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East Saint Louis District 189 Math Curriculum Grade 4

Sequence of Grade 4 Modules Aligned with the Standards

Module 1: Place Value of Whole Numbers 8 Days Module 2: Estimation and Number Theory 12 Days (including benchmark assessment) Module 3: Whole Number Multiplication and Division 17 days Module 4: Tables and Line Graphs 13 Days (including benchmark assessment) Module 5: Data and Probability 14 Days Module 6: Fractions and Mixed Numbers 20 Days (including benchmark assessment) Module 7: Decimals 15 Days Module 8: Adding and Subtracting Decimals 10 Days (including benchmark assessment) Module 9: Angles 9 Days Module 10: Perpendicular and Parallel Line Segments 9 Days Module 11: Squares and Rectangles 10 Days (including benchmark assessment) Module 12: Area and Perimeter 24 Days Module 13: Symmetry 10 Days Module 14: Tessellations 2 Days (including benchmark assessment)

Summary of Year Fourth grade mathematics is about (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions—concepts, skills, and problem solving Required Fluency: 4.NBT.4 Add and subtract within 1,000,000.

Adapted from Math In Focus


CCSS Major Emphasis Clusters Operations and Algebraic Thinking

Use the four operations with whole numbers to solve problems.

Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations – Fractions 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 decimal fractions.

Rationale for Module Sequence in Grade 4 Module 1 begins with a study of large numbers. Students are familiar with big units. For example, movies take about a gigabyte (1,000,000,000 bytes) to store on a computer while songs take about a megabyte (1,000,000 bytes). Place-value concepts are reviewed and extended to the ten thousands place. Students will compare numbers large numbers up to 100,000 and stating which number is greater or less. Students will be able to order a given set of numbers and identify patterns and relationships within patterns of numbers. Students will state a rule for number patterns and find missing numbers in the pattern.

Estimation is a critically important skill for students to quickly and accurately assess the reasonableness of their answers. Students will learn various methods of estimating in Module 2. Students will be introduced to factors, multiples, least common multiples, and greatest common factor. Students will make lists of factors to find the LCM and GCF. They are introduced to “double division” method by successively dividing two numbers by any common divisor. This will also help them to determine the LCM and GCF of two numbers.

In earlier grades, students learned their multiplication facts up to 10x10. In Module 2, students will extend their knowledge to multiplying and dividing multi-digit numbers. The place-value concept is used to facilitate understanding of multiplying with and without regrouping. Students will be able to multiply and divide in vertical form by the end of the module. Students should be comfortable with using the Commutative Property of Multiplication. Teachers should encourage the use of precise vocabulary in this chapter and review terms such as product, quotient, divisor and remainder. Students will apply their work in all four operations to solve real-world problems.

In primary grades, students learned to construct and analyze frequency tables, picture graphs, bar graphs, and line plots. They also used four operations to solve problems based on their graphs. In Module 4, students will continue this work by collecting and organizing data and interpreting line graphs and tables. Students will compare, analyze and classify data as they look for patterns and trends in the graphs.



Students are introduced to line graphs which have two numerical axes. Students will recognize that data flows continuously from left to right in preparation for their work with functions in middle school grades.

Students will use a variety of tools in Module 5 to analyze data, such as average, median and probability. Vocabulary will play a key role in helping students learn the new topics introduced throughout this module. Students will apply their understanding of place value and graphs to develop and use stem-and-leaf plots to find mean, median, mode and range. Students will learn to describe the possibility of the occurrence of different outcomes as a fraction. They will be given opportunities to solve real-world problems to check their understanding and ability to make projections based on the data they are given using different data representations.

In earlier grades, students learned to find equivalent fractions. In Module 6, students will learn how to add and subtract like and unlike fractions with and without renaming. They will be introduced to the concept of fractions of a set and will learn to apply this to real-world problems. Concrete materials are used extensively to illustrate the addition and subtraction of fractions. Students will learn correct vocabulary such as numerator and denominator to refer to their work with fractions. Students will learn to convert from improper fractions to mixed numbers and vice versa. Students will apply their knowledge of finding common factors and multiples to add and subtract unlike but related fractions. Bar models will be used to illustrate adding and subtracting real-world problems to help students visualize the problems they are solving.

In Module 7, students will learn to recognize, compare and round decimals in tenths and hundredths with the use of a number line. Students will be introduced to the meaning and concept of a decimal point and that the digits to the right represent fractional parts of a whole. Students will apply their knowledge of equivalent fractions to decimals through models and number lines. Students will develop an understanding of the rule to describe a sequence of decimals and complete sequences by studying number patterns.

Students will add and subtract decimals up to two places in Module 8. They will learn that the same algorithms for adding and subtracting whole numbers can be applied to decimal numbers. Students will review place value concepts of decimals to aid in working with regrouping in addition and subtraction of decimals. Bar models are a good way to translate the words in a problem into a visual picture from which students can decide what strategy to adopt to solve that problem. Students will extend that skill to drawing bar models for real-world problems with two-step decimal problems.

Students learn that angles can be seen everywhere around them. In Grade 3, students estimated the size of angles by comparing them to right angles. In Module 9, students learn how to estimate angle measures and measure angles with a protractor. They will learn to draw angles up to 180° using a protractor. Another important concept is turns and their relation to angle measure. Students will use the work from Grade 3 (congruence, slides, flips and turns) to relate right angles to fractions of a turn. In Module 10, students extend their knowledge of line segments and continue to explore parallel and perpendicular line segments. Students will learn to use a protractor or drawing triangle to draw perpendicular line segments when a grid is not provided. Students will also learn how to draw parallel line segments using a drawing triangle. Students will identify horizontal and vertical lines.



Students will learn the properties of squares and rectangles in Module 11. They will identify and define squares and rectangles based on their knowledge of angles and perpendicular and parallel line segments. Students will also learn to decompose shapes made up of square and rectangles. Students will learn to find the measures of adjacent angels of a right angle in a square or rectangle. They will also learn to find the side lengths of composite figures by using the properties of a square and rectangle.

In earlier grades, students learned to count grid squares to find the area of a figure. This is extended in Module 12 to find the area of a rectangle by using the formula. Students connect this model to the area model for multiplication. Students have previously learned to add the lengths of all the sides of a figure to find its perimeter. Students will apply what they have learned to find the perimeter of composite figures. They will also learn to find one side of a rectangle or square when given its perimeter or area. Students will be required to apply their knowledge of area and perimeter to solve real-world problems.

In Module 13, students learn to identify lines of symmetry of figures and to make symmetric shapes and patterns. This is a continuation of previous chapters on drawing, analyzing, comparing and classifying two-dimensional shapes based on attributes and properties. Students will solve problems involving congruence and symmetry. Students should be given many opportunities to experiment with making their own symmetrical shapes and identifying the line of symmetry. Students also learn to identify figures with rotational symmetry through hands-on activities.

Module 14 can be done if there is time. This is not a major focus of the Common Core Standards. Two days will be used for assessment for end of year. Those items on the assessment can be ignored or whited out.



Alignment ChartModule and Approximate Number of Instructional Days

Common Core Learning Standards Addressed in Grade 4 Modules

Vocabulary Number Talks and Instructional Strategies

Performance Based Tasks/ Assessments

Module 1: Place Value of Whole Numbers (8 days)

Do not forget Common Core Lesson 1.2a Page 276A and 1.2b from Page 276B

M.P. 1M.P. 4M.P. 6M.P. 7

Generalize place value understanding for multi-digit whole numbers. 4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Generate and analyze patterns. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way

Ten thousand,Hundred thousand,Standard form,Word form,Expanded form,Greater than >,Less than <,More than,Greatest, Least,Order,

Visuals; place value charts, place value disks; place value chart, number lineNumber lines help show the value of the numbers. Place value chart shows how to organize the digits – use place value chart to line numbers up vertically is a strategy to order several numbers. Place value strips are another tool to use.Use skip counting by 10, 100, 1000 from any given number forward and backward.Write number sequences - start with 4 digit number and show 5 terms in the sequence - increase by 10's, decrease by 100's, etc. Ask questions find the number that is 100 less than 20,000? 23,400 is how much more than 22,400? 89,341 is how much less than 99, 341? Find the number that is 10 less than 10,200.Key in on place value patterns, appropriate wording.



Module and Approximate Number of Instructional Days




Module 2: Estimation and Number Theory (12 days—includes 1 day for benchmark assessment.)

M.P. 1M.P. 2M.P. 3M.P. 6



4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.


Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation

Estimate,Reasonable,Front-end estimation,Rounding,Product,Quotient,Factor,Common factor,Greatest common factor,Prime number,Composite number,Multiple,Common multiple,Least common multiple

Place value disks are a valuable tool for showing relationships of the place values for 4.NBT.A.1.Find LCM and GCF of two numbers by making lists of multiples or factors.Then "double division" method - successively dividing both numbers by any common divisor, repeating processes, find all the common divisors (factors) of two numbers. Products of these common divisors is the GCF of 2 numbers. LCM of numbers is the product of the common divisors and the two numbers that remain.Extend the act hands-on activity.Students can use a laminated hundred grid with counters or markers. They can find the numbers that have a factor of two. With another color, find factors of 4. Are all numbers a factor of both 2 and 4? What patterns do you see? A







strategies including rounding.

Gain familiarity with factors and multiples. 4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite

strategy for finding a number that ends in 4 is choose a number, subtract 20 until you get a number that is divisible by 4. Then that number is divisible by 4.Find patterns of multiple and factors on the hundred board with 3, 6, 9, etc.

Module 3: Whole Number Multiplication and Division(17 days)

Additional Common Core Lessons for Chapter 3:Lesson 3.0 Pg. 276DLesson 3.1a Pg. 276ELesson 3.5a Pg. 276F

M.P. 4M.P. 5M.P. 6M.P. 7



4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place.


Round,Estimate,Product,Regroup,Rename,Quotient, Divisor, Dividend, Remainder

Multiplication as scaling is the big idea (not repeated addition). A key strategy is to make estimates for the problems first to build number sense before beginning any paper/pencil computation. Round to compatible numbers (related facts) or largest place value for students. Compatible numbers are especially important during the division section. Use the place value disks to begin all the operations. Keep working on number talks – multiplication and division with multiplication strings and one digit by 2 digit numbers.







4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Use the four operations with whole numbers to solve problems. 4.OA.A.1 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 many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Continue number talks that have students estimate these types of problems for the remainder of the year. You can also give students one or two problems a day to do paper and pencil to continue to practice.

Mastery of multi-digit multiplication and division is not an expected mastery until 5th and 6th grades. However, addition and subtraction of multi-digit numbers is an expected mastery.







Module 4: Tables and Graphs(13 days--includes 2 days for benchmark assessment)

M.P. 1M.P. 3M.P. 6M.P. 7

Build fractions from unit fractions.4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Represent and interpret data. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Data, Table,Tally chart,Row,Column,Intersection,Line graph,Horizontal axis,Vertical axis

This units is missing an important piece with line plots and fractions. http://www.mathworksheetsland.com/4/26measfrac/guided.pdf has a good lesson. Replace the Put on Your Thinking Cap with this activity. This will not affect your end of module assessment.

Module 5: Data and Probability(14 days)

M.P. 1M.P. 3M.P. 4M.P. 6

Extend understanding of fraction equivalence and ordering. 4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which

Average,Mean,Median,Mode,Range,Line plot,Stem and leaf plot,Outlier,Outcome,Certain, More likely,Equally likely,Less likely,

Even though probability and measures of central tendency are not specifically stated in the CCSS for mathematics, the lessons give practical application for operations with numbers. The unit connects measurements, fractions, and scaling. Do not extend this unit. .


http://www.mathworksheetsland.com/4/26measfrac/guided.pdf








remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Impossible,Favorable outcome,Probability

Module 6: Fractions and Mixed Numbers (20 days—includes 2 days for benchmark assessment) Additional Common Core Lessons for Chapter 6:Lesson 6.0 Pg. 276HLesson 6.7a Pg. 276ILesson 6.8a Pg. 276J

M.P. 2M.P. 3M.P. 4M.P. 6


4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions.4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations

Numerator, Denominator,Equivalent fraction,Unlike fraction,Mixed number,Simplest form,Improper fractionFraction bar,Division rule,Multiplication rule

Understanding fractions as a number is very important, not just as a part to a whole. Fraction is number of parts out of a total number of equal parts. Denominator represents ordinal numbers. Fractions are numbers, represent quantity amounts, can be shown on a number line, and can be used to perform operations. Estimation of fraction operations is important. Rely on the benchmark fractions students should master, 0, 1, ½, ¼, ¾.To reinforce that the fractions need like denominators, write addition of fractions as

16+ 26=1+26

=36

Simplifying the fractions can be done, but credit should be given if they have the appropriate fraction. Equivalent fractions are created by multiplying or dividing







and the relationship between addition and subtraction.

4.NF.B.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Solve problems involving measurement and conversion of measurements.4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

by another representation of 1. Remember to compose and decompose fractions just as you whole numbers, and using the fraction strips.Remember, in comparing fractions, a strategy can be to convert to the same numerator to help, i.e. 2/5 and 1/3. You can create an equivalent fraction for 1/3 which is 2/6. So you have 2/5 and 2/6. Which is bigger? Have students focus on the size of the unit fraction. Which is bigger 1/5 or 1/6?The standards give good examples of fraction operations.


http://www.corestandards.org/Math/Content/4/MD/A/2






Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Represent and interpret data. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Use the four operations with whole numbers to solve problems. 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Module 7: Decimals(15 days)

M.P. 1

Solve problems involving measurement and conversion of measurements.4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement

Tenth,Decimal form,Decimal point,Expanded form,Hundredth,Placeholder

Students need lots of practice with verbally reading the decimals numbers. Reinforce 2.3 as two and 3 tenths. Do not say point. As you work with renaming fractions and decimals, ask







M.P. 4M.P. 6M.P. 7

equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...




Build fractions from unit fractions.4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the

zero,More than,Less than,Greater than,Least, Greatest,Order, Round,Equivalent fraction

How many tenths are there in 0.4?How many tenths are there in 1?How many tenths are there in 1.4?How many tenths are there in 4?What is the decimal number for 42 tenths?Do the same types of questions as you move to hundredths.Continue with number talks with decimals and key on the students’ familiarity with money. Have students break up numbers into the different place values and write it in different representations. As,

4.6; 4 610 ; 4.60; 4

60100 .

Remember that the same strategies we used to make 100 will be used with decimals to make 1.







same whole.

Understand decimal notation for fractions, and compare decimal fractions. 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Generate and analyze patterns. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.







Module 8: Adding and Subtracting Decimals (10 days—includes 1 day for benchmark assessment) M.P. 1M.P. 4M.P. 7M.P. 8




Understand decimal notation for fractions, and compare decimal fractions. 4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with

There is a decimal game on page 30 that can be played throughout the unit. Change the rules to have students draw two cards and get the sum. Students can check on a calculator to see if they are correct.Number talks can include adding and subtracting with tenths and hundredths, as in the examples in the standards, i.e. 4/10 + 4/100.Practice in writing and saying the numbers can be included in this chapter also.







whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.


4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Module 9: Angles Draw and identify lines and angles, and Ray,

Vertex,Vocabulary journals will be very important in this module.







(9 days) Additional Common Core Lessons for Chapter 9:Lesson 9.3a Pg. 242ALesson 9.3b Pg. 242B

M.P. 2M.P. 3M.P. 5M.P. 6

classify shapes by properties of their lines and angles. 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Geometric measurement: understand concepts of angle and measure angles. 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

4.MD.C.5a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

4.MD.C.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an

Protractor,Degrees,Inner scale,Outer scale,Acute angle,Obtuse angle,Straight angle,Turn,Additive

You may need to play some vocabulary games each day, as riddles, guess my word, word wall categories, etc. The circle is a very important concept – having 360 degrees. The Babylonians may have decided on 360 since there was 360 days in their year. 360 is easily divisible by many factors which makes it easy to work with.Students should be able to measure to the nearest degree. Always have them look at an angle to estimate first, knowing it is obtuse, acute, right, etc.







equation with a symbol for the unknown angle measure.

Module 10: Perpendicular and Parallel Line Segments (9 days) M.P. 1M.P. 3M.P. 5M.P. 6

Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles

Perpendicular line segments,Drawing triangle,Parallel line segments,Base,Horizontal lines,Vertical lines

Having a real life picture from the internet of a railroad center, city, park, etc. where students can identify parallel and perpendicular lines is motivating for students Keep reinforcing the vocabulary from previous module. Number talks that use angles and lines will help students keep strategies for whole number operations.

Module 11: Squares and Rectangles (10 days—includes 2 days for benchmark assessment) M.P. 3M.P. 5M.P. 6M.P. 7

Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Solve problems involving measurement and conversion of measurements.4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb,

Square,Rectangle,Right angle,Parallel,

This module should embed previous 2 modules understandings and reasoning. Students should master appropriate notation of geometric shapes, angles, segments, etc..







oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...


Geometric measurement: understand concepts of angle and measure angles. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with







whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Module 12: Area and Perimeter - Measurement (24 days—includes 2 days for benchmark assessment) Additional Common Core Lessons for Chapter 12:

Lesson 12.0a Pg. 242DLesson 12.0b Pg. 242GLesson 12.0c Pg. 242ILesson 12.0 d Pg. 242K

M.P. 2



4.MD.A.3 Apply the area and perimeter formulas for

Length,Width,Composite figure,Area,Perimeter

Students need to memorize the area and perimeter formulas for a rectangle. This module embeds both metric and customary units. This materials should be mastered at this grade level.







M.P. 4M.P. 5M.P. 6M.P. 8

rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Use the four operations with whole numbers to solve problems. 4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Module 13: Symmetry

(10 days) M.P. 1M.P. 3M.P. 6M.P. 7

Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Generate and analyze patterns. 4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number

Line of symmetry,Symmetric figure,Rotation,Rotational symmetry,Center of rotation,Clockwise,Counter-clockwise,

Embed the properties of lines and angles that was studied in early modules. The students should be fluent with using the vocabulary to describe the symmetry.







1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Module 14: Tessellations (2 days for assessment)

If time permits, three websites could be useful. http://www.shodor.org/interactivate/activities/FloorTiles/ and http://www.shodor.org/interactivate/activities/Tessellate/ and http://nlvm.usu.edu/en/nav/frames_asid_163_g_2_t_3.html?open=activities&from=category_g_2_t_3.html.The sites have instructor ideas for lessons.

Key: Major Clusters; Supporting Clusters; Additional Clusters

Examples of Linking Supporting Clusters to the Major Work of the Grade

Gain familiarity with factors and multiples: Work in this cluster supports students’ work with multi-digit arithmetic as well as their work with fraction equivalence.

Represent and interpret data: The standard in this cluster requires students to use a line plot to display measurements in fractions of a unit and to solve problems involving addition and subtraction of fractions, connecting it directly to the Number and Operations — Fractions clusters.


http://nlvm.usu.edu/en/nav/frames_asid_163_g_2_t_3.html?open=activities&from=category_g_2_t_3.html



http://www.shodor.org/interactivate/activities/Tessellate/

http://www.shodor.org/interactivate/activities/Tessellate/

http://www.shodor.org/interactivate/activities/FloorTiles/

http://www.shodor.org/interactivate/activities/FloorTiles/

east saint louis district 189 math curriculum grade 4 web vieweast saint louis district 189 math...

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