculum Contributors**

Candace Wallace

Ron Nelkin

Maria Pankin

James DeLoatch

Meghan Barrios

**BOARD OF EDUCATION 6**

Philosophy 4

Vision 4

Purpose 5

**Math Focus Points 6**

Blueprint 10

**Mathematics Curriculum Guide**

Grades 3-5

Philosophy

The philosophy upon which the Mathematics Curriculum Guide is to encourage and support the enjoyment of learning mathematics, as a way to make sense of the world in students’ everyday lives. Mathematics is everywhere, from the practicalities of counting, to find easier ways of organizing numbers and data to model and represent daily life experiences. Mathematics involves other disciplines, and is a way in which ideas are communicated, such as in tables and graphs.

Mathematics is developmental by nature. Therefore it is important that should any concerns arise related to mathematics understanding, that this is communicated with the student’s teacher as soon as possible. There are varied approaches used to teach and learn mathematics, which is referred to as a balanced mathematics approach. This includes traditional algorithms to approaching the study of mathematics that have been used for many years, along with newer and varied approaches, to provide multiple representations to model solving a problem.

The study of mathematics provides pathways to higher level thinking skills. As students learn mathematics, specialized terminology assist their development. This enables students to not only learn mathematics in a routine way, but to enable them to become problem solvers in novel situations, able to draw on a repertoire of skills and approaches.

We hope these beliefs will assist students to develop their understanding to use mathematics to make meaning, as well as to promote their critical thinking and development as lifelong learners. The goals are to promote problem-solving, and communication, to foster an understanding of the world, that has a conceptual foundation in the study of mathematics.

Vision

In Orange, we recognize that each student is unique and that the purpose of education is to enable every student to acquire the learning skills necessary to compete in the global community. It is essential that we provide a rigorous, high-quality Mathematics curriculum that allows each student’s talents and abilities to be developed to their full potential.

Purpose

The Curriculum Guide was prepared by teachers and administrators with input from consultants who have expertise in Mathematics. Students and parents are welcome to read, review, and ask questions about the curriculum, to understand what they and their children are learning.

The Mathematics Curriculum Guide is based on an alignment with the New Jersey Core Content Curriculum Standards, and the Common Core State Standards which are a national set of shared standards which adopted by over 30 states. It is also based on national standards shared through the National Council of Teachers of Mathematics, which develops agreed upon content at each grade level, referred to as Curriculum Focal Points.

Content was designed with a student development perspective across each grade, as well as a vertical articulation, with spirals learning upward, based on the foundation that is developed. Mathematics is developmental in nature, so that it is important for students and parents to address any learning needs with the student’s teacher as soon as possible.

A curriculum must include assessment, as evidence of learning. Assessments are both formative and summative, and may include culminating projects related to a topic or unit, as well as traditional and standardized testing.

**Math Focus Points**

## Grade 3

Numbers and Operations – Students develop an understanding of multiplication and division, and strategies for basic multiplication facts.

· Review Grade 2 Goal: Add and subtract numbers of up to 3-digit numbers·

**Understand the meaning of multiplication (e.g. equal groups, seeing different models, repeated addition, proportional relationship)**

· Understand how multiplication and addition differ

· Know where multiplication is used

· Know how the product increases when the multiplier increases by 1

· Understand the concept of the multiplier and multiplicand (know how many groups and how many items in a group)

· Use properties of addition and multiplication to multiply whole numbers (associative, commutative, distributive property, property of zero)

·

**Practice recall of 1-digit multiplication facts with cards and games to mastery**

· Multiply 2-digit by 1-digit numbers

· Understand the meaning of division (partitive and quotitive)

· Divide 2-digit by 1-digit numbers as related to multiplication facts

· Understand the meaning of fraction as a unit

· Understand commonly used fractions as part of a whole, part of a set, and on the number line

· Read and write numbers up to 1,000,000

· Units and relative size of numbers up to 1,000,000

· Understand the relative size of large numbers

· Understand the meaning and structure of decimal notation system

· Construct and solve simple open sentences involving addition and subtraction

Geometry and Measurement – Students deepen their understanding of linear measurement. Students describe and analyze properties of 2-d shapes.

· Identify and describe many plane and solid figures (rectangle, square, triangle, circle, hexagon, octagon, pentagon, and cube, rectangular prism, sphere, cylinder, cone, pyramid)· Know about triangles and quadrilateral by examining the elements that compose the figures

· Draw basic geometric shapes (square, rectangles, triangles, right

· triangles)

· Understand properties of right angles

· Understand elements that compose 3-d solids by observing and making figures

· Measure length to the 1/2 inch, inch, foot, yard and cm, mm, meter

· Determine area by counting square units

· Describe relationships among units of length

· Describe relationships among units of time

· Tell time to the minute

Process Standards- Students use mathematical processes to solve problems and communicate mathematical ideas. These processes are embedded in the goals above.

· Write and interpret number sentences· Write two-step problem in one number sentence

· Explain strategies and present ideas to class

### · Listen and apply others’ strategies

## Grade 4

Number and Operation and Algebra – Students continue to practice quick recall of multiplication facts. Students develop recall of related division facts and fluency with multi-digit multiplication.

Review Grade 3 Goals:

· Practice recall of 1-digit multiplication facts with cards and games to mastery### · Multiply 2-digit or 3-digit numbers by 1-digit numbers

In addition:

· Multiply 2-digit or 3-digit numbers by 2-digit· Understand the meaning of division with larger numbers (e.g. finding the unit, seeing different models, repeated subtraction, ratio relationship, opposite of multiplication)

· Know where division is used

· Understand the two types of division and how remainder is involved

· Understand the meaning of dividend, divisor, and quotient

### · Practice recall of basic division facts with cards and games to mastery

### · Divide 2-digit or 3-digit numbers by 1-digit numbers with remainder

### · Understand the meaning of fraction as a unit

### · Notice commonly used fractions as part of a whole, part of a set, and on the number line

### · Know how to order/compare fractions by finding equivalent

### · Read and write numbers up to 1,000,000,000 and decimals to thousandths

### · Understand the units and relative size of numbers up to a billion and decimals to thousandths

· Do simple calculations with money

· Describe and extend patterns

· Understand and apply properties of operations and numbers

· Use concrete and pictorial models to explore basic concept of functions

· Understand relationship between two quantities (ex. function machines)

Geometry and Measurement – Students deepen their understanding of linear measurement. Students describe and analyze properties of 2-d shapes.

· Use properties of 3-d and 2-d shapes to identify, classify, and describe them· Understand and apply concepts involving lines, angles, and circles

· Understand parallel and perpendicular lines

· Experience simple transformations (slide, flip, turn)

· Locate and name points on a grid

· Select and use appropriate standard units of measure and measurement tools to solve problems

· Use strategies to estimate measurements

· Draw and construct basic shapes with tools (compass and protractor)

· Solve problems using elapsed time

· Distinguish between perimeter and area to solve problems

· Measure and compare volume of 3-d objects using cubes

Process Standards- Students use mathematical processes to solve problems and communicate mathematical ideas. These processes are embedded in the goals above.

· Write and interpret more complex number sentences· Explain strategies and present ideas to class

· Listen and apply others’ strategies

· Understand multiple strategies

## Grade 5

Number and Operation and Algebra – Students develop an understanding of and fluency with division of multi-digit whole numbers, and addition and subtraction of fractions and decimals.

· Review Grade 4 Goal: Practice recall of basic division facts with cards and games to mastery· Divide 2-digit or 3-digit numbers by 2-digit numbers with remainder

· Convert improper and proper fractions

· Add and subtract fractions with like and unlike denominators

· Add and subtract decimals numbers

· Estimate with large numbers

· Develop and apply number theory concepts (prime, factors, and multiples)

· Describe and apply order of operations

· Describe, extend, and create patterns using tables, verbal rules, simple equations, and graphs

· Describe arithmetic operations as functions

· Use number sentences to model situations (use variable for unknown)

· Solve simple linear equations with manipulatives and informally

Geometry and Measurement – Students describe 2-d and 3-d shapes and analyzing their properties, including volume and surface area.

· Relate 2-d and 3-d shapes and analyze their properties· Understand how to find volume

· Understand how to find surface area

· Develop and apply strategies and formulas for perimeter and area (Rectangles)

· Understand and apply concepts involving lines and angles (Parallel, perpendicular, intersecting, sum of interior angles in a triangle)

· Identify, describe, compare, and classify polygons

· Map one figure to another congruent figure using translation, reflection, or rotation

· Create shapes on a coordinate grid in the first quadrant

· Calculate area of rectangles, parallelograms, triangles, and volume of a prism using formulas

· Select and use appropriate units to measure angles and area

· Convert measurement within a system

· Measure and construct figures using tools (compass and protractor)

Process Standards- Students use mathematical processes to solve problems and communicate mathematical ideas. These processes are embedded in the goals above.

· Write and interpret more complex number sentences· Explain strategies and present ideas to class

· Listen and apply others’ strategies

· Understand and connect multiple strategies

60

GRADE 3**Numbers, Number Systems and Number Relationships**

A. Count using whole numbers (to 10,000) and by 2’s, 3’s, 5’s, 10’s, 25’s and 100’s.

B. Use whole numbers and fractions to represent quantities.

C. Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols.

D. Use drawings, diagrams or models to show the concept of fraction as part of a whole.

E. Count, compare and make change using a collection of coins and one-dollar bills.

F. Apply number patterns (even and odd) and compare values of numbers on the hundred board.

G. Use concrete objects to count, order and group.

H. Demonstrate an understanding of one-to-one correspondence.

I. Apply place-value concepts and numeration to counting, ordering and grouping.

J. Estimate, approximate, round or use exact numbers as appropriate.

K. Describe the inverse relationship between addition and subtraction.

L. Demonstrate knowledge of basic facts in four basic operations. /

**Students understand different representations of numbers, the relationship between/among numbers and number systems.**

1. Know and understand verbal names, written names and standard numerals for whole numbers through hundred thousands or more, as well as common decimals, fractions, and percents.

2. Understand and work with whole numbers through hundred thousands, commonly used fractions, and decimals.

3. Know that two numbers in different forms are

equivalent or non-equivalent using whole numbers, fractions, and decimals in the context of money.

4. Recognize and represent equivalent forms of

fractions, decimals, and percents.

5. Understand place value in base ten system to include decimals up to hundredths.

6. Know the place value of digits in numbers to 100,000 and more, including writing expanded forms of numbers.

7. Explore numbers less than zero.

8. Recognize other number systems and

compare these to the Decimal System, including the Roman Numeral System, using numerals I, V, X, L, and C.

**NS4: Students make reasonable estimates**

1. Understand the various strategies used for estimating numbers

2. Justify verbally and in writing estimation choices for real world problems

3. Estimate quantities of objects to 300 or more / By the end of 3rd grade students will be able to:

Read, write, and identify whole numbers through hundred

thousands or more.

Write story problems using whole numbers through hundred thousands or more.

Use real-life experiences, physical materials, and

technology to construct meanings for numbers (unless

otherwise noted, all indicators for grade 3 pertain to these

sets of numbers as well) with 80% accuracy

· Whole numbers through hundred thousands

· Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line

Demonstrate an understanding of whole number place

value concepts with 85% accuracy

Identify whether any whole number is odd or even with 90% accuracy

Explore the extension of the place value system to decimals

through hundredths.

Understand the various uses of numbers

· Counting, measuring, labeling (e.g., numbers on baseball uniforms)