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4th Grade Learning Progression (v2)

Page history last edited by Christine Koerner 2 years, 7 months ago

Welcome to the new progression for 4th Grade. This progression builds upon Math Framework Project Phase 1 work (see Progression v1 here), taking many of the best features and building in an Overarching Question, Essential Questions, and Big Ideas for each unit. This new model takes the work of bundling standards to the next level by grouping together grade level concepts under Big Ideas. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner we believe to be more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are not a replacement for the objectives. 

 

Click on the unit numbers below to see essential understandings, student activities, and suggested sequencing.

 

The use of an asterisk (*) indicates an objective is repeated in another unit or an objective that is partially taught in a unit and will be taught in its entirety in a later unit. The parts of the objective that will be taught in a later unit is indicated by the “strikethroughs.” Occasionally, new words are added to the objective to ensure the objective still makes sense considering the strikethroughs.

 

Unit

Overarching Question

Essential Questions

Big Ideas

Full Objectives

Unit 0:

Growth Mindset

How does improving student attitudes toward math affect their learning?  

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.

Timing

 1 week

Unit 1:

Number Relationships


Timing

4 weeks

(Big Idea 2 =

2 weeks)


Objectives

4.N.1.1

4.N.1.2

4.N.1.3

4.N.1.4

4.N.1.5

4.N.1.6

4.N.1.7

4.A.2.1

4.A.2.2

 

How do number relationships help us solve real-world problems?

  1. How does place value play a part in number operations?
  2.  Why do we use multiplication and division?
  3.  How can we     represent and solve real-world situations using unknowns and all operations?
  1. The place value system is based on multiplication and division and is useful when estimating and comparing.
  2. Multiplication and division are related to each other and give us information about real-world situations. 
  3. 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 Demonstrate fluency with multiplication and division facts with factors up to 12.

4.N.1.2 Use an understanding of place value to multiply or divide a number by 10, 100, and 1,000.

4.N.1.3 Multiply 3-digit by 1-digit or 2-digit by 2-digit whole numbers, using efficient and generalizable procedures and strategies, based on knowledge of place value, including but not limited to standard algorithms.

4.N.1.4 Estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers using rounding, benchmarks and place value to assess the reasonableness of results. Explore larger numbers using technology to investigate patterns.

4.N.1.5 Solve multi-step real-world and mathematical 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.1.6 Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties). 

4.N.1.7 Determine the unknown addend or factor in equivalent and non-equivalent expressions. (e.g., 5 + 6 = 4 + r, 3 x 8 < 3 x b)

A.2.1 Use number sense, properties of multiplication and the relationship between multiplication and division to solve problems and find values for the unknowns represented by letters and symbols that make number sentences true.

4.A.2.2 Solve for unknowns in problems by solving open sentences (equations) and other problems involving addition, subtraction, multiplication, or division with whole numbers.  Use real-world situations 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 Create growth patterns involving geometric shapes and define the single operation rule of the pattern.

 

Unit 3:

Equal Partitioning: Concepts

Timing

5 weeks


Objectives

4.N.2.1

4.N.2.2

4.N.2.5

4.N.2.6

4.N.2.7

4.N.2.8

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

4.N.2.2 Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) to locate additional fractions on a number line.  Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.

4.N.2.5 Represent tenths and hundredths with concrete models, making connections between fractions and decimals.

4.N.2.6 Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money.

4.N.2.7 Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.

4.N.2.8 Compare benchmark fractions (1/4, 1/3, 1/2, 2/3, 3/4) ad decimals (0.25, 0.50, 0.75) in real-world and mathematical situations.

Unit 4:

Equal partitioning: Fraction Operations


Timing

2 weeks


Objectives

4.N.2.3

4.N.2.4

 

 

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.2.3 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 (e.g., 3/4 = 1/4 + 1/4 + 1/4).

4.N.2.4 Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations.

 

Unit 5:

Measurement


Timing

4 weeks


Objectives 

4.GM.2.2

4.GM.2.3

4.GM.2.4

4.GM.2.5

4.GM.3.1

4.GM.3.2

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

  1. What can be measured?
  2. How do we communicate the outcome of measurement?
  3. What tools can we use to measure? 
  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 that can be decomposed into rectangles.

4.GM.2.3 Using a variety of tools and strategies, 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 appropriate measurements, such as cm cubed.

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

4.GM.2.5 Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric).

4.GM.3.1 Determine elapsed time.

4.GM.3.2 Solve problems involving the conversion of one measure of time to another.

 

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 contexts.

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

4.GM.1.3 Given two three-dimensional shapes, identify similarities and differences.

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.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 Represent data on a frequency table or line plot marked with whole numbers and fractions, using appropriate titles, labels, and units.

4.D.1.2 Use tables, bar graphs, timelines, and Venn diagrams to display data sets.  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.D.1.3 Solve one- and two-step problems using data in whole number, decimal, or fraction form in a frequency table or line plot.

 

 

Culminating Unit


Timing

4 weeks


Objectives

4.N.1.1

4.N.1.5

4.N.1.6

 

4.N.2.2

4.N.2.5

4.N.2.6

 

4.GM.2.4

4.GM.2.5

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.1.1 Demonstrate fluency with multiplication and division facts with factors up to 12.

4.N.1.5 Solve multi-step real-world and mathematical 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.1.6 Use strategies and algorithms based on knowledge of place value, equality and properties of operations to divide 3-digit dividend by 1-digit whole number divisors (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties).

4.N.2.2 Use benchmark fractions (0, 1/4, 1/3, 1/2, 2/3, 3/4, 1) to locate additional fractions on a number line.  Use models to order and compare whole numbers and fractions less than and greater than one using comparative language and symbols.

4.N.2.5 Represent tenths and hundredths with concrete models, making connections between fractions and decimals.

4.N.2.6 Represent, read and write decimals up to at least the hundredths place in a variety of contexts including money.

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

4.GM.2.5 Solve problems that deal with measurements of length, when to use liquid volumes, when to use mass, temperatures above zero and money using addition, subtraction, multiplication, or division as appropriate (customary and metric).

4.GM.3.1 Determine elapsed time.

4.GM.3.2 Solve problems involving the conversion of one measure of time to another.

 

 

 

 

 

Distance Learning Resources/
Supplemental Activities
How can students develop and show evidence of understanding?     Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning.

 


Introduction to the OKMath Framework

4th Grade Introduction

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