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# 5th Grade Learning Progression (v2)

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Welcome to the learning progression for Fifth Grade. This progression incorporates the overall topics of this grade-level's mathematics and is formatted with  Overarching Questions, Essential Questions, and Big Ideas for each unit. This progression model takes the work of bundling standards to the next level by grouping together grade-level concepts in the Big Ideas sections. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner that is more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are for progression and planning and are not a replacement for the OAS-M objectives.

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

The parts of the objective that will be taught in a later unit is indicated by the “strikethroughs.”

The objectives with an * are supplemental objectives.

### Full Objectives

Unit 0:

Growth Mindset

Timing

1 week

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.

Unit 1:

Timing

4-5 weeks

Objectives

5.N.1.1

5.N.1.2

5.N.1.3

5.N.1.4

5.N.2.4

How do we represent parts of wholes and connect them to real world situations?

1. What are decimals and fractions and how can they be represented?

2. How do you read and write decimals?

3. How do you find equivalents for fractions and decimals?

4. How do you compare and order fractions and decimals?

5. What is the relationship between place values?

BIG IDEA 1: The relationship of digits and their values communicate information about the fractional part of a number.

BIG IDEA 2: Equivalencies exist among fractions and decimals and can be compared and ordered.

5.N.1.1 Represent decimal fractions (e.g., 1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers.

5.N.1.2 Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.

5.N.1.3 Compare and order decimals and fractions, including mixed numbers and fractions less than one, and locate on a number line.

5.N.1.4 Recognize and generate equivalent terminating decimals, fractions, mixed numbers, and fractions in various models.

5.N.3.4 Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 0.001 less than a number.

*5.GM.3.2 Measure the length of an object to the nearest whole centimeter or up to 1/16 inch using an appropriate instrument.

*5.GM.3.3 Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems.

*5.GM.3.4 Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems.

Unit 2:

Whole Number Operations

Timing

4-5 weeks

Objectives

5.N.1.1

5.N.1.2

5.N.2.1

5.N.2.2

5.N.2.3

5.N.2.4

How do we work with whole numbers in real world situations?

1. How can the outcome of division be communicated?

2. What information can be gathered from division?

3. How can we represent and solve real-world situations using all operations and unknowns?

BIG IDEA 1: Whole numbers can be divided to solve real world problems.

BIG IDEA 2:  Students can use multiple strategies to achieve accurate results of real world problems.

5.N.1.1 Represent decimal fractions (e.g., 1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers.

5.N.1.2 Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.

5.N.2.1 Estimate solutions to division problems to assess the reasonableness of results.

5.N.2.2 Divide multi-digit numbers, by one- and two-digit divisors, based on knowledge of place value, including but not limited to standard algorithms.

5.N.2.3 Recognize that remainders can be represented in a variety of ways, including a whole number, fraction, or decimal. Determine the most meaningful form of a remainder based on the context of the problem.

5.N.2.4 Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

*5.A.2.1 Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).

*5.A.2.2 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.

*5.A.2.3 Evaluate expressions involving variables when values for the variables are given.

Unit 3:

Decimal and Fraction Operations

Timing

5-6 weeks

Objectives

5.N.3.1

5.N.3.2

5.N.3.3

How do we add and subtract with decimals and fractions in real world situations?

1. How can estimation help determine reasonableness?

2. How do we add and subtract decimal numbers?

3. How are decimals related to money in the real world?

4. How does understanding fractions on a number line help with determining the reasonableness of an answer?

5. How do we add or subtract fractions to answer real world problems?

BIG IDEA 1: The same reasoning for calculating with whole numbers applies to decimals since they are an extension of the base 10 number system.

BIG IDEA 2:  Adding and subtracting fractions require same size parts.

5.N.3.1 Estimate sums and differences of fractions with like and unlike denominators, mixed numbers, and decimals to assess the reasonableness of the results.

5.N.3.2 Illustrate addition and subtraction of fractions with like and unlike denominators, mixed numbers, and decimals using a variety of mathematical models (e.g., fraction strips, area models, number lines, fraction rods).

5.N.3.3 Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms.

5.N.3.4 Apply mental math and knowledge of place value (no written computations) to find 0.1 more or 0.1 less than a number, 0.01 more or 0.01 less than a number, and 0.001 more or 0.001 less than a number.

*5.A.2.1 Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).

*5.A.2.2 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.

*5.A.2.3 Evaluate expressions involving variables when values for the variables are given.

Unit 4:

Patterns, Relationships, and Data

Timing

5-6 weeks

Objectives

5.D.1.2

5.N.1.2

5.N.2.4

5.A.1.1

5.A.1.2

5.A.2.1

5.A.2.2

5.A.2.3

How do we use patterns, relationships, and data in real world situations?

1. How do we create graphs from data sets to create visuals for the real world?

2. How do we analyze the data from a graph and what do we do with it?

3. How do we find patterns of change to make predictions and generalizations within data sets?

4. How can we visualize patterns of change?

5. How do we work with equations and expressions to solve problems?

6. How do we apply the order of operations to an equation or expression?

BIG IDEA 1: Operational knowledge is required to analyze graphs and data sets.

BIG IDEA 2: Tables and rules can be used to visualize patterns of change on a coordinate plane.

BIG IDEA 3: Properties and Order of Operations are used to evaluate and compare expressions.

5.D.1.1 Find the measures of central tendency (mean, median, or mode) and range of a set of data. Understand that the mean is a “leveling out” or central balance point of the data.

5.D.1.2 Create and analyze line and double-bar graphs with increments of whole numbers, fractions, and decimals.

5.N.1.2 Read, write, and represent decimals using place value to describe decimal numbers including fractional numbers as small as thousandths and whole numbers up to seven digits.

5.N.2.4 Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

5.A.1.1 Use tables and rules with up to two operations to describe patterns of change and make predictions and generalizations about various mathematical situations.

5.A.1.2 Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.

*5.A.2.1 Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).

5.A.2.2 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.

5.A.2.3 Evaluate expressions involving variables when values for the variables are given.

Unit 5:

Two-Dimensional Forms

Timing

8-10 weeks

Objectives

5.GM.1.1

5.GM.1.2

5.N.3.3

5.N.2.4

5.A.2.1

5.GM.1.3

5.GM.3.1

5.GM.3.2

5.GM.3.3

5.GM.3.4

How do we use geometry and measurement in real world situations?

1. How can you collect information about two-dimensional shapes?

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

3. How do we communicate the outcome of measurement?

4. What information can we gather from measuring?

BIG IDEA 1: Angle measurements must be used to classify triangles.

BIG IDEA 2: Customary and metric measurement can be used to find perimeter.

BIG IDEA 3: Capacity of rectangular prisms can be found with cubes and dimension measurement.

5.GM.1.1 Describe, identify, classify, and construct triangles (equilateral, right, scalene, isosceles) by their attributes using various mathematical models.

5.GM.1.2 Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models.

5.GM.2.1Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism a ⋅ b ⋅ c = n. Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if a ⋅ b ⋅ c = p ⋅ q ⋅ r = n.

5.GM.2.2 Estimate the perimeter of polygons and create arguments for reasonable perimeter values of shapes that may include curves.

5.N.3.3 Add and subtract fractions with like and unlike denominators, mixed numbers, and decimals, involving money, measurement, geometry, and data. Use various models and efficient strategies, including but not limited to standard algorithms.

5.N.2.4 Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
5.A.2.1 Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).

5.GM.1.3 Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid).

5.GM.3.1 Measure and compare angles according to size using various tools.

5.GM.3.2 Measure the length of an object to the nearest whole centimeter or up to 1/16 inch using an appropriate instrument.

5.GM.3.3 Apply the relationship between inches, feet, and yards to measure, convert, and compare objects to solve problems.

5.GM.3.4 Apply the relationship between millimeters, centimeters, and meters to measure, convert, and compare objects to solve problems.

5.GM.3.5 Estimate lengths and geometric measurements to the nearest whole unit, using benchmarks in customary and metric measurement systems.

Unit 6:

Three-Dimensional Forms

Timing

2-3 weeks

Objectives

5.GM.1.2

5.GM.1.3

5.GM.2.1

How do we work with three-dimensional shapes in real world situations?

1. What information can we gather from measuring?
2. How do we communicate the outcome of measurement?
3. What information can you gather from three-dimensional forms?
4. How can we identify similarities and differences in geometric figures?
5. What could happen if you deconstruct a three-dimensional figure?
6. How can we measure a three-dimensional figure?

BIG IDEA 1: Capacity of rectangular prisms can be found with cubes and dimension measurement.

BIG IDEA 2: Understanding of three-dimensional figures is necessary to determine volume efficiently.

5.GM.1.2 Describe, identify, and classify three-dimensional figures (cubes, rectangular prisms, and pyramids) and their attributes (number of edges, faces, vertices, shapes of faces), given various mathematical models.
5.GM.1.3 Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid).

5.GM.2.1 Determine the volume of rectangular prisms by the number of unit cubes (n) used to construct the shape and by the product of the dimensions of the prism a ⋅ b ⋅ c = n. Understand rectangular prisms of different dimensions (p, q, and r) can have the same volume if a ⋅ b ⋅ c = p ⋅ q ⋅ r = n.

*5.N.2.4 Construct models to solve multi-digit whole number problems requiring addition, subtraction, multiplication, and division using various representations, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

*5.N.1.1 Represent decimal fractions (e.g., 1/10, 1/100) using a variety of models (e.g., 10 by 10 grids, base-ten blocks, meter stick) and show the rational number relationships among fractions, decimals and whole numbers.

Culminating Unit

Timing

2-3 weeks

How can students apply their learning in a variety of real world situations?

1. Can students apply their math skills to real-world STEM situations?

2. Can students apply their math skills to real-world situational tasks?

BIG IDEA 1: Students can apply their math skills to STEM activities.

BIG IDEA 2:  Can students apply their math skills to real-world situational tasks?

• 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

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