third grade math curriculum project

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David Lynch 3rd Grade Math Curriculum Mapping Project

Introduction

Math skills are important, but not simply content knowledge. Concepts need to be understood

by students in order for them to succeed in math beyond the classroom. Moving them from th

concrete to the abstract in thought can be difficult, but not impossible. Engaging students by

showing them math in their own lives does not have to be scary. My third grade math

curriculum accomplishes all of these goals with very little heartbreak or strain.

An understanding of concepts versus content is like gauging your knowledge of electricity by

asking you to switch on a light switch. If you can turn the lights on in a room, then you must

know how the power gets through the house to the bulb. No? Well, what if I explain to you ho

the power moves through wires in the walls until it gets to the bulb? Could you draw a wiring

diagram for your house based on that knowledge? Then just because you can pick the correct

slice of pie in a question about fractions doesn’t mean you understand what to do with eight

screws when you have to hang four pictures. “All students need more engaging and relevant

math,” Wagner (2008). Relevancy goes beyond the test.

Tony Wagner (2008) asks, “How many students…do not understand math as a way of thinkin

about how to solve problems?” Students are being taught the content, but not how math applie

to the world around them, or when they will use it. Relevance is an old question asked by

students, so much so it has become a cliché: “Why do we need to know this? We’ll never nee

it!” I believe what we, as teachers need to do is answer that question with our teaching. Show




the students the math as it exists around them, and show them how and when it is used in real

situations.

If students see the use of math in their lives, it acquires relevancy, and if they understand the

concept, they will be able to pass the test and use what they know when problems surface In t

world outside of school. My curriculum becomes a pathway leading the students through the

standards in ways which help them see connections to their own lives, the usefulness of the

problem solving skills, and a transition from concrete thought to abstract.

Rationale

My curriculum map covers third grade math according to the Washington State standards

provided by OSPI in 2008. The map assumes the students are versed in some addition and

subtraction covered in second grade, but addition and subtraction are covered in a summarize

form at the beginning of the unit. Students are shown concrete examples of the math concepts

so they may see and hold them, engaging more than one sense. At the same time, students are

given examples from the world around them in order to emphasize the real world applications

and connections. One of the lessons involves the students building a grid out of math blocks;

it is described as a city block of houses or an apartment building, the students can grasp the

image more readily and it will stimulate engagement and relevancy.




Assessments

Assessments are used formatively throughout this unit to allow the learning to flow along at a

natural rate. Lessons should move from one to the next and seem interconnected because the

students should come to an understanding of this parallel to math itself. All math concepts are

interrelated, and the students should be given the opportunity to see this as they progress.

Answering the essential questions and showing each concept in more than one way are metho

the teacher may use to mark student progress. Remember, the emphasis here is on the student

understanding the concepts and being able to apply them in more than one way. Assessments

should bear this out.

Lessons

Many of the lessons included here were inspired by lessons in Using Manipulatives to Develo

Thoughtful Behavior in the Mathematics Classroom, edited by John Firkins. Assembled by th

Washington State Mathematics Council, this guide contains many more ways to help use

primary student’s concrete thought processes in the understanding of abstract math concepts.




The first sample lesson builds on the student’s use of addition and subtraction to give them

practice skip counting and counting by multiples. This will provide a transition from addition

multiplication as the students construct arrays out of equivalent sets of blocks: 2 blocks, 5

blocks, and 10 blocks.

Concept / Essential Question:What is skip counting?

How can I show skip counting?

Standards Addressed:

3.1.C Fluently and accurately add and subtractwhole numbers using the standardregrouping algorithms.

3.1.E Solve single- and multi-step word problemsinvolving addition and subtraction of whole

numbers and verify the solutions

General Goal(s):

Use skip counting to solve various problems.

Use arrays to represent skip counting.

Specific Objectives:

Students will create arrays beginning with two blocks and adding 2 more at a time to build an array.

Required Materials:

Connecting Blocks or flat shapes could both be used here. The idea is to have the students see and touc

the multiple numbers of items as they add them.

Anticipatory Set (Lead-In):




Teacher David has a line of students and their partners. In order to count them quickly he counts each

set of partners as one. Put ten pairs of students (blocks) together, how many students are in ten pairs?

Step-By-Step Procedures:

Whichever set of manipulatives are being used allow time for the students to become comfortable with

them before beginning the lesson. Time for exploration will aid in the learning process and improve

engagement and discipline.

Assessment:

Once the students have built the required pairs construction, ask them to build, and count, with sets of

five, and ten, also give different story problems to increase concept versus content comprehension.

Extensions:

This concept can be taken to another level by asking the students to make a square with the smallest

number of square shapes or blocks (one). Next, ask them to find the next number of blocks to make a

bigger square (four). Continuing in this way, a connection can be made to multiplication (each of the

square arrays is a line of multiples), and the concept of the square number.




The second lesson extends from the multiples in arrays to the same patterns as multiplication.

may take nothing at all to move from skip counting to multiplication, or it may take some in-

between lessons. The important thing to remember is that varying the materials or varying the

types of problems the students must answer will emphasize the concept. Don’t lock the

student’s thinking into a particular material or a standard question; it is important for them to

see the universal nature of math in the world and the numerous connections between math

concepts.

Concept / Essential Question:How can I show multiplication in an array?

How can I use multiplication to solve a problem?

Standards Addressed:

3.2.A Represent multiplication as repeated addition, arrays, counting by

multiples, and equal jumps on the number line, and connect eachrepresentation to the related equation.

3.2.H Solve single- and multi-step word problemsinvolving multiplication and division and verifythe solutions.

General Goal(s):

Understand how skip counting and arrays correspond to the concept of multiplication.

Specific Objectives:

Students will create arrays and use them to express multiplication.

Required Materials:




Counting blocks and shapes could be used in this lesson as well, but to reinforce the concept over conte

theme, another manipulative would be recommended. Something such as: a paper folded into multiple

squares, or any small items which could be laid out in a grid pattern.

Anticipatory Set (Lead-In):

An apartment building is laid out in a grid five apartments high and five wide; how many families coul

live here? Or, a garden is set up in five rows and five columns, how many different seeds could be

planted?

Step-By-Step Procedures:

Encourage the students to explore the design and patterns and to discover how much Area the grid

covers (multiplication). Also, ask them to “walk the perimeter” of the garden to determine how big

around it is.

Assessment:

Ask the students how this lesson compares to the arrays they built earlier. Ask them to build different

combinations of grids and write out the multiplication model (5 X 5 = 25).

Extensions:

Deconstruction of the grids in rows or multiples can introduce the concept of division. Furtherdeconstruction into individual pieces can enhance the general concept of division as sharing.




Unit_____Multiplication and Fractions___________ Month_________ Grade 3

Essential

Questions

Content/Standards Skills Activities Assessments

How can knowingthe addition and

subtraction facts

help me?

What is skip

counting?

How can I show

skip counting?

When would I skip

count to solve a

problem?

3.1. Core Content: Addition, subtraction,and place value

3.1.C Fluently and accuratelyadd and subtractwhole numbers using thestandardregrouping algorithms.

3.1.E Solve single- and multi-step word problemsinvolving addition andsubtraction of wholenumbers and verify thesolutions.

Students Will: createarrays beginning with two

blocks and adding 2 more

at a time to build an array.

They will then do the samewith 5 blocks and 10

blocks.

SWBAT: Use skipcounting to solve various

problems.

Use arrays to represent

skip counting.

How can knowing

Multiplication help

me?

How can I show

multiplication in

an array?

How can I use

multiplication tosolve a problem?

3.2. Core Content:Concepts of

multiplication and division

3.2.A Representmultiplication as repeatedaddition, arrays, counting bymultiples, and equal jumpson the number line, andconnect each representationto the related equation.

3.2.H Solve single- andmulti-step word problems

involving multiplication anddivision and verifythe solutions.

3.6. Core Processes:Reasoning, problemsolving, and communication

3.6.A-H (Processes are usedto carry out and reflect on

Students Will: Create

arrays and use them to

express multiplication.

SWBAT: Understand how

skip counting and arrays

correspond to the conceptof multiplication.




the activities.)

How can knowingMultiplication help

me?

When would I use

multiplication tosolve a problem?

3.2. Core Content:Concepts of multiplication and division

3.2.C Determine products,quotients, and missingfactors using the inverserelationship betweenmultiplication and division.3.2.D Apply and explainstrategies to computemultiplication facts to 10 X10 and the relateddivision facts.3.2.E Quickly recall thosemultiplication facts forwhich one factor is 1, 2, 5, or10 and therelated division facts.3.2.F Solve and create wordproblems that matchmultiplication or divisionequations.

Students Will: Practicemultiplication with

numbers and word problems.

SWBAT: Discover the

reverse relationshipmultiplication has with

division.

How can knowing

Division help me?

How can I show

Division in an

array?

How can I use

Division to solve a

problem?

3.2. Core Content:Concepts of

multiplication and division

3.2.B Represent division asequal sharing, repeatedsubtraction, equal jumps onthe number line, andformation of equal groups of objects,and connect eachrepresentation to the relatedequation.

3.2.H Solve single- andmulti-step word problemsinvolving multiplication anddivision and verifythe solutions.


Students Will:

Deconstruct their arrays

and use them to expressdivision.

SWBAT: Understand theconcept of sharing and

how it relates to division.




3.6.A-H (Processes are usedto carry out and reflect onthe activities.)

How can knowingDivision help me?

When would I use

Division to solve a

problem?

3.2. Core Content:Concepts of multiplication and division

3.2.C Determine products,quotients, and missingfactors using the inverserelationship betweenmultiplication and division.3.2.D Apply and explainstrategies to computemultiplication facts to 10 X10 and the relateddivision facts.3.2.E Quickly recall thosemultiplication facts forwhich one factor is 1, 2, 5, or10 and therelated division facts.3.2.F Solve and create wordproblems that matchmultiplication or divisionequations.

Students Will: Practicedivision with numbers and

word problems.

SWBAT: Begin to

understand fractionalconcepts.

How can I use

fractions in reallife?

How can I show anunderstanding of

fractions (from

1/12ths to 1/2)?

How can I explain

the meaning of a

fraction and its

numerator anddenominator?

How can I use my

understanding to

represent and

compare fractions?

3.3. Core Content:Fraction concepts

3.3.A Represent fractionsthat have denominatorsof 2, 3, 4, 5, 6, 8, 9, 10, and12 as parts of a whole, parts of a set, andpoints on thenumber line.3.3.B Compare and orderfractions that havedenominators of 2, 3, 4, 5, 6,8, 9, 10, and 12.3.3.C Represent and identifyequivalent fractions withdenominators of 2, 3, 4, 5, 6,8, 9, 10, and 12.3.3.D Solve single- andmulti-step word problemsinvolving comparison of fractions and verifythe solutions.

3.5. Additional Key Content

Students Will: Use paper

folded into fractional

columns and rows to seethe concept of division.

SWBAT: Understand andexplain the concept of

fractions and their

comparisons.




3.5.A Determine whethertwo expressions are equaland use “=” to denoteequality


3.6.A-H (Processes are usedto carry out and reflect onthe activities.)

References

Wagner, T. (2008). The Global Achievement Gap: Why Even Our Best Schools Don’t Teach t

New Survival Skills Our Children Need – and What We Can Do About It . New York: Perseus

2010.

Washington State Mathematics Council. (1990). Using Manipulatives to Develop Thoughtful

Behavior in the Mathematics Classroom. Spokane: WSMC. 1990.

third grade math curriculum project

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