Aligned Resources

Alaska Performance Standards
Grade 10
Numeration
The student demonstrates conceptual understanding of real numbers.

Lessons  •  Activities  •  Show All

Lessons (16)

Introduces students to modular (clock) arithmetic and how modular arithmetic can be used to encode messages using simple shift, multiple and affine ciphers.

Audiences: Grades 6-8, Grades 9-12

Primary Subjects: Algebra, Discrete, Number and Operations

Related Topics: addition, affine cipher, arithmetic, cipher, cryptography, decipher, division, encrypt, factors, inverse, modular, multiples, multiplication, remainders, shift cipher, subtraction, time

Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: comparing, converting, decimals, denominator, division, divisors, factors, fractions, number line, numerator, ordering, proportion, rational numbers, reducing fraction, subtraction

Students learn about factoring by using manipulatives and computer applets.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Number and Operations

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Finding the factors of whole numbers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Number and Operations

Related Topics: area, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Uses modular (clock) arithmetic to find patterns in Pascal's Triangle.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: addition, arithmetic, division, divisors, integers, modular, pascal's triangle, pascals triangle, pattern, remainders, sum, triangle, whole numbers

Students learn how to convert from fractions to decimals.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: addition, converting, decimals, denominator, division, fractions, numerator, rational numbers, reducing fraction, subtraction

Students learn how to convert from fractions to percentages.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: converting, decimals, denominator, division, fractions, multiplication, numerator, percentages, percents, rational numbers, reducing fraction

Introduces students to fractions and explores basic mathematical operations with fractions, comparing fractions, and converting fractions into decimals or percents.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: addition, arithmetic, decimals, denominator, division, fractions, inverse, lowest common denominator, multiplication, numerator, percents, rational numbers, subtraction

Students and teacher play a game called "Fraction King" to understand the idea of taking fractional parts of whole numbers then use manipulatives and several computer applets to cement the idea.

Audiences: Grades 3-5

Primary Subjects: Number and Operations

Related Topics: arithmetic, comparing, denominator, fractions, multiplication, number line, numerator, ordering, rational numbers, subtraction

Introduces students to modular (clock) arithmetic and its uses in real world problem-solving.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Number and Operations

Related Topics: addition, arithmetic, division, elapsed time, modular, multiplication, remainders, time

Reinforces skills associated with multiplying fractions and mixed numbers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: arithmetic, denominator, division, fractions, geometric sequences, graph, improper, iteration, mixed numbers, multiplication, numerator, recursion, sequences, whole numbers

Introduces students to the concept of base ten and how to use other base number systems.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Number and Operations

Related Topics: addition, algorithm, arithmetic, base, converting, counting, exponents, modular, multiplication, place value, subtraction

Looks at how Pascal's Triangle can be used to generate Sierpinski triangle-like results.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: area, arithmetic, combinatorics, distance, division, factors, fractals, fractions, generator, geometric sequences, geometry, infinity, initiator, integers, iteration, length, limit, lines, multiples, multiplication, pascals triangle, pattern, percents, perimeter, quotient, recursion, remainders, scale, segment, self-similarity, sequences, sets, whole numbers

Shows students that number patterns exist in the Pascal's Triangle, and reinforces student's ability to identify patterns.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Geometry, Number and Operations

Related Topics: arithmetic, binomial, chaos, coefficient, combinatorics, decimals, dimension, division, divisors, factors, fractals, fractions, geometric sequences, geometry, infinity, integers, iteration, length, lines, multiples, multiplication, pascal's triangle, pattern, probability, rectangles, recursion, remainders, segment, self-similarity, sequences, surface area, symmetry, triangle, whole numbers

Students practice arithmetic skills. Can be tailored for practice of all types of single operation arithmetic ranging from simple addition to operations with integers and decimals.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: addition, algorithm, arithmetic, coordinate, data, decimals, division, fractions, graph, integers, linear equations, linear functions, multiplication, subtraction

Students get practice working with conversion of fractions, decimals, percents through using several of the Interactivate activities.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Number and Operations

Related Topics: area, circle graph, circles, converting, decimals, division, fractions, percents, pie chart, proportion, rational numbers

Activities (28)

Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Fractions, Number and Operations

Related Topics: addition, arithmetic, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers

Arithmetic Quiz gives the user randomized questions to answer on arithmetic with whole numbers and integers. Parameters: Level of difficulty and types of questions. Arithmetic Quiz is one of the Interactivate assessment quizzes.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Fractions, Number and Operations

Related Topics: addition, arithmetic, associative, commutative, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers

The same as "Bounded Fraction Pointer" but there is no arrow to help the user determine the value of a fraction between the two endpoints. Bounded Fraction Finder is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: comparing, fractions, number line, ordering, rational numbers

Determine the value of two fractions you have chosen (which are represented as points on a number line). Then find a fraction whose value is between your two fractions (using an arrow on the number line as a guide) and determine its value. Bounded Fraction Pointer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: comparing, fractions, number line, ordering, rational numbers

Work with various types of clocks in order to learn about modular arithmetic operations. Parameters: Number of hours on the clock.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Discrete, Number and Operations

Related Topics: addition, division, elapsed time, modular, multiplication, remainders, time

Color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that are multiples of the number rolled, thereby practicing multiplication tables, investigating number patterns, and investigating fractal patterns. Coloring Multiples in Pascal's Triangle is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: algebra, combinatorics, division, divisors, factors, fractals, integers, multiples, pascal's triangle, pascals triangle, pattern, triangle, whole numbers

Color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that have the same remainder when divided by the number rolled, thereby practicing division and remainders, investigating number patterns, and investigating fractal patterns. Coloring Remainders in Pascal's Triangle is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: algebra, combinatorics, division, divisors, factors, fractals, integers, modular, pascal's triangle, pascals triangle, pattern, remainders, triangle, whole numbers

Compare two sets of objects, using estimation to determine which is greater. Estimate a number of objects, the length of a line, or the area of a shape. Parameter: error tolerance. Comparison Estimator is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: area, assessment, comparing, counting, estimation, length, scale

Converts fractions to decimals and decimals to fractions. Observe the relationships between fractions and decimals.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Fractions, Number and Operations

Related Topics: decimals, division, fractions, rational numbers

Visually represent two unique fractions that are equivalent to a given fraction. The fractional value is shown on a number line after you check to see if your fraction is correct. Equivalent Fraction Finder is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: comparing, fractions, identity, multiples, number line, proportion, rational numbers

Visually represent two unique fractions that are equivalent to a given fraction. The fractional value is shown on a number line as you color in the fraction. Equivalent Fraction Pointer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: comparing, fractions, identity, multiples, number line, ordering, proportion, rational numbers

Practice estimation skills by determining the number of objects, the length of a line, or the area of a shape. Parameters: error tolerance of estimate. Estimator is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: area, assessment, counting, estimation, length, scale

Play a "Connect-Four" style game, earning a game piece each time you answer an estimation question correctly. This game asks the players to estimate the answer to addition, multiplication, and percentage questions. Choose difficulty level, question types, and time. Estimator Four is one of the Interactivate assessment games.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: addition, arithmetic, assessment, estimation, integers, multiplication, percentages, percents

Test your estimation skills by answering questions. This quiz asks you to estimate the answer to addition, multiplication, and percentage questions. Choose difficulty level, question types, and time. Estimator Quiz is one of the Interactivate assessment quizzes.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: addition, arithmetic, assessment, counting, distributive, integers, multiplication, percentages, percents

Visualize factors through building rectangular areas on a grid. First enter all the factorizations of a number, then draw each factor set as an area on the grid. Factorize is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: area, arithmetic, commutative, divisors, factors, grouping, multiples, multiplication, rectangles, whole numbers

Visualize factors through building rectangular areas on a grid. As you draw each factor set on the grid, the factors will be listed. Factorize 2 is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Fractions, Geometry, Number and Operations

Related Topics: area, commutative, division, divisors, factors, multiples, multiplication, rectangles, whole numbers

Determine the value of two given fractions represented as points on a number line. Then find a fraction whose value is between the two given fractions and determine its value. Fraction Finder is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: arithmetic, comparing, fractions, number line, ordering, rational numbers, subtraction

Students play a generalized version of connect four, gaining the chance to place a piece after simplifying fractions, converting fractions to decimals and percentages, and answering algebra questions involving fractions. Choose difficulty level, question types, and time. Fraction Four is one of the Interactivate assessment games.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Algebra, Fractions, Number and Operations

Related Topics: addition, algebra, arithmetic, decimals, division, fractions, mixed numbers, multiplication, percentages, percents, rational numbers, solving equations, subtraction

Determine the value of two given fractions represented as points on a number line. Then find a fraction whose value is between the two given fractions (using an arrow on the number line as a guide) and determine its value. Fraction Pointer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: arithmetic, comparing, fractions, number line, ordering, rational numbers, subtraction

Test your fraction skills by answering questions. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. Choose difficulty level, question types, and time. Fraction Quiz is one of the Interactivate assessment quizzes.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Algebra, Fractions, Number and Operations

Related Topics: addition, algebra, arithmetic, decimals, division, divisors, fractions, integers, mixed numbers, multiplication, percentages, percents, subtraction

Visualize fractions by coloring in the appropriate portions of either a circle or a square, then order those fractions from least to greatest. Fraction Sorter is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: area, circles, comparing, fractions, number line, ordering, proportion, rational numbers, squares

Mixtures allows exploration of percents through two piles of colored and uncolored chips. The user must decide how many chips to color to create the desired percentage of colored chips compared to the total pile. Mixtures is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: assessment, counting, percentages, percents, proportion, sets

Practice estimation skills by determining whether the number of objects, the length of a line, or the area of a shape is more or less than the number given. Parameters: error tolerance of estimate. More or Less Estimator is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: area, comparing, counting, estimation, length, scale

Visually explore counting and place value with different number bases, from base 2 to base 16, and up to the hundreds place using a clock like interface. The activity also allows you to look at the numbers on the clock in base 10 or in your other chosen base to explore the relationship between those values.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Discrete, Number and Operations

Related Topics: arithmetic, counting, exponents, modular

This activity allows the user to practice order of operations with addition/subtraction, multiplication/division, exponents, and parentheses. Order of Operations Quiz is one of the Interactivate assessment quizzes.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: addition, arithmetic, assessment, associative, commutative, division, exponents, integers, multiplication, negative number, order of operations, subtraction

Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering order of operations questions (addition/subtraction, multiplication/division, exponents, and parentheses). Parameters: time, difficulty level, types of questions. Order of Operations Four is one of the Interactivate assessment games.

Audiences: Grades 3-5, Grades 6-8, Grades 9-12

Primary Subjects: Number and Operations

Related Topics: addition, arithmetic, assessment, associative, commutative, division, exponents, integers, multiplication, negative number, order of operations, subtraction

Determine the value of a given fraction represented as a point on a number line. Then find a fraction whose value is a given fraction. Fraction Pointer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: equivalent, fractions, number line

Determine the value of a given fraction represented as a point on a number line. Then find a fraction whose value is the given fraction using an arrow on the number line as a guide. Single Fraction Pointer is one of the Interactivate assessment explorers.

Audiences: Grades 3-5, Grades 6-8

Primary Subjects: Fractions, Number and Operations

Related Topics: equivalent, fractions, number line