- Home
- Find Gizmos
- Browse by Core Curriculum
- Holt Textbooks
- Course 1: Numbers to Algebra (2008)
Course 1: Numbers to Algebra (2008)
1: Algebraic Reasoning
1.3: Order of Operations

Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
1.6: Writing Algebraic Expressions

Using Algebraic Expressions
Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview
1.8: Solving Equations by Subtracting

Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
1.9: Solving Equations by Adding

Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
2: Integers
2.1: Introduction to Integers

Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
2.2: Adding Integers

Adding on the Number Line
Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview

Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
2.3: Subtracting Integers

Adding and Subtracting Integers
Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

Adding and Subtracting Integers with Chips
Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview
2.6: The Coordinate Plane

Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
2.8: Graphing Equations

Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
3: Number Theory and Fractions
3.1: Prime Factorization

Factor Trees (Factoring Numbers)
The Factor Trees Gizmo has two modes. In Factor mode, you can create factor trees to factor composite numbers into primes. In Build mode, you can build numbers by multiplying primes together. Can you build all composite numbers up to 50? Any whole composite number up to 999 can be factored or built with the Gizmo. 5 Minute Preview

Finding Factors with Area Models
Find factors of a number using an area model. Reshape the area rectangle to see different factorizations of the number. Find the prime factorization using a factor tree. 5 Minute Preview
3.3: Least Common Multiple

Pattern Flip (Patterns)
In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview
3.4: Equivalent Fractions and Mixed Numbers

Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
3.5: Equivalent Fractions and Decimals

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
3.6: Comparing and Ordering Rational Numbers

Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview
4: Operations with Rational Numbers
4.1: Estimating with Fractions

Estimating Sums and Differences
Estimate the sum or difference of two fractions using area models. Compare estimates to exact sums and differences. 5 Minute Preview
4.2: Adding and Subtracting Fractions

Adding Fractions (Fraction Tiles)
Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview

Fractions with Unlike Denominators
Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview
4.4: Multiplying Fractions and Mixed Numbers

Multiplying Mixed Numbers
Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
4.5: Dividing Fractions and Mixed Numbers

Dividing Fractions
Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

Dividing Mixed Numbers
Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
4.7: Adding, Subtracting, and Multiplying Decimals

Adding Whole Numbers and Decimals (Base-10 Blocks)
Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying when adding. Four sets of blocks are available to model different place values. 5 Minute Preview

Multiplying Decimals (Area Model)
Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview

Multiplying with Decimals
Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the mat to the other to help understand regrouping and borrowing. Four sets of blocks are available to model different place values. 5 Minute Preview

Sums and Differences with Decimals
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line. 5 Minute Preview
4.10: Solving Equations Containing Decimals

Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
5: Proportional Relationships
5.1: Ratios

Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
5.2: Rates

Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview

Road Trip (Problem Solving)
Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview
5.3: Identifying and Writing Proportions

Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview

Proportions and Common Multipliers
Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview
5.4: Solving Proportions

Beam to Moon (Ratios and Proportions)
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
5.6: Similar Figures and Proportions

Similar Figures
Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview
5.7: Using Similar Figures

Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview

Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
5.8: Scale Drawings and Scale Models

Perimeters and Areas of Similar Figures
Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare. 5 Minute Preview
6: Percents
6.1: Introduction to Percents

Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
6.2: Fractions, Decimals, and Percents

Fraction, Decimal, Percent (Area and Grid Models)
Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Percents, Fractions, and Decimals
Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
6.4: Percent of a Number

Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
6.5: Solving Percent Problems

Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview
6.6: Percent of Change

Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
6.7: Simple Interest

Compound Interest
Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview
7: Collecting, Displaying, and Analyzing data
7.1: Mean, Median, Mode, and Range

Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview

Mean, Median, and Mode
Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview
7.4: Analyzing Data Displays

Graphing Skills
Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview
7.6: Populations and Samples

Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview

Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population. 5 Minute Preview
7.7: Selecting Samples

Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
8: Probability
8.1: Introduction to Probability

Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
8.2: Experimental Probability

Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview

Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
8.3: Theoretical Probability

Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
8.4: Sample Spaces

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
8.5: Disjoint Events

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
8.6: Independent and Dependent Events

Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
9: Geometric Figures
9.3: Angle Relationships

Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
9.6: Classifying Triangles

Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
9.7: Angle Measures in Triangles

Triangle Inequalities
Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles. 5 Minute Preview
9.8: Classifying Quadrilaterals

Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
9.9: Congruent Figures

Quilting Bee (Symmetry)
Participate in an old-fashioned quilting bee and create a colorful, symmetrical quilt. Quilts can be created with a vertical, horizontal, or diagonal line of symmetry. Quilts can be folded to look for reflections, or rotated to test for rotational symmetry. 5 Minute Preview

Rock Art (Transformations)
Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings. 5 Minute Preview
10: Measurement and Geometry
10.2: Circles and Circumference

Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
10.3: Area of Parallelograms

Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
10.4: Area of Triangles and Trapezoids

Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
10.5: Area of Circles

Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
10.8: Volume of Prisms

Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
10.9: Volume of Cylinders

Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
10.10: Surface Area

Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview

Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
11: Multi-Step Equations and Inequalities
11.1: Solving Two-Step Equations

Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview

Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
11.3: Solving Multi-Step Equations

Solving Formulas for any Variable
Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps. 5 Minute Preview
11.4: Solving Equations with Variables on Both Sdes

Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
11.5: Introduction Inequalities

Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
11.6: Solving Inequalities by Adding or Subtracting

Solving Linear Inequalities in One Variable
Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview
11.7: Solving Inequalities by Multiplying or Dividing

Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
How Free Gizmos Work

Start teaching with 20-40 Free Gizmos. See the full list.

Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.

All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.

Free Gizmos change each semester. The new collection will be available January 1 and July 1.
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.

Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap

STEM Cases take between 30-90 minutes for students to complete, depending on the case.

Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.

Multiple grade-appropriate versions, or levels, exist for each STEM Case.

Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
Find Your Solution
Start playing, exploring and learning today with a free account. Or contact us for a quote or demo.
Sign Up For Free Get a Quote