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3rd Grade Learning Progression (v2)

Page history last edited by Christine Koerner 1 year, 5 months ago

Welcome to the new progression for 3rd 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


Timing

1-2 weeks


How does mindset affect learning of mathematics?  

1. Math is about learning, not about performing.

2. Math is about making sense.

3.  Math is filled with conjectures, creativity, and uncertainty.

4. Mistakes are beautiful things.

  • Develop a deep and flexible conceptual understanding
  • Develop accurate and appropriate procedural fluency
  • Develop strategies for problem solving
  • Develop mathematical reasoning
  • Develop a productive mathematical disposition
  • Develop the ability to make conjectures, model, and generalize
  • Develop the ability to communicate mathematically

Unit 1:

Number Relationships Additive Thinking


Timing

6-7 weeks


Objectives

3.N.1.1

3.N.1.2

*3.N.1.4

3.N.2.3

 3.N.2.4

*3.A.2.2

3.N.1.3

3.N.2.5

*3.N.1.4

*3.A.1.1

3.A.1.2

*3.A.2.1

*3.A.1.3

 

How can we use addition strategies to solve real world problems?

  1. How can we represent numbers in different ways?

  2. What relationships do we find in mathematics?

  3. How do we apply addition and subtraction strategies when problem solving?

  4. How do we use properties of addition?

 

 

 

 

 

 

  1. Numbers have value that can be represented in different ways.
  2. Flexible methods of addition and subtraction computation involve taking apart (decomposing) and combining (composing) numbers in a wide variety of ways.
  3. The commutative, associative, and identity properties are used to find equivalent expressions.
  4. Number relationships determine the pattern, rule, or unknown number. 
  5. Estimation is a problem solving strategy when finding sums and differences of numbers. 

3.N.1.1 Read, write, discuss, and represent whole numbers up to 100,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives.

3.N.1.2 Use place value to describe whole numbers between 1,000 and 100,000 in terms of ten thousands, thousands, hundreds, tens and ones, including expanded form.

3.N.1.4 Use place value to compare and order whole numbers up to 100,000, using comparative language, numbers, and symbols.

3.N.2.3 Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers.

3.N.2.4 Recognize when to round numbers and apply understanding to round numbers to the nearest ten thousand, thousand, hundred, and ten and use compatible numbers to estimate sums and differences.

3.A.2.2 Recognize, represent and apply the number properties (commutative, and identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.

3.N.1.3 Find 10,000 more or 10,000 less than a given four- or five-digit number. Find 1,000 more or 1,000 less than a given four- or five-digit number. Find 100 more or 100 less than a given four- or five-digit number.

3.N.2.5 Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.

3.N.1.4 Use place value to compare and order whole numbers up to 100,000, using comparative language, numbers, and symbols.

3.A.1.1 Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.

3.A.1.2 Describe the rule (single operation) for a pattern from an input/output table or function machine involving addition, subtraction or multiplication.

3.A.2.1 Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences.

3.A.1.3 Explore and develop visual representations of growing geometric patterns and construct the next steps. 

Unit 2:

Number Relationships (Multiplicative Thinking)


Timing

5-6 weeks


Objectives

3.N.2.1

*3.A.2.2

3.N.2.2

3.N.2.6

3.N.2.7

3.N.2.8

*3.A.1.1

3.A.1.2

*3.A.2.1

*3.A.1.3

 

 

 

 

 

 

How can we use multiplication strategies to solve real world problems? 

  1. How can we represent numbers in different ways?

  2. What patterns and relationships do we find in mathematics?

  3. How do we apply multiplication and division strategies when problem solving?

  4. How do we use properties of multiplication?

 

 

 

  1. Multiplication is the total number of items when given a number of equal groups and the number of items in each group.
  2. The commutative, associative, and identity properties are used to find equivalent expressions.
  3. Division is sharing a number into equal groups and finding the number of groups or the number of items in each group.
  4. Number relationships determine the pattern, rule, or unknown number.  
  5. Place value strategies can be applied when multiplying two-digit by one-digit numbers.

 

3.N.2.1 Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting.

3.A.2.2 Recognize, represent and apply the number properties (commutative, and identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.

3.N.2.2 Demonstrate fluency of multiplication facts with factors up to 10.

3.N.2.6 Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups.

3.N.2.7 Recognize the relationship between multiplication and division to represent and solve real-world problems.

3.N.2.8 Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number

3.A.1.1 Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.

3.A.1.2 Describe the rule (single operation) for a pattern from an input/output table or function machine involving addition, subtraction or multiplication.

3.A.2.1 Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences.

3.A.1.3 Explore and develop visual representations of growing geometric patterns and construct the next steps

Unit 3:

Equal Partitioning


Timing

3-4 weeks


Objectives

3.N.3.1

3.N.3.2

3.N.3.4

*3.N.3.3

3.GM.3.1

3.GM.3.2

3.N.4.1

3.N.4.2

 

How do we decide what strategy will work best when solving a problem with equal partitioning?
  1. How does equal partitioning help us understand mathematical concepts?
  1. Fractions are numbers that describe parts of a whole.
  2. Minutes are parts of a whole hour.  
  3. Coins are part of a whole dollar. 

3.N.3.1 Read and write fractions with words and symbols.

3.N.3.2 Construct fractions using length, set, and area models.

3.N.3.4 Use models and number lines to order and compare fractions that are related to the same whole.

3.N.3.3 Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions.

3.GM.3.1 Read and write time to the nearest 5-minute (analog and digital).

3.GM.3.2 Determine the solutions to problems involving addition and subtraction of time in intervals of 5 minutes, up to one hour, using pictorial models, number line diagrams, or other tools.

3.N.4.1 Use addition to determine the value of a collection of coins up to one dollar using the cent symbol and a collection of bills up to twenty dollars.

3.N.4.2 Select the fewest number of coins for a given amount of money up to one dollar.

Unit 4:

Measurement


Timing

2 weeks


Objectives 

3.N.3.3

3.GM.2.3

3.GM.2.5

3.GM.2.4

3.GM.2.6

How does finding measurements help solve real world problems?
  1. What information can we gather when measuring?

  2. When are accurate measurements necessary?

  3. How do we investigate mathematical measurements in the real world?

 

 

  1. Standard and nonstandard measurement are used to find the lengths of objects.
  2. Temperature is measured using thermometers. 

 

3.N.3.3 Recognize unit fractions and use them to compose and decompose fractions related to the same whole. Use the numerator to describe the number of parts and the denominator to describe the number of partitions.

3.GM.2.3 Choose an appropriate measurement instrument and measure the length of objects to the nearest whole centimeter or meter.

3.GM.2.5 Using common benchmarks, estimate the lengths (customary and metric) of a variety of objects.

3.GM.2.4 Choose an appropriate measurement instrument and measure the length of objects to the nearest whole yard, whole foot, or half inch.

3.GM.2.6 Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius

Unit 5:

Data


Timing

2 weeks


Objectives

3.D.1.2

3.N.2.5

*3.A.2.1 

3.D.1.1 

How does data collection better represent information in the real world?
  1. How can we interpret data?

  2. How can we present data in a meaningful way?

 


 

 

 
  1. Data can be interpreted in a graphical format. 
  2. Graphs present data in a purposeful way. 

3.D.1.2 Solve one- and two-step problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.

3.N.2.5 Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Use various strategies, including the relationship between addition and subtraction, the use of technology, and the context of the problem to assess the reasonableness of results.

3.A.2.1 Find unknowns represented by symbols in arithmetic problems by solving one-step open sentences (equations) and other problems involving addition, subtraction, and multiplication. Generate real-world situations to represent number sentences.

3.D.1.1 Summarize and construct a data set with multiple categories using a frequency table, line plot, pictograph, and/or bar graph with scaled intervals.

Unit 6: 

Geometry


Timing

3-4 weeks


Objectives

3.GM 1.1

3.GM.1.2

3.GM.1.3

3.GM.2.7

3.N.2.8

3.GM.2.1

  3.N.2.3 *

3.GM.2.8

3.GM.2.2

How does classifying geometric shapes and objects help us solve real world problems?

  1. How can we classify a shape through investigations?

  2. How can we identify similarities and differences in geometric figures?

  3. What information can we gather from analyzing shapes?

  4. How do we investigate measurable attributes of objects?

 

 

  1. An angle is determined by its measurement or size.
  2. Tools and algorithms help define the perimeter and area of a 2-D shape.
  3. Three-dimensional shapes are classified by their attributes. 

 

3.GM 1.1 Sort three-dimensional shapes based on attributes.

3.GM.1.2 Build a three-dimensional figure using unit cubes when picture/shape is shown.

3.GM.1.3 Classify angles as acute, right, obtuse, and straight.

3.GM.2.7 Counts cubes systematically to identify number of cubes needed to pack the whole or half of a 3-D structure.

3.N.2.8 Use strategies and algorithms based on knowledge of place value, equality and properties of addition and multiplication to multiply a two-digit number by a one-digit number.

3.GM.2.1 Find perimeter of polygon, given whole number lengths of the sides, in real-world and mathematical situations.

3.N.2.3 Use strategies and algorithms based on knowledge of place value and equality to fluently add and subtract multi-digit numbers.

3.GM.2.8 Find the area of 2-D figures by counting total number of same size unit squares that fill the shape without gaps or overlaps

3.GM.2.2 Develop and use formulas to determine the area of rectangles. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns.

Culminating Unit:

 

Timing

3-4 weeks


Objectives

 

How do we problem solve and why is it important?
  1. How do we apply problem solving strategies to different operations?

  2. How is equal partitioning used in our daily lives? 

 

 

 

 

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

3rd Grade Introduction

 

 

 

 

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