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# 4th Grade Learning Progression

last edited by 4 years, 10 months ago

* Indicates an objective that 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.

### Full Objectives

Unit 1:

Place Value and Decimals

Timing

1-2 weeks

Objectives

4.N.1.1

(taught all year)

4.N.1.2

4.N.2.5

Students begin with the basics of place value and decimals. This unit begins to explore the relationships between place value decimals and fractions with an emphasis on decimals.

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

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.

Unit 2:

Timing

1-2 weeks

4.N.1.1

4.N.2.1

4.N.2.5

This bundle begins to explore the relationships between place value, decimals and fractions, with an emphasis on fractions. Students will use area models, fraction strips, number lines, and parts of a set models to rename equivalent fractions. Benchmark fractions will be used to locate additional fractions on a number line.

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

4.N.2.1 Represent and rename equivalent fractions using fraction models.

4.N.2.2 Use benchmark fractions to locate additional fractions on a number line.  Use models to order and compare whole numbers and fractions less than and greater than 1 using comparative language and skills.

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

Unit 3:

Multiplying and Dividing

Timing

1 - 2 weeks

Objectives

4.N.1.1

4.N.1.4

Students will begin to estimate products of 3-digit by 1-digit or 2-digit by 2-digit whole numbers while using their skills in basic facts and place value.

*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.1.4 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.

Unit 4:

Problem Solving

Timing

2 weeks

Objectives

4.N.1.1

4.N.1.5

4.N.1.7

Students will solve real world problems with unknown addends.  This bundle will also focus on addition and subtraction in real-world problems. Multiplication and finding factors of expressions will be taught in a later unit.

*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.

*4.N.1.7 Determine the unknown addend(s) or factor(s) in equivalent and nonequivalent expressions.

Unit 5:

Geometry

Timing

2 weeks

Objectives

4.N.1.1

4.GM.1.2

4.GM.2.2

Students will focus on the geometry concepts of describing and classifying various quadrilaterals as well as extending that knowledge in order to create growth patterns.

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

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

*4.GM.2.2 Find the area of polygons that can be decomposed into rectangles.

4.A.1.3 Create growth patterns involving geometric shapes and define the single operation rule of the pattern.

Unit 6:

Patterns and Problem Solving

Timing

1 week

Objectives

4.N.1.1*

4.A.1.1*

4.A.1.2*

Students will focus on determining the unknown addend in equivalent and nonequivalent expressions while reviewing input and output tables using a single operation.  All of these objectives are taught fully except for 4.N.1.7. This bundle will focus only on finding the unknown addend in equivalent or nonequivalent expressions.

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

*4.A.1.1 Create an input/output table or chart 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.N.1.7 Determine the unknown addend or factor in equivalent and nonequivalent expressions.

Unit 7:

Place Value and Decimals

Timing

1 - 2 weeks

Objectives

4.N.1.1

4.N.2.6

Students will focus  on finding change (limited to whole dollars or coins) up to \$20. Students will also be practicing place value through hundredths (read,write, and represent these numbers).

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

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.3.1 Given a total cost (whole dollars up to \$20 or coins) and amount paid (whole dollars up to \$20 or coins), find the change required in a variety of ways.  Limited to whole dollars up to \$20 or sets of coins.

Unit 8:

Fractions and Decimals

Timing

1 week

Objectives

4.N.1.1

4.N.2.8

4.GM.2.4

Using an appropriate measuring device, students will measure to the nearest whole centimeter while incorporating benchmark fractions and decimals. From this information, a data table can be constructed to show whole numbers and fractions.

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

4.N.2.8 Compare benchmark fractions (¼, ⅓, ½, ⅔, ¾ ) and decimals (0.25, 0.50, 0.75) in real-world and mathematical situations.

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

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.

Unit 9:

Decomposing Fractions

Timing

1 week

Objectives

4.N.1.1

Students will begin to see that a fraction can be decomposed in more than one way. There will be emphasis on concrete, pictorial, and symbolic representations.

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

*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. ¾ = ¼ + ¼ + ¼ )

Unit 10:

Multiplying and Dividing

Timing

1 week

Objectives

4.N.1.1

4.N.1.3

Students will continue to utilize various strategies to solve multiplication problems, emphasizing 3-digit by 1-digit and 2-digit by 2 digit multiplication. The area model of multiplication will be enhanced through the real-world application of finding the area of polygons that can be separated into rectangles.

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

4.N.1.3 Multiply 3-digit by 1-digit or a 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.GM.2.2 Find the area of polygons that can be decomposed into rectangles.

Unit 11:

Problem Solving

Timing

1 week

Objectives

4.N.1.1

4.N.1.5

4.N.1.7

As students progress to unit 11, they will now utilize their ability to multiply multi digit whole numbers.  Real world problems will include multiplication. Students will also now find an unknown factor in an expression.

*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.1.7 Determine the unknown addends(s) or factor(s) in equivalent and nonequivalent expressions.

Unit 12:

Time and Measurement

Timing

1 week

Objectives

4.N.1.1

4.GM.2.5

4.GM.3.2

4.GM.3.1

This bundle will focus on converting measurements such as time and length. Students will be solving many types of problems that include various customary and metric measurements.  While grasping the concept of elapsed time, students will also focus on conversions of time.

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

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

*4.GM.3.1 Determine elapsed time.

Unit 13:

Geometry

Timing

1 week

Objectives

4.N.1.1

4.GM.1.3

Students will focus their attention to the application of three dimensional shapes.  These shapes will be compared and contrasted.  Within the comparison, students will also be finding the area using unit cubes.

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

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

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 cm3.

Unit 14:

Patterns and Problem Solving

Timing

1 week

Objectives

4.N.1.1

Students will focus their attention to the application of three dimensional shapes.  These shapes will be compared and contrasted.  Within the comparison, students will also be finding the area using unit cubes.

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

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

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 cm3.

Unit 15:

Place Value and Decimals

Timing

1 - 2 weeks

Objectives

4.N.1.1

4.GM.2.5

Students will go through this unit to review place value, fractions, and decimals and then apply those skills when problem solving with various measurements.

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

*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).

Unit 16:

Fractions and Decimals

Timing

1 -2 weeks

Objectives

4.N.1.1

4.D.1.2

4.D.1.3

Students will review fractions, decimals, frequency tables, and line plots and apply those skills to now use other types of graphs (bar graph, timeline, Venn diagram) and solve multi step problems.

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

4.D.1.2 Use tables, bar graphs, timelines, and Venn diagrams to display data sets.  The data may include benchmark fractions or decimals ( ¼, ⅓, ½, ⅔, ¾, 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 and line plot.

Unit 17:

Decomposing Fractions

Timing

1 -2 weeks

Objectives

4.N.1.1

4.N.2.3

4.N.2.4

Students will focuses on decomposing fractions and applying that knowledge from unit 9 in order to solve real-world problems.

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

*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. ¾ = ¼ + ¼ + ¼ ).

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

Unit 18:

Multiplying and Dividing

Timing

1 week

Objectives

4.N.1.1

4.N.1.5

4.N.1.6

Students will begin this bundle with a review of multiplying and dividing whole numbers.  4.N.1.5 will extend to now teach multiplication in real world problems.  Students will now be able to follow strategies and algorithms to divide 3 digit dividends by 1 digit whole numbers.

*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 multidigit 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).

Unit 19:

Problem Solving

Timing

2 weeks

Objectives

4.N.1.1

4.N.1.5

4.A.2.2

4.D.1.3

Students will combine what they have learned thus far in a culmination of all of the problem solving.  Students will solve real world problems by now including a letter or symbol that makes the number sentence true.

*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 multidigit 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.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.

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

Unit 20:

Timing

1 week

Objectives

4.N.1.1

4.GM.3.2

Students will carry on their focus of solving problems involving time. Students will continue to practice elapsed time and conversions of time.

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

*4.GM.3.1 Determine elapsed time.

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

Unit 21:

Geometry

Timing

1 week

Objectives

4.N.1.1

4.GM.1.1

Students will be introduced to various types of lines while reviewing quadrilaterals and three dimensional shapes. These lines will be made into angles which will then be analyzed in real objects.  A protractor will be used to measure the angles.

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

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

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

Unit 22:

Patterns and Problem Solving

Timing

1 week

Objectives

4.N.1.1

4.A.1.1

4.A.1.2

This bundle reviews these four objectives to allow students to completely grasp the importance of using different methods to find a single rule operation and to extend numerical patterns using addition and multiplication.

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

*4.N.1.7 Determine the unknown addends(s) or factor(s) in equivalent and nonequivalent 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.

Introduction to the OKMath Framework