2022 4th Grade Learning Progression

Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:

Growth Mindset

Timing

 1 week

BIG IDEA 1: Math is about learning not performing.

BIG IDEA 2: Math is about making sense.

BIG IDEA 3: Math is filled with conjectures, creativity, and uncertainty.

BIG IDEA 4: Mistakes are beautiful things. 

• Students will understand the importance of a growth mindset (e.g., that math is not about talent or natural ability but is about thoughtful practice) and what it means to talk and listen. Students will also understand that class is where students practice thinking and doing math.
• Students will learn the value of taking time to think about math and listen to how others make sense of their work to arrive at a common understanding.
• Students will build the habits of using precise language, practicing, and sharing their thoughts.

Unit 1:

Place Value Patterns and Operation Relationships

Timing

4 weeks

Objectives

4.N.1.1

4.N.1.2

4.N.1.3

4.N.1.4

4.N.2.1

4.N.2.2

4.N.2.3

4.N.2.4

4.N.2.5

4.A.2.3

4.A.2.1

4.A.2.2

1. How does whole number place value play a part in number patterns?

2. How can we represent whole number place values and their patterns?

3. How does place value play a part in number operations, specifically multiplication and division?
4. How can we represent and solve real-world situations using unknowns and all operations? 

1. Understanding place value patterns allows work with larger quantities and numbers. 

2.  Decomposing and composing numbers allows for greater understanding of the flexibility of number.

3. The place value system is based on multiplication and division and is useful when estimating and comparing.

4. Multiplication and division are related to each other and give us information about real-world situations. 

5. We can use a letter or symbol to represent an unknown quantity and use knowledge of operations to solve for the unknown.   

4.N.1.1 Read, write, discuss, and represent whole numbers up to 1,000,000. Representations may include numerals, words, pictures, number lines, and manipulatives. 
4.N.1.2 Use place value to describe whole numbers between 1,000 and 1,000,000 in terms of millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones with written, standard, and expanded forms. 
4.N.1.3 Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000. 
4.N.1.4 Use place value to compare and order whole numbers up to 1,000,000, using comparative language, numbers, and symbols. 

4.N.2.1 Demonstrate fluency with multiplication and division facts with factors up to 12.

4.N.2.2 Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms.

4.N.2.3 Estimate products of 3-digit by 1-digit and 2-digit by 2-digit whole number factors using a variety of strategies (e.g., rounding, front-end estimation, adjusting, compatible numbers) to assess the reasonableness of results.  Explore larger numbers using technology to investigate patterns. 

4.N.2.4 Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.

4.N.2.5 Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders. 

4.A.2.3 Determine the unknown addend or factor in equivalent and non-equivalent expressions (e.g., 5 + 6 = 4 + ____ , 3 ∙ 8 < 3 ∙ _____)

4.A.2.1 Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true.

4.A.2.2 Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa. 

Unit 2:

Patterns and Algebraic Reasoning

Timing

2 weeks

Objectives

4.A.1.1

4.A.1.2

4.A.1.3

How does identifying patterns help us solve real-world problems?

1. How do we organize data to aide in identifying patterns?
2. How do we describe numerical patterns?
3. How can we use mathematical expressions with unknowns to describe geometric patterns? 

1. Number patterns can be represented by mathematical expressions and displayed in input/output tables.
2. Growing geometric patterns can be represented by mathematical expressions.

4.A.1.1 Create an input/output chart or table to represent or extend a numerical pattern.

4.A.1.2 Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number.

4.A.1.3 Construct models to show growth patterns involving geometric shapes and define the single operation rule of the pattern.

Unit 3:

Timing

5 weeks

Objectives

4.N.3.1

4.N.3.2

4.N.3.3

4.N.3.5

4.N.3.6

4.N.3.7

4.N.3.8

4.N.3.9

4.N.4.1

4.N.4.2

Are all numbers whole numbers?

1. How can we model/represent numbers that are not whole?
2. What are the different ways to represent a fraction?
3. How do we judge the size of numbers that are not whole? 

1. Fractions are numbers representing parts of unit wholes and can be represented in a variety of ways.
2. We can evaluate the size of fractions using models, benchmarks, equivalent forms, and number lines.
3. Decimals are numbers representing parts of unit wholes and can be represented in a variety of ways. 
4.  We can evaluate the size of decimals using models, benchmarks, place value, and number lines.
5. We can use the relationship between fractions and decimals to compare quantities in real-world and mathematical situations. 

4.N.3.1 Represent and rename equivalent fractions using fraction models (e.g., parts of a set, area models, fraction strips, number lines).

4.N.3.2 Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4,1) to locate additional fractions with denominators up to twelfths on a number line.

4.N.3.3 Use models to order and compare whole numbers and fractions less than and greater than one, using comparative language and symbols. 

4.N.3.5 Use models to add and subtract fractions with like denominators.

4.N.3.6 Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals.

4.N.3.7 Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money.

4.N.3.8 Compare and order decimals and whole numbers using place value and various models including but not limited to grids, number lines, and base 10 blocks.

4.N.3.9 Compare and order benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) and decimals (0, 0.25, 0.50, 0.75, 1.00) in a variety of representations.

4.N.4.1 Select the fewest number of coins for a given amount of money up to one dollar.

4.N.4.2 Given a total cost (dollars and coins up to twenty dollars) and amount paid (dollars and coins up to twenty dollars), find the change required in a variety of ways.

Unit 4:

Equal partitioning: Fraction Operations

Timing

2 weeks

Objectives

4.N.3.4

4.N.3.5

How does adding and subtracting fractions help us solve real-world problems?

1. How can non-unit fractions be decomposed?
2. How is operating with fractions different than operating with whole numbers? 
3. What happens when the sum of the fractions is greater than one? 

1. We can use a variety of manipulatives and pictorial models to decompose fractions and record the results with symbolic representations.
2. We can use models to add and subtract fractions with like denominators in real-world and mathematical situations. 

4.N.3.4 Decompose a fraction into a sum of fractions with the same denominator in more than one way, using concrete and pictorial models and recording results with numerical representations (e.g.,  3/4 = 1/4 +1/4 +1/4 and 3/4 = 2/4 + 1/4). 

4.N.3.5 Use models to add and subtract fractions with like denominators.

Unit 5:

Measurement

Timing

4 weeks

Objectives 

4.GM.2.2

4.GM.2.3

4.GM.2.4

4.GM.2.5

4.N.2.1*

4.GM.2.6

4.N.1.3*

4.GM.2.7

4.GM.3.1

4.GM.3.2

How do we use measurement to solve real-world problems?

1. What information can we gather from measurement?
2. How do we communicate the outcome of measurement?
3. When are accurate measurement necessary in the real world? 

1. Length, liquid volume (capacity), mass, temperature, and time can all be precisely measured.
2. We can use a variety of strategies and the relationship between units of time to determine the amount of time that has passed.
3. We can find the area of a figure by decomposing it into rectangles.
4. The volume of a rectangular prism can be found by counting the number of cubes in it. 

4.GM.2.2 Find the area of polygons by determining if they can be decomposed into rectangles.
 

4.GM.2.3 Develop the concept that the volume of rectangular prisms with whole-number edge lengths can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use a variety of tools and create models to determine the volume using appropriate measurements (e.g., cm³ ).

4.GM.2.4 Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter inch.

4.GM.2.5 Recognize and use the relationship between inches, feet, and yards to measure and compare objects.

4.N.2.1 Demonstrate fluency with multiplication and division facts with factors up to 12.

4.GM.2.6 Recognize and use the relationship between millimeters, centimeters, and meters to measure and compare objects.

4.N.1.3 Applying knowledge of place value, use mental strategies (no written computations) to multiply or divide a number by 10, 100 and 1,000. 

4.GM.2.7 Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length).

4.GM.3.1 Determine elapsed time.

4.GM.3.2 Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models.

Unit 6:

Geometric Figures

Timing

4 weeks

Objectives

4.GM.1.1

4.GM.1.2

4.GM.1.3

4.GM.2.1

How do geometric terms apply to real-world objects?

1. What attributes constitute a polygon?
2. How can we identify similarities and differences when comparing quadrilaterals?
3. How can we use measurement to understand and compare angles?
4. How can we identify similarities and differences when comparing two three-dimensional figures? 

1. Polygons are made up of lines, line segments, rays, points, and angles.
2. Quadrilaterals can be compared and classified based on the characteristics of their sides and angles.
3. Specific tools can be used to measure angles in geometric figures and real-world objects.
4. Three-dimensional figures can be compared based on a variety of geometric attributes. 

4.GM.1.1 Identify points, lines, line segments, rays, angles, endpoints, and parallel and perpendicular lines in various models.

4.GM.1.2 Describe, classify, and construct quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms, and kites. Recognize quadrilaterals in various models.

4.GM.1.3 Given two three-dimensional shapes, identify each shape. Compare and contrast their similarities and differences based on their attributes.

4.GM.2.1 Measure angles in geometric figures and real-world objects with a protractor or angle ruler.

Unit 7: 

Data Analysis

Timing

1 week

Objectives

4.D.1.1

4.D.1.2

4.N.3.2*

4.D.1.3

How do we use data to solve real-world problems?

1. How can we use data to represent and solve real-world situations?
2. Why is accurate interpretation of data important in problem solving? 

1. Frequency tables, line plots, bar graphs, timelines, and Venn diagrams can be used to represent real-world situations. 

4.D.1.1 Create and organize data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.

4.D.1.2 Organize data sets to create tables, bar graphs, timelines, and Venn diagrams. The data may include benchmark fractions or decimals ( 1/4, 1/3, 1/2, 2/3, 3/4 , 0.25, 0.50, 0.75).

4.N.3.2 Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4,1) to locate additional fractions with denominators up to twelfths on a number line.

4.D.1.3 Solve one- and two-step problems by analyzing data in whole number, decimal, or fraction form in a frequency table and line plot.

Culminating Unit

Timing

4 weeks

Objectives

4.N.2.1

4.N.2.4

4.N.2.5

4.N.3.2

4.N.3.6

4.N.3.7

4.GM.2.4

4.GM.2.7

4.GM.3.1

4.GM.3.2

How can I use what I have learned to problem solve?

1. How do we use all operations to solve real world problems?

2. How do we use place value to compare decimals and fractions?

3. What information can we gather from measuring?

4. How can games help keep up practice of math skills?

1. Measurement: Time, weight, distance, and unit conversions.
2. Decimals and fractions are numbers representing part of a whole. 
3. Solving Real World Problems using a variety of operations.  
4. Use games to practice math skills. 

4.N.2.1 Demonstrate fluency with multiplication and division facts with factors up to 12. 

4.N.2.4 Apply and analyze models to solve multi-step problems requiring the use of addition, subtraction, and multiplication of multi- digit whole numbers. Use various strategies, including the relationship between operations, the use of appropriate technology, and the context of the problem to assess the reasonableness of results.

4.N.2.5 Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders. 

4.N.3.2 Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4,1) to locate additional fractions with denominators up to twelfths on a number line.

4.N.3.6 Represent tenths and hundredths with concrete and pictorial models, making connections between fractions and decimals.

4.N.3.7 Read and write decimals in standard, word, and expanded form up to at least the hundredths place in a variety of contexts, including money.

4.GM.2.4 Choose an appropriate instrument to measure the length of an object to the nearest whole centimeter or quarter inch.

4.GM.2.7 Determine and justify the best use of customary and metric measurements in a variety of situations (liquid volumes, mass vs. weight, temperatures above 0 (zero) degrees, and length).

4.GM.3.1 Determine elapsed time.

4.GM.3.2 Convert one measure of time to another including seconds to minutes, minutes to hours, hours to days, and vice versa, using various models.