Standard 1: Real and Complex Number SystemsArchived

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Expand and deepen understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. Use the properties of real numbers to simplify algebraic expressions and equations, and convert between different measurement units using dimensional analysis.
General Information
Number: MA.912.A.1
Title: Real and Complex Number Systems
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Algebra

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Independent

MA.912.A.1.In.a
Identify and use equivalent forms of fractions, such as halves, fourths, thirds, sixths, eighths, tenths, and sixteenths; decimals to the hundredths place; and percents, such as 25%, 50%, 75%, 100%, 33%, and 67%, using visual and numerical representation
MA.912.A.1.In.b
Identify examples of positive and negative whole numbers in real-world situations.
MA.912.A.1.In.c
Determine the value of numbers to 10 with the exponents 2 and 3, such as 42 and 33, using physical and visual patterns.
MA.912.A.1.In.d
Compare and order numbers, including whole numbers, fractions, decimals, and percents, expressed in the same form to solve problems in real-world situations.
MA.912.A.1.In.e
Simplify fractions and decimals by reducing to lowest terms.
MA.912.A.1.In.f
Simplify fractions greater than 1, such as 8/4, by using division facts.
MA.912.A.1.In.g
Select the operation and solve two-step mathematical problems involving addition, subtraction, multiplication, and division of two- and three-digit numbers in real-world situations using problem-solving strategies, such as recognizing symbols and key info
MA.912.A.1.In.h
Use tools, including charts and technology, to convert standard units of measurement within the same system, such as money, length, capacity, time, and weight.

Supported

MA.912.A.1.Su.a
Identify equivalent forms of fractions, such as halves, thirds, and fourths; percents, such as 50%, 33%, and 25%; and decimals in the context of money, using visual and numerical representation in real-world situations.
MA.912.A.1.Su.b
Identify the value of numbers to 5 with the exponent 2 using physical and visual models.
MA.912.A.1.Su.c
Compare and order whole numbers, fractions, including halves, fourths, thirds, and sixths; and decimals including .25, .50, .75, 1.00, in real-world situations.
MA.912.A.1.Su.d
Simplify whole numbers to 100 using place value and grouping with visual representation.
MA.912.A.1.Su.e
Use repeated addition of the same number to solve one-digit multiplication facts and repeated subtraction of the same number to solve one-digit division facts in real-world situations.
MA.912.A.1.Su.f
Select the operation and solve one-step mathematical problems involving addition and subtraction of one-digit and two-digit numbers in real-world situations using physical and visual representations and problem-solving strategies, such as recognizing key information and symbols.
MA.912.A.1.Su.g
Use tools, such as simple charts and technology, to convert standard units of measurement within the same system, such as money, length, and capacity.

Participatory

MA.912.A.1.Pa.a
Identify and express quantity in sets to 10 using objects, pictures, symbols, or number names.
MA.912.A.1.Pa.b
Recognize half and whole sets of objects to 10.
MA.912.A.1.Pa.c
Demonstrate one-to-one correspondence by counting objects or actions to 10.
MA.912.A.1.Pa.d
Identify a given quantity to 9 and add 1 more to solve problems.
MA.912.A.1.Pa.e
Identify a given quantity to 10 and take away 1 to solve problems.
MA.912.A.1.Pa.f
Identify tools used for measurement, such as clocks, calendars, rulers, or gallon containers.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Video/Audio/Animations

MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Video/Audio/Animations

MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Video/Audio/Animation

Averages:

This Khan Academy video tutorial introduces averages and algebra problems involving averages.

Type: Video/Audio/Animation