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.
CCSS Major Emphasis Clusters
Operations and Algebraic Thinking
- Use the four operations with whole numbers to solve problems.
- Generalize place value understanding for multi-digit whole numbers.
- Use place value understanding and properties of operations to perform multi-digit arithmetic.
- 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 Chart
Module 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. 1
M.P. 4
M.P. 6
M.P. 7 /
Generalize place value understanding for multi-digit whole numbers.
4.NBT.A.1Recognize 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.2Read 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 line
Number 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 2: Estimation and Number Theory
(12 days—includes 1 day for benchmark assessment.)
M.P. 1
M.P. 2
M.P. 3
M.P. 6 /
Generalize place value understanding for multi-digit whole numbers.
4.NBT.A.1Recognize 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.2Read 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.
4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.
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.
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.
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 / 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 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. 276D
Lesson 3.1a Pg. 276E
Lesson 3.5a Pg. 276F
M.P. 4
M.P. 5
M.P. 6
M.P. 7 /
Generalize place value understanding for multi-digit whole numbers.
4.NBT.A.1Recognize 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.2Read 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.
4.NBT.A.3Use place value understanding to round multi-digit whole numbers to any place.
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.
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. / 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.
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. 1
M.P. 3
M.P. 6
M.P. 7 /
Build fractions from unit fractions.