Explore the relationship between scale factor and side lengths in this activity. 

[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]

Putting It All Together

Exploring Scaled Figures Using Models

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Stelle Funktionen grafisch dar und führe Berechnungen in 3D durch

Erforsche Funktionen, löse Gleichungen, konstruiere geometrische Formen

Erforsche geometrische Konzepte und Konstruktionen in einer dynamischen Umgebung

Visualisiere Gleichungen und Funktionen mit interaktiven Diagrammen und Plots

Erkunde Verschiedenes mit kostenlosen Tools für Geometrie, Tabellenkalkulation und CAS

Führe Berechnungen mit Brüchen, Statistiken und Exponentialfunktionen durch

Rechner

Löse mithilfe von Symbolen Gleichungen und finde Muster heraus

Übe grundlegende Operationen wie Additionen, Subtraktionen und Divisionen

Untersuche Folgen und Reihen, löse Differentialgleichungen

Beziehungen, die Eingaben bestimmten Ausgaben in der Mathematik zuordnen

Studiere Formen, Größen und räumliche Beziehungen in der Mathematik

Quantifiziere und vergleiche Attribute wie Länge, Gewicht und Volumen

Verstehe Zahlen, ihre Beziehungen und numerisches Denken

Führe mathematische Operationen wie Additionen, Subtraktionen und Divisionen durch

Analysiere die Unsicherheit und Wahrscheinlichkeit von Ereignissen und Ergebnissen

Untersuche Winkel, Dreiecke sowie trigonometrische Funktionen und Verhältnisse

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Evaluate absolute value expressions to solve number and word problems, including finding horizontal and vertical distances between points and lines.

Absolute Value Expressions

Add and subtract decimals using models and pictures to explain the process and record the results.

Adding and Subtracting Decimals

Add and subtract fractions and mixed numbers with like denominators (without regrouping) in number and word problems.

Adding and Subtracting Fractions or Mixed Numbers with Like Denominators

Add and subtract fractions and mixed numbers with unlike denominators in number and word problems.

Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators

Model or compute with integers using addition or subtraction in number and word problems.

Adding and Subtracting Integers

Identify additive inverses (opposites) and multiplicative inverses (reciprocals) and use them to solve number and word problems.

Additive and Multiplicative Inverse

Rewrite or simplify algebraic expressions including the use of the commutative, associative, and distributive properties, and inverses and identities in number and word problems.

Algebraic Properties

Use a variety of triangles, quadrilaterals, and other polygons to draw conclusions about the sum of the measures of the interior angles.

Angle Sum Properties of Triangles, Quadrilaterals, and Polygons

Identify the congruent and supplementary relationships of the angles formed by cutting parallel lines by a transversal.

Angles Formed by Parallel Lines

Identify and label the vertex, rays, and interior and exterior of an angle. Use appropriate naming conventions to identify angles.

Angles

Estimate and calculate areas with scale drawings and maps.

Area in Scale Drawings and Maps

Determine the area of rectangles, squares, and composite figures using nonstandard units, grids, and standard units in number and word problems.

Area of Rectangles, Squares, and Composite Figures

Use grids to develop the relationship between the total numbers of square units in a rectangle and the length and width of the rectangle (l x w); find area using the formula in number and word problems.

Area of Rectangles with Grids

Recognize the effect of scale factors or ratios on areas and volumes of similar geometric figures; use formulas to solve number and word problems.

Area and Volume of Similar Geometric Figures

Organize, display, and interpret information in bar graphs.

Bar Graphs

Organize, display, and interpret information in box-and-whisker plots.

Box and Whisker Plots

Estimate and calculate using numbers expressed in scientific notation.

Calculating Using Scientific Notation

Organize, display, and interpret information in circle graphs using ratios and percents.

Circle Graphs

Identify combinations of fractions that make one whole.

Combinations of Fractions

Compare decimals (tenths and hundredths) with and without models.

Comparing Decimals

Compare and order fractions using common numerators or denominators.

Comparing Fractions

Compare and order integers with and without models.

Comparing Integers

Compare and order numbers less than 10,000.

Comparing Numbers Less Than 10,000

Compare and order rational numbers with and without models.

Comparing Rational Numbers

Define and identify complementary and supplementary angles.

Complementary and Supplementary Angles

Locate points in all quadrants of the coordinate plane using ordered pairs in number and word problems.

Coordinate Plane and Ordered Pairs

Locate a point in Quadrant I of a coordinate grid given an ordered pair; name the ordered pair for a point in Quadrant I of a coordinate grid.

Coordinate Plane

Use proportions to express relationships between corresponding parts of similar figures.

Corresponding Parts of Similar Figures

Estimate and compute the cost of items greater than $1.00; make change.

Cost of Items and Making Change

Determine the sample space for an event using counting strategies (include tree diagrams, permutations, combinations, and the fundamental counting principle).

Counting Strategies for Sample Spaces

Describe cross-sectional views of three-dimensional figures.

Cross Sections of Solids

Describe data using or selecting the appropriate measure of central tendency; choose a measure of central tendency based on the shape of the data distribution.

Data, Data Distribution, and Central Tendency

Read, write, and compare numbers with decimal place values to the thousandths place or numbers greater than one million.

Decimals Greater Than One Million

Write equations to represent direct variation and use direct variation to solve number and word problems.

Direct Variation

Use the distance formula to find the distance between two points. Use the midpoint formula to find the coordinates of the midpoint of a segment.

Distance Formula and Midpoint Formula

Calculate distances from scale drawings and maps.

Distance in Scale Drawings and Maps

Use the distributive property to represent and simplify numerical expressions.

Distributive Property

Divide two fractions or a fraction and a whole number in number or word problems.

Dividing Fractions

Model division in a variety of ways including sharing equally, repeated subtraction, rectangular arrays, and the relationship with multiplication.

Division Models

Draw and measure angles using a protractor. Understand that a circle measures 360 degrees.

Drawing and Measuring Angles with a Protractor

Describe the effect of operations on size and order of numbers.

Effect of Operations on Numbers

Identify outliers and determine their effect on the mean, median, and range of a set of data.

Effect of Outliers on Mean, Median, and Range of Data Sets

Elapsed Time

Write an equation to describe the algebraic relationship between two defined variables in number and word problems, including recognizing which variable is dependent.

Equations in Two Variables

Solve equations involving powers and roots by using inverse relationships.

Equations Involving Powers and Roots

Convert fractions and terminating decimals to the thousandths place to equivalent forms without models; explain the equivalence.

Equivalent Fractions and Decimals

Use models to write equivalent fractions, including using composition or decomposition or showing relationships among halves, fourths, and eighths, and thirds and sixths.

Equivalent Fractions Models

Use reasoning with equivalent ratios to solve number and word problems.

Equivalent Ratios

Estimate and compute sums and differences with decimals.

Estimating Decimal Sums and Differences

Estimate the measure of an object in one system given the measure of that object in another system.

Estimating Measurements

Estimate and compute products of whole numbers with multi-digit factors.

Estimating Products of Whole Numbers

Estimate and solve division problems with multi-digit divisors; explain solution.

Estimating Quotients of Whole Numbers

Estimate the square root of a number between two consecutive integers with and without models. Use a calculator to estimate the square root of a number.

Estimating Square Roots to the Nearest Integer

Apply appropriate type of estimation for sums and differences.

Estimating Sums and Differences

Evaluate algebraic expressions in number and word problems.

Evaluating Algebraic Expressions

Use exponential notation and repeated multiplication to describe and simplify exponential expressions.

Exponential Expressions

Simplify numerical expressions that may contain exponents.

Expressions with Exponents

Understand that many whole numbers factor in different ways.

Factors of Whole Numbers

Identify and make figures with line symmetry.

Figures with Symmetry

Calculate the areas of triangles, parallelograms, trapezoids, circles, and composite figures in number and word problems.

Finding the Area of a Triangles, Parallelograms, Trapezoids, Circles, Composite Figures

Find the fractional part of a whole number or fraction with and without models and pictures.

Finding the Fractional Part

Identify or generate numerical and geometric patterns; correct errors in patterns or interpret pattern features.

Finding the Rule of a Number Pattern

Use models to find volume for prisms and cylinders as the product of the area of the base (B) and the height. Calculate the volume of prisms in number and word problems.

Finding Volume with Base and Height

Use models to develop formulas for finding areas of triangles, parallelograms, trapezoids, and circles in number and word problems.

Formulas for Area of Triangles, Parallelograms, Trapezoids, and Circles

Find the lateral area and surface area of a right prism, pyramid, right circular cylinder, and cone using formulas.

Formulas for Lateral Surface Area of Solids

Generate a set of ordered pairs using a rule which is stated in verbal, algebraic, or table form; generate a sequence given a rule in verbal or algebraic form.

Generating Ordered Pairs and Sequences

Use ordered pairs derived from tables, algebraic rules, or verbal descriptions to graph linear functions.

Graphing Linear Functions Using Ordered Pairs

Graphically solve systems of linear equations.

Graphing Systems of Linear Equations

Organize, display, and interpret multiple sets of information in the same graph including multiple bar, multiple stem-and-leaf, and multiple line graphs.

Graphs with Multiple Sets of Information

Organize, display, and interpret information in graphs containing scales that represent multiple units.

Graphs with Scales That Represent Multiple Units

Find factors, common factors, and the greatest common factor of numbers; explain.

Greatest Common Factor

Organize and compare one set of information in histograms and bar graphs.

Histograms vs. Bar Graphs

Organize, display, and interpret information in histograms.

Histograms

Identify proportional parts of similar figures using rulers and protractors.

Identifying Similar Figures Using Measurement

Graph or identify simple inequalities using symbol notation >, <, ≤, ≥, and ≠ in number and word problems.

Inequalities Using Symbolic Notation >, <, ≤, ≥, and ≠

Use concepts of positive numbers, negative numbers, and zero (e.g., on a number line, in counting, in temperature, in "owing") to describe quantities in number and word problems.

Integers

Identify and interpret the intercepts of a linear relation in number and word problems.

Intercepts of Linear Relations

Use properties, definitions, and theorems of polygons to solve problems related to the interior and exterior angles of a convex polygon.

Interior and Exterior Angles of Polygon

Use remainders in problem-solving situations and interpret the remainder with respect to the original problem.

Interpreting Remainders

Identify, draw, and name: points, rays, line segments, lines, and planes.

Introduction to Geometry

Use models to investigate the concept of the Pythagorean Theorem.

Investigating the Pythagorean Theorem

Use rules of exponents to simplify numeric and algebraic expressions.

Laws of Exponents

Find multiples, common multiples, and the least common multiple of numbers; explain.

Least Common Multiple

Write a problem given a simple linear equation or inequality.

Linear Equations and Inequalities in Word Problems

Identify relations as directly proportional, linear, or nonlinear using rules, tables, and graphs.

Linear, Nonlinear, and Directly Proportional Relations

Identify linear and nonlinear relationships in data sets.

Linear and Nonlinear Relationships in Data Sets

Define and identify alternate interior, alternate exterior, corresponding, adjacent and vertical angles.

Lines and Angles

Identify the number of lines of symmetry in a figure and draw lines of symmetry.

Lines of Symmetry

Divide using single-digit divisors with and without remainders.

Long Division

Mean of Data Sets

Median of Data Sets

Mode of Data Sets

Approximate a linear model that best fits a set of data; use the linear model to make predictions.

Modeling Data and Making Predictions

Construct or complete a table of values to solve problems associated with a given relationship.

Modeling with Tables

Determine the value of sets of coins and bills using cent sign and dollar sign appropriately. Create equivalent amounts with different coins and bills.

Money Math

Write a multiplication or a division sentence to represent a number or word problem; solve.

Multiplication and Division Sentences

Multiply or divide two decimals or a decimal and a whole number in number and word problems.

Multiplying and Dividing Decimals

Model or compute with integers using multiplication or division in number and word problems.

Multiplying and Dividing Integers

Multiply or divide with mixed numbers in number and word problems.

Multiplying and Dividing Mixed Numbers

Multiply two fractions or a fraction and a whole number in number and word problems.

Multiplying Fractions

Multiply a multi-digit whole number by a 1-digit whole number or a 2-digit multiple of 10.

Multiplying Multi-digit Numbers

Read and write word names for numbers from 1,000 to 9,999.

Numbers from 1,000 to 9,999

Read, write, and compare whole numbers from 10,000 to less than one million using standard and expanded notation.

Numbers from 10,000 to One Million

Read and write word names for whole numbers from 101 to 999.

Numbers from 101 to 999

Read, write, or model numbers in expanded form using decimal fractions or exponents.

Numbers in Expanded Form

Write whole numbers in scientific notation; convert scientific notation to standard form; investigate the uses of scientific notation.

Numbers in Scientific Notation

Solve one-step linear equations and inequalities and graph solutions of the inequalities on a number line in number and word problems.

One-step Linear Equations and Inequalities

Use order of operations including parentheses and other grouping symbols to simplify numerical expressions.

Order of Operations

Use properties, definitions, and theorems of angles and lines to solve problems related to adjacent, vertical, complementary, supplementary, and linear pairs of angles.

Pairs of Angles

Patterns and Problem Solving

Solve number and word problems involving percent increase and percent decrease.

Percent Increase and Decrease

Calculate or estimate the percent of a number including discounts, taxes, commissions, and simple interest.

Percent of a Number

Solve number and word problems using percent proportion, percent equation, or ratios.

Percent Problems

Determine perimeter using concrete models, nonstandard units, and standard units in number and word problems.

Perimeter

Investigate and determine the relationship between the diameter and the circumference of a circle and the value of pi; calculate the circumference of a circle.

Pi as a Relationship between Diameter and Circumference

Place Value with Thousands

Write the equation of and graph linear relationships given two points on the line.

Point Point Form of a Line

Write the equation of and graph linear relationships given the slope and one point on the line.

Point Slope Form of Line

Points on a Number Line

Distinguish between a population and a sample and draw conclusions about the sample (random or biased).

Population vs. Sample

Identify prime and composite numbers less than 100.

Prime and Composite Numbers

Prime Factorization

Determine a simple probability using geometric figures.

Probabilities in Geometry

Describe the probability of a chance event using a fraction or ratio.

Probability of an Event as Fractions or Ratios

Determine the probability of compound events (with and without replacement).

Probability of Compound Events

Use a coordinate grid to solve number and word problems. Describe the path between given points on the plane.

Problems in the Coordinate Plane

Use the commutative and associative properties to add or multiply numerical expressions.

Properties of Addition and Multiplication

Interpret and compare properties of linear functions, graphs, and equations.

Properties of Linear Functions, Graphs, and Equations

Use manipulatives, pictorial representations, and appropriate vocabulary (e.g., polygon, side, angle, vertex, diameter) to identify and compare properties of plane figures.

Properties of Plane Figures

Write a proportion to model a word problem; solve proportions.

Proportions

Use the Pythagorean Theorem and its converse to solve number and word problems, including finding the distance between two points.

Pythagorean Theorem and its Converse

Determine the quartiles or interquartile range for a set of data.

Quartiles and Interquartile Range of Data

Determine the ratio or rate of change of a relation given a table or graph.

Ratio or Rate Given a Table or Graph

Describe, use, and compare real numbers. Use the definition of rational numbers to derive and distinguish irrational numbers.

Real, Rational, and Irrational Numbers

Locate, given the coordinates of, and graph plane figures which are the results of translations or reflections in all quadrants of the coordinate plane.

Reflections in the Coordinate Plane

Define and distinguish between relations and functions, dependent and independent variables, and domain and range; identify whether relations are functions numerically and graphically.

Relations and Functions

Relate a percent to its equivalent fraction or decimal.

Relationship Between Percent and Fraction or Decimal

Use models to investigate the relationship of the volume of a cone to a cylinder and a pyramid to a prism with the same base and height.

Relationship Between Volume of a Cone and a Cylinder or a Pyramid and a Prism

Identify and draw intersecting, parallel, skew, and perpendicular lines and line segments. Identify midpoints of line segments.

Relationships Between Two Lines and Midpoints of Line Segments

Represent fractions concretely and symbolically, including representing whole numbers as fractions.

Representing Fractions

Rewrite and compare decimals to fractions (tenths and hundredths) with and without models and pictures.

Rewriting Fractions and Decimals

Locate, given the coordinates of, and graph plane figures which are the results of rotations (multiples of 90 degrees) with respect to a given point.

Rotations in the Coordinate Plane

Round decimals to a given place value; round fractions and mixed numbers to a whole number or a given fractional place value.

Rounding Decimals, Fractions, and Mixed Numbers

Given a list of ordered pairs in a table or graph, identify either verbally or algebraically the rule used to generate and record the results.

Rules for Generating Ordered Pairs

Determine and use scale factors to reduce and enlarge drawings on grids to produce dilations.

Scale Factors

Organize, display, and interpret information in scatter plots. Approximate a trend line and identify the relationship as positive, negative, or no correlation.

Scatter Plots

Use proportional reasoning to solve problems related to similar polygons.

Similar Polygons

Use properties of triangles to solve problems related to similar triangles and the relationships of their corresponding parts.

Similar Triangles and Correspondence

Identify corresponding parts of similar and congruent figures.

Similarity and Congruence

Describe the slope of a line given in the context of a problem situation; compare rates of change in linear relationships represented in different ways.

Slope as Rate of Change

Write the equation of and graph linear relationships given the slope and y-intercept.

Slope Intercept Form of a Line

Find the slope of a line given two points on a line, a table of values, the graph of the line, or an equation of the line in number and word problems.

Slope of a Line

Solve linear equations using the associative, commutative, distributive, and equality properties and justify the steps used.

Solving Linear Equations

Use geometric models and equations to investigate the meaning of the square of a number and the relationship to its positive square root. Know perfect squares to 625.

Squares and Square Roots

Relate standard and expanded notation to 3- and 4-digit numbers.

Standard and Expanded Notation of 3 and 4-digit Numbers

Organize, display, and interpret information in stem-and-leaf plots.

Stem and Leaf Plots

Subtract 2- and 3-digit numbers with and without models for number and word problems that require regrouping.

Subtracting 2- and 3-digit Numbers

Use nets or formulas to find the surface area of prisms, pyramids, and cylinders in number and word problems.

Surface Area of Solids

Write and solve systems of linear equations in two or more variables algebraically in number and word problems.

Systems of Linear Equations in Two or More Variables

Organize, display, and interpret information in tables and graphs (frequency tables, pictographs, and line plots).

Tables and Graphs

Determine the probability from experimental results or compare theoretical probabilities and experimental results.

Theoretical vs. Experimental Probability

Identify the place value of each digit in a multi-digit number to the thousandths place.

Thousandths Place in Decimals

Transform (translate, reflect, rotate, dilate) polygons in the coordinate plane; describe the transformation in simple algebraic terms.

Transformations in the Coordinate Plane

Use models or points in the coordinate plane to illustrate, recognize, or describe rigid transformations (translations, reflections, and rotations) of plane figures.

Transforming Plane Figures

Locate, given the coordinates of, and graph points which are the results of rigid transformations in all quadrants of the coordinate plane; describe the path of the motion using geometric models or appropriate terms.

Transforming Points in the Coordinate Plane

Translate between models or verbal phrases and algebraic expressions.

Translating Algebraic Expressions

Write a linear equation or inequality to represent a given number or word problem; solve.

Translating Linear Equations and Inequalities

Solve two-step linear equations and inequalities and graph solutions of the inequalities on a number line.

Two-step Linear Equations and Inequalities

Identify and draw angles (acute, right, obtuse, and straight).

Types of Angles

Name polygons by the number of sides. Distinguish quadrilaterals based on properties of their sides or angles; relate quadrilaterals based upon their hierarchical attributes.

Types of Quadrilaterals

Identify and classify triangles according to the measures of the interior angles and the lengths of the sides; relate triangles based upon their hierarchical attributes.

Types of Triangles

Convert measures of length, area, capacity, weight, and time expressed in a given unit to other units in the same measurement system in number and word problems.

Unit Conversion for Length, Area, Capacity, Weight, and Time

Calculate unit rates in number and word problems, including comparison of unit rates.

Unit Rate

Use benchmark numbers (zero, one-half, one) and models to compare and order fractions.

Using Benchmark Numbers with Fractions

Use definitions and theorems of angles formed when a transversal intersects parallel lines.

Using Theorems for Angles Formed by Parallel Lines

Make predictions based on theoretical probabilities or experimental results.

Using Theoretical and Experimental Probability to Make Predictions

Find the value of a variable in a number sentence.

Value of a Variable in a Number Sentence

Analyze graphs, identify situations, or solve problems with varying rates of change.

Variable Rate of Change

Venn Diagrams

Calculate the volume of cylinders, pyramids, and cones in number and word problems.

Volume of Solids

Describe the meaning of an unknown in the context of a word problem.

Word Problems with One Unknown

Discover free and interactive resources for exploring and practicing algebra, organized by grade level for easy browsing. Ideal for teachers and students in grades 4-8.

Algebra illustration featuring a computer displaying graph of a mathematical function.

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Learn Algebra - GeoGebra Math Resources

Discover free and interactive resources for exploring and practicing geometry, organized by grade level for easy browsing. Ideal for teachers and students in grades 4-8.

Geometry illustration featuring a compass.

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Discover free and interactive resources for exploring and practicing measurement, organized by grade level for easy browsing. Ideal for teachers and students in grades 4-8.

Illustration of measurement tools - ruler and protractor.

Make math come alive with our collection of over {1} free and interactive GeoGebra resources for measurement for grades 4-8. Enhance students' understanding of measurement with our engaging and interactive resources. Improve math proficiency and increase student engagement with GeoGebra's collection of measurement tasks.

Learn Measurement - GeoGebra Math Resources

Discover free and interactive resources for exploring and practicing number sense, organized by grade level for easy browsing. Ideal for teachers and students in grades 4-8.

Illustration of number sense including a blackboard with numbers.

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Illustration of numerical operations in math featuring a calculator.

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Find free, ready-to-use math resources for algebra, geometry, number sense, measurement, operations, statistics and probability across grades 4-8 to enhance student exploration and practice!

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Explore Free Interactive Math Resources for Grades 4-8 - GeoGebra

Discover free and interactive resources for exploring and practicing statistics and probability, organized by grade level for easy browsing. Ideal for teachers and students in grades 4-8.

Illustration of statistics and probability including a bar chart.

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Learn and practice calculating absolute value of numbers and expressions with interactive resources from GeoGebra.

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Learn Congruence and Similarity  - GeoGebra Math Resources

Learn and practice locating points on a number line and in the coordinate plane with interactive resources from GeoGebra.

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Learn and practice calculating the volume of solids with interactive resources from GeoGebra.

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