Module 1
Number Sense and Operations
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Place Value: Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. Read and write numbers to 1,000,000 using base-ten numerals, number names, and expanded form.
Compare and Order Numbers: Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Order numbers from least to greatest or greatest to least.
Rounding: Round multi-digit whole numbers to any place using the vertical number line method.
Addition and Subtraction: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Multiplication: Multiply a four-digit number by a one-digit number and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain multiplication using equations, rectangular arrays, and area models.
Division: 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 the relationship between multiplication and division.
Factors and Multiples: Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Find all factor pairs for a whole number in the range 1–100.
This module covers understanding place value, comparing and operating on multi-digit numbers, and working with factors and multiples.
Learning Objectives
- Understand place value for multi-digit whole numbers
- Compare and order multi-digit whole numbers
- Round multi-digit whole numbers to any place
- Fluently add and subtract multi-digit whole numbers
- Multiply a four-digit number by a one-digit number and two two-digit numbers
- Find whole-number quotients and remainders with four-digit dividends and one-digit divisors
- Determine factors and multiples for whole numbers 1-100
Key Topics
Place Value
Comparing and Ordering Numbers
Rounding Numbers
Addition and Subtraction
Multiplication
Division
Factors and Multiples
Assessment Tasks
- ● Word problems involving multi-digit arithmetic operations
- ● Finding factors and multiples for given whole numbers
- ● Explaining strategies used for multi-digit operations
Detailed Lesson
Place Value: Understand that the four digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones. Read and write numbers to 1,000,000 using base-ten numerals, number names, and expanded form.
Compare and Order Numbers: Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Order numbers from least to greatest or greatest to least.
Rounding: Round multi-digit whole numbers to any place using the vertical number line method.
Addition and Subtraction: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Multiplication: Multiply a four-digit number by a one-digit number and multiply two two-digit numbers using strategies based on place value and the properties of operations. Illustrate and explain multiplication using equations, rectangular arrays, and area models.
Division: 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 the relationship between multiplication and division.
Factors and Multiples: Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Find all factor pairs for a whole number in the range 1–100.
Knowledge Check
Q1: What is the value of the 5 in 25,647?
5,000
Q2: Order the following numbers from least to greatest: 7,235, 7,305, 7,253, 7,530
7,235, 7,253, 7,305, 7,530
Q3: What is 2,378 rounded to the nearest hundred?
2,400
Module 2
Fractions and Decimals
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Equivalent Fractions: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models. Generate equivalent fractions and explain why the fractions are equivalent.
Comparing Fractions: Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction like 1/2. Recognize comparisons are valid only when the two fractions refer to the same whole.
Operations on Fractions: Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. Solve word problems involving addition and subtraction of fractions with like denominators.
Relating Fractions and Decimals: Express a fraction with denominator 10 as an equivalent fraction with denominator 100 to show it as a decimal. Add two fractions with respective denominators 10 and 100.
This module covers generating equivalent fractions, comparing and operating on fractions, and relating decimals to fractions.
Learning Objectives
- Generate equivalent fractions
- Compare fractions with different numerators and denominators
- Add and subtract fractions with like denominators
- Relate fractions to decimals through equivalence
Key Topics
Equivalent Fractions
Comparing Fractions
Adding and Subtracting Fractions
Fractions and Decimals
Assessment Tasks
- ● Word problems on fraction operations
- ● Comparing fractions using visual models
- ● Converting fractions to decimals and vice versa
Detailed Lesson
Equivalent Fractions: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models. Generate equivalent fractions and explain why the fractions are equivalent.
Comparing Fractions: Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or by comparing to a benchmark fraction like 1/2. Recognize comparisons are valid only when the two fractions refer to the same whole.
Operations on Fractions: Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. Solve word problems involving addition and subtraction of fractions with like denominators.
Relating Fractions and Decimals: Express a fraction with denominator 10 as an equivalent fraction with denominator 100 to show it as a decimal. Add two fractions with respective denominators 10 and 100.
Knowledge Check
Q1: Generate three equivalent fractions for 2/3.
4/6, 6/9, 8/12
Q2: Which fraction is greater: 5/8 or 3/4?
3/4
Q3: What is 1/4 + 3/4?
1 whole or 4/4
Module 3
Geometry
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Angles: Define an angle as formed by two rays with a common endpoint. Identify acute, right, obtuse, and straight angles in two-dimensional figures. Measure angles using a protractor or angle ruler.
Lines and Symmetry: Define a line as a straight path that extends infinitely in both directions, a ray as a straight path with one endpoint, and a line segment as a straight path with two endpoints. Recognize a line of symmetry for a two-dimensional figure.
Classifying Shapes: 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, isosceles triangles, equilateral triangles, and rectangles.
This module covers identifying and classifying angles, understanding lines and symmetry, and classifying 2D shapes.
Learning Objectives
- Identify and measure angles in 2D figures
- Define and distinguish between lines, rays, and line segments
- Recognize lines of symmetry in 2D figures
- Classify 2D shapes based on properties of lines and angles
Key Topics
Angles
Lines
Symmetry
Classifying 2D Shapes
Assessment Tasks
- ● Measuring angles using a protractor
- ● Identifying lines of symmetry in shapes
- ● Classifying shapes based on given properties
Detailed Lesson
Angles: Define an angle as formed by two rays with a common endpoint. Identify acute, right, obtuse, and straight angles in two-dimensional figures. Measure angles using a protractor or angle ruler.
Lines and Symmetry: Define a line as a straight path that extends infinitely in both directions, a ray as a straight path with one endpoint, and a line segment as a straight path with two endpoints. Recognize a line of symmetry for a two-dimensional figure.
Classifying Shapes: 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, isosceles triangles, equilateral triangles, and rectangles.
Knowledge Check
Q1: Identify the type of angle formed by the hands of a clock at 3:00.
Right angle
Q2: Which has no endpoints: a line, ray, or line segment?
A line
Q3: Name a quadrilateral with 4 right angles and 2 pairs of parallel sides.
Rectangle
Module 4
Measurement
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Unit Conversions: Convert among different-sized standard measurement units within the same measurement system by multiplying by conversion factors (e.g., inches to feet; grams to kilograms). Use the four operations to solve word problems involving these conversions.
Perimeter and Area: Find the perimeter of a rectangle by adding the lengths of the sides. Find the area of a rectangle by multiplying its side lengths. Solve real-world problems involving perimeters and areas of rectangles.
Measuring: Select appropriate tools and units to estimate and measure length, weight, and volume. Make reasonable estimates for measurement and use benchmarks such as cm, m, kg, L.
This module covers converting units, finding perimeter and area, and measuring length, weight, and volume.
Learning Objectives
- Convert measurement units within a system
- Calculate perimeter and area of rectangles
- Estimate and measure length, weight, and volume using appropriate tools/units
Key Topics
Unit Conversion
Perimeter and Area
Measuring Length, Weight, and Volume
Assessment Tasks
- ● Measurement word problems
- ● Calculating areas of composite rectangles
- ● Choosing appropriate measurement tools/units
Detailed Lesson
Unit Conversions: Convert among different-sized standard measurement units within the same measurement system by multiplying by conversion factors (e.g., inches to feet; grams to kilograms). Use the four operations to solve word problems involving these conversions.
Perimeter and Area: Find the perimeter of a rectangle by adding the lengths of the sides. Find the area of a rectangle by multiplying its side lengths. Solve real-world problems involving perimeters and areas of rectangles.
Measuring: Select appropriate tools and units to estimate and measure length, weight, and volume. Make reasonable estimates for measurement and use benchmarks such as cm, m, kg, L.
Knowledge Check
Q1: How many inches are in 4 feet?
48 inches
Q2: What is the perimeter of a rectangle with side lengths 8 cm and 5 cm?
26 cm
Q3: Which tool would you use to measure the weight of a textbook?
A scale
Module 5
Data and Probability
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Data Displays: Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition and subtraction of fractions using line plots.
Bar Graphs and Pictographs: Draw bar graphs with multiple categories and organize data into pictographs where the symbols represent different numbers of data values.
Measures of Center: Find the mean (average), median, and mode for a set of data. Explain which measure of center is most appropriate in a given situation.
Range: Understand that the range describes the spread of a data set as the difference between the greatest and least values.
This module covers interpreting and creating data displays, and understanding measures of center and spread.
Learning Objectives
- Create and interpret line plots of fraction data
- Draw bar graphs and pictographs to display data
- Calculate the mean, median, and mode of a data set
- Find the range of a data set
Key Topics
Line Plots
Bar Graphs and Pictographs
Mean, Median, and Mode
Range
Assessment Tasks
- ● Creating data displays from raw data
- ● Interpreting data from graphs, plots, pictographs
- ● Choosing appropriate measures of center for situations
Detailed Lesson
Data Displays: Make a line plot to display a data set of measurements in fractions of a unit. Solve problems involving addition and subtraction of fractions using line plots.
Bar Graphs and Pictographs: Draw bar graphs with multiple categories and organize data into pictographs where the symbols represent different numbers of data values.
Measures of Center: Find the mean (average), median, and mode for a set of data. Explain which measure of center is most appropriate in a given situation.
Range: Understand that the range describes the spread of a data set as the difference between the greatest and least values.
Knowledge Check
Q1: What is the median of the data set: 12, 16, 9, 14, 9?
12
Q2: If each @ symbol represents 5 students in a pictograph, what does @@ represent?
10 students
Q3: What is the range of the heights: 56 inches, 62 inches, 59 inches, 64 inches?
8 inches
Final Assessment
Mastery Check
Demonstrate your understanding and complete the module.