mathematics curriculum map€¦ · 3. compare and order numbers 4. round numbers 5. place value of...

MATHEMATICS CURRICULUM MAP

___4___ Grade

Table of Contents

Overview:

I. Best Practices II. Assessment III. Vocabulary IV. Timeline V. Online Resources for All Standards

Units by Standard:

Unit 1: Place Value of Whole Numbers and Decimals Unit 2: Addition and Subtraction of Whole Numbers and Decimals Unit 3: Multiplication of Whole Numbers Unit 4: Division of Whole Numbers Unit 5: All Operations Unit 6: Fractions Unit 7: Data Representations Unit 8: Measurement Unit 9: Geometry- Points, Lines, and Angles Unit 10: Geometry- Measuring Angles Unit 11: Making Connections Unit 12: Essential Understandings of Fractions

Unit 13: Essential Understandings of All Operations

Best Practices

● Small group ● Modeling ● Guided practice ● Independent practice ● Plans and teaches lessons to support full implementation of mathematics standards ● Supports mathematical communication (student’s ability to explain mathematical process) ● Common math vocabulary ● Uses assessment to support student learning and to guide planning ● Relating concepts to real life situations ● Incorporate word problems within units ● Use concrete examples and have students draw representations of concepts

Physical Environment and Classroom Climate Classroom environment supports mathematics learning. Classroom climate focused on student-centered learning. Math Words Wall Variety of Manipulatives UPS Check Poster Daily Language

Assessment

● Core Practice- Independent Work ● Activities – Showing Understanding ● Quizzes ● Pre/Post-Tests ● Common Assessment ● Observations

Vocabulary

value sum dimensions digit difference perpendicular whole number greatest parallel decimals least angles tenths multiplication measure hundredths division degree expanded notation remainders protractor numerals strip diagrams symmetry fraction equations vertices numerator unknown quantity polygons denominator input-output table volume > (greater than) number pattern mass < (less than) numerical expression data = (equal to) position frequency table addition values dot plot subtraction perimeter stem-and-leaf plot pictorial models area line plot number line rectangle

_____4____ Grade - Concepts

TEKS UNIT # TITLE SKILLS DURATION 4.2A 4.2B 4.2C 4.2E 4.2F 4.2H 4.3G

1 Place Value of Whole Numbers and Decimals

1. Place value through billions 2. 3 forms of numbers: standard, word, and expanded 3. compare and order numbers 4. round numbers 5. place value of decimals through hundredths 6. decimals on a number line 7. compare decimals 8. read and write decimals

10 days

4.2D 4.4A 4.4G 4.10B 4.10E

2 Addition and Subtraction of Whole Numbers and

Decimals

1. Addition 2. Subtraction 3. Add and subtract in word problems 4. Add and subtract money 5. Use estimation 6. Add and subtract decimal numbers 7. Fixed and variable expenses 8. Calculate profit

7 days

4.4B 4.4C 4.4D 4.4G 4.4H 4.5A

3 Multiplication of Whole Numbers

1. Multiplication as repeated addition 2. Square numbers 3. Facts through 10’s 4. Multiply up to a 4 digit number by 1 digit number using various methods 5. Multiply 2 digit by 2 digit numbers using various methods 6. estimation in multiplication

8 days

4.4E 4.4F 4.4G 4.4H 4.5A

4 Division of Whole Numbers 1. Division facts through 10 2. Multiplication and division fact families 3. Model division problems 4. Division word problems 5. Estimation in division problems

11 days

4.4A 4.4H 4.5A 4.5B 4.10A 4.10B

5 All Operations 1. Multi-step problems involving all four operations 2. Strip diagrams and equations with a letter standing for unknown quantity 3. Input/output tables 4. Fixed and variable expenses 5. Calculate profit

14 days

4.2G 4.3A 4.3B 4.3C 4.3D 4.3E 4.3F 4.3G

6 Fractions 1. Relate decimals to fractions that name tenths and hundredths 2. Represent a fraction as a sum of fractions 3. Decompose a fraction in more than one way into a sum of fractions with the same denominator 4. Equivalent fractions 5. Compare fractions 6. Solve addition and subtraction of fractions 7. Evaluate the reasonableness of sums and differences using benchmark fractions 8. Represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

18 days

4.9A 4.9B

7

Data Representations

1. Represent data on a frequency table, dot plot, or stem and leaf plot marked with whole numbers and fractions 2. Solve one and two step problems using data in whole numbers, decimal, and fraction form in a frequency table, dot plot, or stem and leaf plot

7 days

4.5C 4.5D 4.6A 4.8A 4.8B 4.8C

8 Measurement 1. Model perimeter formulas 2. Model area formulas 3. Measurement Benchmarks 4. Customary Units of Length 5. Customary Units of Weight 6. Customary Units of Liquid Volume 7. Mixed Measures 8. Problem Solving- Metric Units of Mass and Liquid Volume 9. Units of Time (Elapsed Time) 10. Add/Subtract, Multiply/Divide Money

14 days

4.6A 4.6B 4.6C 4.6D

9 Geometry- Points, Lines, and Angles

1. Lines, Rays, and Angles 2. Classify Triangles 3. Parallel and Perpendicular Lines 4. Classify Quadrilaterals 5. Symmetry

11 days

4.7A 4.7B 4.7C 4.7D 4.7E

10 Measuring Angles 1. Angles and Fractional Parts of a Circle 2. Degrees 3. Measure and Draw Angles 4. Join and Separate Angles 5. Problem Solving- Unknown Angle Measures

11 days

4.3E 4.4A 4.4H 4.5A 4.5B 4.5D 4.8C 4.9A 4.9B

11

Making Connections

1. Add/Subtract fractions, whole numbers, and decimals 2. One and two-step problems involving multiplication and division 3. Input/Output Tables 4. Area 5. Perimeter 6. Intervals of time 7. Mass 8. Frequency Tables 9. Dot Plots 10. Stem-and-Leaf Plots

14 days

4.2G 4.3A 4.3B 4.3C 4.3D 4.3E 4.3F 4.3G

12 Essential Understandings of

Fractions

1. Decimals to Fractions 2. Represent a fraction as a sum of fractions 3. Decomposing fractions 4. Finding Equivalent Fractions 5. Comparing Fractions 6. Adding/Subtracting Fractions 7. Reasonableness of fractions 8. Fractions and Decimals on a number line

15 days

4.4A 4.4H 4.8C 4.10A 4.10B 4.10C 4.10D

13 Essential Understandings of All Operations

1. Add/Subtract whole numbers, decimals, and fractions 2. One and two-step problems involving multiplication and division 3. Fixed and Variable Expenses 4. Profit 5. Savings Options 6. Spending/Saving/Sharing an Allowance

10 days

4.10E 7. Financial Institutions

Unit 1

Approximate Duration of Study: 10 days

TEKS Essential Question Concept Skills Assessments

Helpful Strategies and Resources

4.2A Why do digits in a number have

different values?

Place value of digits in a number

Recognize the place value of digits in numbers through

billions Recognize that a digit in one place value represents ten times its place to the right

Formative and

Common Assessment

s

Go Math 1.1

4.2B How many different ways can we use place value to write numbers?

Writing numbers in different

forms

Write numbers in standard form

Write numbers using words

Write numbers using expanded form Decimals- Model Tenths and Hundredths

Decimal Place Value

Go Math 1.2, 2.1, and 2.2

4.2C

How can we use place value to

compare and order numbers?

Compare and Order Numbers

Compare and Order Whole Numbers

Go Math 1.3

4.2E How can we represent decimals?

Represent Decimals

Represent decimals, including tenths and hundredths, using concrete and visual models and money.

Go Math 2.5

4.2F How can we compare and order

decimals?

Compare and Order Decimals

Compare and order decimals using

concrete and visual models to the hundredths.

Go Math 2.6 2.7

Vocabulary: Expanded Form, Decimals, Tenths, Hundredths Advanced Extensions:

Unit 2




4.2D How can we round whole numbers to a given place?

Rounding Whole Numbers

Round whole numbers to a given place

through the hundred thousands place.

Formative and

Common Assessment

s

Go Math 1.4

4.4A How can we add and subtract whole

numbers and decimals?

Adding and Subtracting

whole numbers and decimals

Add and Subtract whole numbers and decimals to the hundredths place using the standard

algorithm.

Go Math 6.1 6.2 6.3 6.4 6.5

4.4G How can we round

or use compatible numbers to estimate?

Rounding and using compatible

numbers to estimate

Round to the nearest 10, 100, or 1,000 or use compatible

numbers to estimate solutions involving whole numbers

Go Math 9.4

4.10B

4.10E

How can we find profit?

Profit Calculate profit in a given situation.

Go Math 18.2

What is the purpose of financial institutions?

Financial Institutions

Describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and

lending.

Go Math 18.5

Vocabulary: Advanced Extensions:

Unit 3




4.4B

4.4C

How can we determine

products of a number and 10 or

100?

Products of a number and 10

or 100

Determine products of a number and 10 or 100 using properties of operations and

place value understandings.

Formative and

Common Assessment

s

Go Math 7.1

How can we represent the product of 2 two-digit numbers?

Product of 2 two-digit numbers

Represent the product

of 2 two-digit numbers using arrays,

area models, or equations, including perfect squares through 15 by 15.

Go Math 8.3 8.4

4.4D

4.4G

How can we multiply up to a four-digit number by a one-digit number and

multiply a two-digit number by a

two-digit number?

Product of a four-digit number by one-digit and multiply a two-digit

number by a two-digit number

Use strategies and algorithms, including

the standard algorithm, to multiply up to a four-digit

number by a one-digit number and to

multiply a two-digit number by a two-digit number. Strategies include mental math, partial products, and the commutative, associative, and distributive properties.

Go Math 7.3 7.4 7.5 7.6 7.7 7.8 8.4 8.5 8.6 8.7

How can we estimate to find products?


numbers to estimate


numbers to estimate

Go Math 7.2 8.2

4.4H

How can we solve one and two-step problems involving multiplication?

Word Problems involving

multiplication

Solve with fluency one-and two-step problems involving

multiplication

Go Math 8.7

4.5A How can we represent multi-step problems for multiplication using strip diagrams and equations?

Strip diagrams and equations

for multiplication

Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity.

Go Math 11.3

Vocabulary: Product, Strip Diagrams, Equations, Round, Estimate, Compatible Numbers, Profit, Financial Institutions Advanced Extensions:

Unit 4




4.4E

How can we represent the quotient of up to a four-digit whole number divided by a one-digit whole number?

Representing quotients

Represent the quotient of up to a four-digit number divided by a one-digit whole number using arrays, area models, or equations.

Go Math 9.1 9.5

4.4F How can we divide up to a four-digit dividend by a

one-digit divisor?

Finding quotients using strategies and algorithms

Use strategies and algorithms, including

the standard algorithm, to divide up to a four-digit dividend by a

one-digit divisor.

Go Math 10.1 10.2 10.3 10.4 10.5

4.4G How can we estimate to find

quotients?


numbers to estimate


numbers to estimate

Go Math 9.4

4.4H

4.5A

How can we solve one and two-step problems involving division, including interpreting remainders?

Word Problems involving division

Solve with fluency one and two-step

problems involving division, including

interpreting remainders.

Go Math 9.2

How can we represent multi-step problems for division using strip

Strip diagrams and equations for division

Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a

Go Math 11.4

diagrams and equations?

letter standing for the unknown quantity.

Vocabulary: Quotient, Strip Diagrams, Equations, Round, Estimate, Compatible Numbers, Profit, Financial Institutions Advanced Extensions:

Unit 5




4.4A How do we use the standard algorithm to add and subtract whole numbers and decimals?

Add and subtract Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

Formative Assessment

s and Common

Assessments

Go Math 11.2- Addition

11.2- Subtraction

4.4H How do we solve one and two step problems involving

Multiplication and Division

Solve with fluency one and two step problems involving multiplication and

Go Math 11.3 and 11.4

multiplication and division?

division including interpreting remainders

4.5A

How do we represent multi-step problems involving the four operations?

Multi-step problems

Represent multi-step problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantity

Go Math 11.1 11.2 11.3 11.4

4.5B

How do we represent problems using an input-output table?

Input-output tables

Represent problems using an input-output table and numerical expressions

Go Math 12.1- Number

Patterns 12.2- Find a Rule

4.10A

How do we distinguish between fixed and variable expenses?

Fixed and variable expenses

Distinguish between fixed and variable expenses

Go Math 18.1

4.10B How do we calculate profit?

Profit Calculate profit in a given situation including whole numbers, decimals, addition, subtraction, multiplication and division

Go Math 18.2

Vocabulary: additive numerical pattern, counting numbers, decimal number, dividend, divisor, equation, expense, expression, factor, fixed expenses, fluency, income, input, input-output table, multiplicative numerical pattern, output, product, profit, quotient, sequence, strip diagram, trailing zeros, variable expenses, whole numbers Advanced Extensions:

Unit 6




4.2G How do we relate decimals to fractions?

Decimals to fractions

Relate decimals to fractions that name tenths and hundredths including whole numbers, decimals, fractions, various visual models, area models, decimal disks, base-10 blocks,

Formative and

Common Assessment

s

Go Math 2.3 and 2.4

money, and fraction language

4.3A

How do we represent a fraction as a sum of fractions?

Represent a fraction as a sum

of fractions

Represent a fraction a/b as a sum of fractions 1/b where a and b are whole numbers and b>0, including when a>b

Go Math 3.5

4.3B How do we decompose a fraction in more than one way into a sum of fractions?

Decompose a fraction into a sum of fractions

Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

Go Math 3.5

4.3C How do we determine if two fractions are equivalent?

Equivalent fractions

Determine if two given fractions are equivalent using a variety of methods (number line, area model, strip diagram, arithmetic method)

Go Math 3.1, 3.2, 3.3, 3.4

4.3D

How do we compare two fractions?

Compare Fractions

Compare fractions with different numerators and different denominators including benchmarks, common denominators, common numerators

Go Math 4.1 4.2

4.3E How do we represent and solve addition and subtraction of fractions?

Adding and Subtracting Fractions

Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations

Go Math 5.1, 5.2, 5.3, 5.5,

5.6, and 5.7

4.3F How do we evaluate the reasonableness of sums and

Evaluate reasonableness of sums and differences of fractions

Evaluate the reasonableness of sums and differences of fractions using benchmark fractions 0, ¼, ½, ¾, and 1,

Go Math 5.4

differences of fractions?

referring to the same whole

Vocabulary: associative property of addition, commutative property of addition, counting numbers, decimal number, denominator, equivalent fractions, fraction, improper fraction, least common denominator, least common multiple, mixed number, proper fraction, strip diagram, unit fraction, whole numbers Advanced Extensions:

Unit 7




4.9A How do we represent data?

Represent data Represent data on a frequency table, dot plot, or stem-and-leaf plot marked with

Formative and

Common Assessment

s

Go Math 17.1, 17.3, 17.5

whole numbers and fractions

4.9B How do we solve problems using

data?

Solve problems using data

Solve one and two step problems using data in whole number, decimal, fraction form in a frequency table, dot plot, or stem-and-leaf plot

Go Math 17.2, 17.4, and 17.6

Vocabulary: categorical data, data, dot plot, frequency table, numerical data, steam and leaf plot Advanced Extensions:

Unit 8


TEKS Essential Question

Concept Skills Assessments


4.5C How can we use

models to determine perimeter or

area?

Use models to find perimeter

and area

Calculate the perimeter and area of a rectangle using a formula Perimeter- (l+w+l+w or 2l+2w)

Area- (lxw)

Formative and

Common Assessment

s

Go Math 12.3, 12.4

4.5D How can we use our knowledge of measurements in real world situations?

Finding Perimeter and

Area

Apply formulas in real-life word problems

Go Math 12.5

4.8A

4.8B

What can we use to measure objects?

Understanding Measurement

Units

Recognize measurement units including

km,m,cm;kg,g;lb,oz;l,ml;hr,min,sec

Go Math 15.1, 15.2, 15.3, 15.4,

15.6

How can we compare units of measurement

together?

Converting measurements

Convert measurements from smaller units to larger units Record measurements in a

two-column table Ex. In, ft (1,12) (2,24), (3,36) etc.

Go Math 15.2, 15.3, 15.4, 15.6,

15.7

4.8C

How can we use our knowledge of measurement to solve word problems?

Solving measurement problems

Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction,

multiplication and division

Go Math 15.7, 16.1, 16.2, 16.3,

16.4

Vocabulary: perimeter, area, conversion, length, liquid volume, mass, weight, elapsed time Advanced Extensions:

Unit 9




4.6A What are the

different ways we can use lines in geometry?

Drawing lines Draw points, lines, line segments, and

rays Draw perpendicular and parallel lines

Formative and

Common Assessment

s


4.6B How can we find lines of symmetry?

Identifying lines of symmetry

Recognize a line of symmetry in a 2-D

figure Identify symmetrical

figures Draw lines of symmetry


4.6C 4.6D

How can we recognize two-dimensional figures?

Two-dimensional figures

Classify 2-D figures Classify triangles (acute,

right, and obtuse) Recognize polygons and

non-polygons Identify congruent and

similar figures


Vocabulary: Point, Line, Line Segment, Ray, Parallel, Perpendicular, Symmetry, Acute Triangle, Right Triangle, Obtuse Triangle, Polygon, Congruent Advanced Extensions:

Unit 10




4.7A

4.7B

How can we illustrate the measure of an

angle?

Angles and Fractional Parts of a Circle

Illustrate the measure of an angle as the part

of a circle whose center is at the vertex of the angle that is “cut out” by the rays

of the angle.

Formative and

Common Assessment

s

Go Math 14.1

How can we illustrate degrees in an angle?

Degrees used to measure an

angle

Illustrate degrees as the units used to measure an angle, where 1/360 of any circle is one degree

Go Math 14.2

4.7C

How can we measure an angle?

Measuring angles

Determine the approximate

measures of angles in degrees to the nearest


4.7D

whole number using a protractor

How can we draw an angle?

Drawing angles Draw an angle with a given measure

Go Math 14.3

4.7E How can we determine the measure of an unknown angle?

Measure of unknown angles

Determine the measure of an unknown angle formed by two non-overlapping

adjacent angles given one or both angle

measures

Go Math 14.4, 14.5

Vocabulary: Vertex, Protractor, Adjacent Angles Advanced Extensions:

Unit 11


TEKS Essential Question Concept Skills Assessments Helpful Strategies and Resources

4.3E

4.4A

How can we solve addition and subtraction of fractions?

Addition and Subtraction of Fractions with

Equal Denominators

Represent and solve addition and subtraction of

fractions with equal denominators using objects and pictorial

models.

Formative and

Common Assessments

Teachers Pay Teachers

SuperTeacher Worksheets

Mailbox Teacher Study Jams

How can we add and subtract whole

numbers and decimals?

Add/Subtract whole numbers and decimals

Add and Subtract Whole Numbers and Decimals to the Hundredths Place Using the Standard

Algorithm.

4.4H

How can we solve one and two-step

problems?



Solve with fluency one and two-step problems

involving multiplication and division, including

4.5A


How can we represent multi-step problems?

Multi-step problems

involving the four operations

Represent multi-step problems involving the four operations with whole numbers using strip diagrams and

equations with a letter standing for the

unknown quantity.

4.5B

4.5D

How can we represent problems

using an input-output table?

Input/Output Tables and Numerical Expressions

Represent problems using an input/output table and numerical expressions to

generate a number pattern that follows a

given rule.

How can we solve perimeter and area

problems?

Perimeter and Area

Solve problems related to perimeter and area of rectangles where dimensions are whole

numbers.

4.8C

How can we solve problems that deal with measurements of length, time, liquid volumes, mass, and money?

Measurements of Length Time

Liquid Volumes Mass Money

Solve problems that deal with

measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction,

4.9AB

multiplication, and division.

How can we represent data on a frequency table, dot plot, or stem-and-leaf plot?

Frequency Tables Dot Plots

Stem-and-leaf plots

Represent data on a frequency table, dot plot, or steam-and-leaf

plot marked with whole numbers and fractions. Solve one and two-step problems using data in these

plots.

Vocabulary: Numerator, Denominator, Decimal, Tenths, Hundredths, Remainders, Input/Output Table, Frequency Table, Dot Plot, Stem-and-Leaf Plot Advanced Extensions:

Unit 12




4.2G

4.3A

How can we relate decimals to fractions?

Decimals to Fractions

Relate decimals to fractions that name

tenths and hundredths.

Formative and

Common Assessment

s


Super Teacher Worksheets

Mailbox Teacher Study Jams

How can we represent a

Represent a fraction as a sum

of fractions

Represent a fraction a/b as a sum of

fractions, where a and

fraction a/b as a sum of fractions?

b are whole numbers and b>0, including

when a>b.

4.3B

4.3C

How can we decompose a fraction?

Decomposing fractions

Decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations

How can we determine if two fractions are equivalent?

Finding equivalent

fractions using a number line,

area model, strip diagram, and an

arithmetic method

Determine if two given fractions are equivalent using a variety of methods.

4.3D

How can we compare fractions?

Comparing Fractions

Compare two fractions with

different numerators and denominators and

represent the comparison using the symbols >, =, or <.

4.3E

How can we add and subtract fractions?

Adding and Subtracting Fractions

Represent and solve addition and subtraction of

fractions with equal denominators

4.3F

4.3G

How can we evaluate the reasonableness of fractions?

Reasonableness of fractions

Evaluate the reasonableness of

sums and differences of fractions using

benchmark fractions 0, ¼, ½, ¾, and 1,

referring to the same whole.

How can we represent fractions and decimals on a number line?

Fractions and Decimals on a number line

Represent fractions and decimals to the tenths or hundredths as distances from zero on a number

line.

Vocabulary: Decimal, Decompose, Equivalent, Reasonableness Advanced Extensions:

Unit 13




4.4A

4.4H

How can we add and subtract whole numbers and decimals?

Add/Subtract Whole Numbers and Decimals

Add and Subtract Whole Numbers and Decimals to the Hundredths Place Using the Standard

Algorithm.

Formative and

Common Assessment

s


Super Teacher Worksheets Study Jams

How can we solve one and two-step

problems?



Solve with fluency one and two-step

problems involving multiplication and division, including


4.8C

How can we solve problems that deal with

Measurements of Length Time

Solve problems that deal with

measurements of

4.10A

measurements of length, time, liquid volumes, mass, and money?

Liquid Volumes Mass Money

length, intervals of time, liquid volumes, mass, and money using addition, subtraction,

multiplication, and division.

How can we tell the difference between fixed and variable

expenses?

Fixed and Variable Expenses

Distinguish between fixed and variable

expenses.

Personal Financial Literacy Book from the Texas Council on Economic Education

4.10B

4.10C

How can we calculate profit?

Profit Calculate profit in a given situation.


How can we compare various savings options?

Various Savings Options

Compare the advantages and disadvantages of various savings

options.


4.10D

4.10E

How can we budget a weekly allowance?

Weekly Allowance including spending, saving, and sharing

Describe how to allocate a weekly allowance among

spending, saving, and sharing.


What is the basic purpose of

Financial Institutions

Describe the basic purpose of financial institutions, including

Personal Financial Literacy Book from

financial institutions?

keeping money safe, borrowing money, and

lending.

the Texas Council on Economic Education

Vocabulary: Fixed Expense, Variable Expense, Profit, Allowance, Financial Institutions Advanced Extensions:

Online Resources for All Standards

Interactive Sites for All Concepts examples shown; modify as appropriate

● www.studyjams.com ● www.khanacademy.org

Online Games for All Concepts

● www.reflexmath.com ● www.thinkthroughmath.com

ETC.

http://www.studyjams.com/

http://www.thinkthroughmath.com/

http://www.reflexmath.com/

http://www.khanacademy.org/

mathematics curriculum map€¦ · 3. compare and order numbers 4. round numbers 5. place value of...

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