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  • Alberta Standards
  • Mathematics: 8th Grade Knowledge and Employability

Alberta - Mathematics: 8th Grade Knowledge and Employability

Program of Studies | Adopted: 2006

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.

N: : Number


N.1: : Demonstrate a number sense for whole numbers, common fractions, decimals and percents and apply arithmetic operations to solve problems with whole numbers, fractions, decimals and percents in everyday contexts.

N.1.1: : use estimation strategies to estimate quantities and read and write numerals and number words to 1 000 000

Screenshot of Modeling Whole Numbers and Decimals (Base-10 Blocks)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Rounding Whole Numbers (Number Line)

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Treasure Hunter (Decimals on the Number Line)

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.3: : represent an understanding of place value to the hundredths concretely, pictorially and symbolically

Screenshot of Modeling Decimals (Area and Grid Models)

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling Whole Numbers and Decimals (Base-10 Blocks)

Modeling Whole Numbers and Decimals (Base-10 Blocks)

Model numbers with base-10 blocks. Drag flats, rods, and individual cubes onto a mat to model a number. Blocks can be exchanged from one area of the mat to the other. Four sets of blocks are available to model a variety of whole numbers and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.4: : recognize, model and describe multiples, factors, composites and primes to 100 concretely, pictorially and symbolically

Screenshot of Factor Trees (Factoring Numbers)

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


Lesson Info
Launch Gizmo
Screenshot of Finding Factors with Area Models

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


Lesson Info
Launch Gizmo
Screenshot of Pattern Flip (Patterns)

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


Lesson Info
Launch Gizmo

N.1.5: : represent and describe proper fractions, mixed numbers and equivalent fractions concretely, pictorially and symbolically

Screenshot of Equivalent Fractions (Fraction Tiles)

Equivalent Fractions (Fraction Tiles)

Explore fractions using the Fractionator, the machine that makes fraction tiles. Compare fractions and find equivalent fractions by arranging the tiles on two horizontal rows. Explore simplifying fractions. Add fractions and express sums as improper fractions or mixed numbers. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Fraction Artist 1 (Area Models of Fractions)

Fraction Artist 1 (Area Models of Fractions)

Develop understanding of fractions by making modern paintings. Find different ways to divide a canvas into equal-sized sections. Make paintings to represent simple fractions and to find fractions that are equivalent to one-half. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Fraction Artist 2 (Area Models of Fractions)

Fraction Artist 2 (Area Models of Fractions)

Extend understanding of fractions by making modern paintings in the style of Piet Mondrian. Create and analyze paintings with different-sized sections. Compare the sizes of unit fractions. Find creative ways to color one-half of a painting. This can be a nice introduction to adding fractions with unlike denominators. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Improper Fractions and Mixed Numbers

Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling Fractions (Area Models)

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.6: : compare and order proper fractions and decimals to the hundredths

Screenshot of Comparing and Ordering Decimals

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Modeling Decimals (Area and Grid Models)

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling Fractions (Area Models)

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Treasure Hunter (Decimals on the Number Line)

Treasure Hunter (Decimals on the Number Line)

Drive a desert highway searching for buried treasure. Learn to use the car's tens, ones, tenths, and hundredths gears, along with a GPS system (number line), to find the right place to dig. Plot your findings on a zoomable number line map. Can you become a master Treasure Hunter? 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.7: : estimate and apply arithmetic operations to whole numbers and decimals to the hundredths in everyday contexts

Screenshot of Adding Whole Numbers and Decimals (Base-10 Blocks)

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


Lesson Info
Launch Gizmo
Screenshot of Cargo Captain (Multi-digit Subtraction)

Cargo Captain (Multi-digit Subtraction)

You are the captain of an interplanetary cargo ship, delivering important supplies to the outer planets. The cargo can be stored in barrels, crates, and holds. (There are 10 barrels in a crate, and 10 crates in a hold.) Model multi-digit subtraction by unloading cargo on each planet. 5 Minute Preview


Lesson Info
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Screenshot of Chocomatic (Multiplication, Arrays, and Area)

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Multiplying Decimals (Area Model)

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying with Decimals

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


Lesson Info
Launch Gizmo
Screenshot of No Alien Left Behind (Division with Remainders)

No Alien Left Behind (Division with Remainders)

The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Subtracting Whole Numbers and Decimals (Base-10 Blocks)

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


Lesson Info
Launch Gizmo
Screenshot of Sums and Differences with Decimals

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


Lesson Info
Launch Gizmo
Screenshot of Target Sum Card Game (Multi-digit Addition)

Target Sum Card Game (Multi-digit Addition)

Play an addition card game! The goal is to create a sum that is as close as possible to the target sum. Students will deepen their understanding of place value as they get better at playing the game. Many game options allow students to vary the game for more practice. The game can be played with one or two players. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Whole Numbers with Base-10 Blocks

Whole Numbers with Base-10 Blocks

Use base-10 blocks to model, add, and subtract whole numbers. Learn about place value using flats (hundreds), rods (tens), and cubes (ones). Group or ungroup blocks as needed to add or subtract. This regrouping is often called "carrying" when adding, and "borrowing" when subtracting. 5 Minute Preview


Lesson Info
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N.1.8: : estimate and apply arithmetic operations to proper fractions with like denominators concretely, pictorially and symbolically

Screenshot of Adding Fractions (Fraction Tiles)

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


Lesson Info
Launch Gizmo
Screenshot of Dividing Fractions

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


Lesson Info
Launch Gizmo
Screenshot of Estimating Sums and Differences

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


Lesson Info
Launch Gizmo
Screenshot of Modeling Fractions (Area Models)

Modeling Fractions (Area Models)

Model and compare fractions using area models. Set the denominators with the arrow buttons, and then set the numerators with the arrow buttons or by clicking in the models. Compare fractions visually, on a number line, or numerically using the least common denominator. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Multiplying Fractions

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.9: : identify decimal equivalents for commonly used fractions, such as halves, quarters and tenths

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.10: : estimate and apply arithmetic operations to decimals to the hundredths concretely, pictorially and symbolically to solve problems in everyday contexts

Screenshot of Adding Whole Numbers and Decimals (Base-10 Blocks)

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Decimals (Area Model)

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying with Decimals

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


Lesson Info
Launch Gizmo
Screenshot of Subtracting Whole Numbers and Decimals (Base-10 Blocks)

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


Lesson Info
Launch Gizmo
Screenshot of Sums and Differences with Decimals

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


Lesson Info
Launch Gizmo

N.1.11: : represent and explain the meaning of percentage and the relationship between percentage and decimals concretely, pictorially and symbolically

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo
Screenshot of Percents and Proportions

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


Lesson Info
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Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview


Lesson Info
Launch Gizmo

N.1.12: : assess the reasonableness of calculations and problem-solving strategies, using a variety of tools and/or strategies; e.g., estimation, mental mathematics, tables, graphs, calculators and/or computers

Screenshot of Estimating Sums and Differences

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Decimals (Area Model)

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying with Decimals

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


Lesson Info
Launch Gizmo

N.1.14: : identify common uses of positive and negative numbers, including above/below sea level and temperatures

Screenshot of Adding on the Number Line

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


Lesson Info
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Screenshot of Integers, Opposites, and Absolute Values

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


Lesson Info
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PR: : Patterns and Relations


PR.1: : Construct, extend and summarize patterns, including those found in nature and within their environments, using rules, charts, mental mathematics, calculators and other strategies/tools.

PR.1.1: : identify and describe patterns and relationships in nature and everyday contexts in spoken or written form

Screenshot of Arithmetic Sequences

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview


Lesson Info
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Screenshot of Finding Patterns

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview


Lesson Info
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Screenshot of Geometric Sequences

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Pattern Flip (Patterns)

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


Lesson Info
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PR.1.2: : represent a rule for a pattern, make predictions using the rule and extend the rule

Screenshot of Arithmetic Sequences

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Arithmetic and Geometric Sequences

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Finding Patterns

Finding Patterns

Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Geometric Sequences

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview


Lesson Info
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PR.2: : Use informal and concrete representations of equality and operations to solve problems in everyday contexts.

PR.2.1: : describe everyday situations using variables

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling and 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


Lesson Info
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Screenshot of Solving Two-Step Equations

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
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PR.2.2: : represent and explain the meaning of preservation of equality by balancing or using models and diagrams

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling and 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


Lesson Info
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Screenshot of Solving Equations on the Number Line

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview


Lesson Info
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PR.2.3: : use pre-algebra strategies to solve equations with one unknown and with whole numbers

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Modeling and 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


Lesson Info
Launch Gizmo
Screenshot of Solving Algebraic Equations II

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview


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Screenshot of Solving Equations on the Number Line

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview


Lesson Info
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Screenshot of Solving Two-Step Equations

Solving Two-Step Equations

Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview


Lesson Info
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SS: : Shape and Space


SS.1: : Use measurement concepts, appropriate tools and results of measurements to solve problems in everyday contexts.

SS.1.1: : recognize and explain the meaning of length, width, height, depth, thickness, perimeter and circumference

Screenshot of 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


Lesson Info
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Screenshot of Area of Triangles

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview


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Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview


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Screenshot of Perimeter and Area of Rectangles

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview


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Screenshot of Prisms and 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


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Screenshot of Pyramids and Cones

Pyramids and Cones

Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview


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Screenshot of Surface and Lateral Areas of Prisms and Cylinders

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


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Screenshot of Surface and Lateral Areas of Pyramids and Cones

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


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SS.1.2: : estimate and use everyday metric (SI) tools and units to take accurate linear measurements; e.g., millimetre, centimetre, metre, kilometre

Screenshot of Measuring Trees

Measuring Trees

Measure the height, diameter, and circumference of trees in a forest. Count growth rings to determine the age of each tree. Grow the trees for several years and investigate how growth is affected by precipitation. 5 Minute Preview


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Screenshot of Measuring Volume

Measuring Volume

Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview


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Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview


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SS.1.4: : estimate, measure and calculate the perimeters of quadrilaterals and triangles to solve problems in everyday contexts

Screenshot of 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


Lesson Info
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Screenshot of Area of Triangles

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview


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Screenshot of Perimeter and Area of Rectangles

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview


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SS.1.5: : estimate, measure and calculate the perimeter and area of irregular shapes by dividing them into parts, e.g., area, using manipulatives and diagrams

Screenshot of Area of Triangles

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview


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SS.1.6: : demonstrate the relationships among the circumference, radius and diameter of circles

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview


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SS.1.7: : calculate and solve everyday problems that involve mass (weight) and volume (capacity), using metric and Imperial units

Screenshot of Beam to Moon (Ratios and 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


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Screenshot of Beam to Moon (Ratios and Proportions) - Metric

Beam to Moon (Ratios and Proportions) - Metric

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


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Screenshot of Measuring Volume

Measuring Volume

Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview


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Screenshot of Prisms and 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


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SS.1.8: : use concrete objects to relate cm³ to mL

Screenshot of Measuring Volume

Measuring Volume

Measure the volume of liquids and solids using beakers, graduated cylinders, overflow cups, and rulers. Water can be poured from one container to another and objects can be added to containers. A pipette can be used to transfer small amounts of water, and a magnifier can be used to observe the meniscus in a graduated cylinder. Test your volume-measurement skills in the "Practice" mode of the Gizmo. 5 Minute Preview


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SS.1.9: : use conversion charts, calculators and/or other tools to compare and convert common metric (SI) and Imperial linear units, as required in everyday contexts

Screenshot of Unit Conversions

Unit Conversions

Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview


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Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview


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SS.1.10: : recognize the relationships among seconds, minutes, hours, days, weeks, months, years, centuries and millennia, using a variety of tools; e.g., calendars and technology

Screenshot of Elapsed Time

Elapsed Time

Calculate the difference between the times given by two analog clocks. Rotate the hands of the clocks to change the time and see how the calculation changes. 5 Minute Preview


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Screenshot of Unit Conversions

Unit Conversions

Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview


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Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview


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SS.1.12: : convert between hours and minutes and between minutes and seconds, as required in everyday contexts

Screenshot of Elapsed Time

Elapsed Time

Calculate the difference between the times given by two analog clocks. Rotate the hands of the clocks to change the time and see how the calculation changes. 5 Minute Preview


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Screenshot of Unit Conversions

Unit Conversions

Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Unit Conversions 2 - Scientific Notation and Significant Digits

Unit Conversions 2 - Scientific Notation and Significant Digits

Use the Unit Conversions Gizmo to explore the concepts of scientific notation and significant digits. Convert numbers to and from scientific notation. Determine the number of significant digits in a measured value and in a calculation. 5 Minute Preview


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SS.2: : Use visualization and symmetry to extend their awareness of objects and shapes and solve problems that involve classification and sketching.

SS.2.13: : identify, classify, describe and construct models of 3-D objects; e.g., rectangular prisms, cubes, cylinders, cones and spheres

Screenshot of Balancing Blocks (Volume)

Balancing Blocks (Volume)

This Gizmo provides you with two challenges. First, use blocks to build a figure with a given volume. Then, try to balance the blocks on a platform that sits on the tip of a cone. The dimensions of the platform can be adjusted, and blocks can be added or deleted by clicking on the model. 5 Minute Preview


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Screenshot of Prisms and 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


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Screenshot of Pyramids and Cones

Pyramids and Cones

Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview


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SS.2.14: : design and construct nets for 3-D objects

Screenshot of Surface and Lateral Areas of Prisms and Cylinders

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


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Screenshot of Surface and Lateral Areas of Pyramids and Cones

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


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SS.2.15: : recognize and identify, from everyday observations and experiences, points, lines, parallel lines, intersecting lines, perpendicular lines, vertical lines, horizontal lines and line segments

Screenshot of Parallel, Intersecting, and Skew Lines

Parallel, Intersecting, and Skew Lines

Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview


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SS.2.17: : recognize and label the quadrants on a grid

Screenshot of Points in 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


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SS.2.18: : identify and plot points in the first quadrant of a coordinate grid, using ordered pairs

Screenshot of City Tour (Coordinates)

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview


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Screenshot of Function Machines 2 (Functions, Tables, and Graphs)

Function Machines 2 (Functions, Tables, and Graphs)

Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview


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Screenshot of Linear Functions

Linear Functions

Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview


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Screenshot of Points, Lines, and 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


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SS.3: : Describe motion in terms of slides (translation), turns (rotation) or flips (reflection) and use coordinates to describe and create 2-D objects, including tessellations.

SS.3.20: : recognize and describe motion as a slide (translation), a turn (rotation) or a flip (reflection)

Screenshot of Reflections

Reflections

Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview


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Screenshot of Rock Art (Transformations)

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


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Screenshot of Rotations, Reflections, and Translations

Rotations, Reflections, and Translations

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview


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Screenshot of Translations

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview


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SP: : Statistics and Probability


SP.1: : Implement a plan for collecting, displaying and examining information and data gathered from appropriate sources within everyday contexts.

SP.1.2: : use a variety of strategies to interpret information from prepared graphs and/or charts; e.g.,

SP.1.2.a: : read axis and column subheadings and text under, beside or above

Screenshot of Graphing Skills

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


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SP.1.2.b: : compare and examine pictures, bars, lines, symbols or markers

Screenshot of Box-and-Whisker Plots

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


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Screenshot of Describing Data Using Statistics

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview


Lesson Info
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Screenshot of Graphing Skills

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


Lesson Info
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Screenshot of Histograms

Histograms

Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview


Lesson Info
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Screenshot of Reaction Time 1 (Graphs and Statistics)

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview


Lesson Info
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Screenshot of Reaction Time 2 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview


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SP.1.2.c: : find trends or patterns

Screenshot of Correlation

Correlation

Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview


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Screenshot of Least-Squares Best Fit Lines

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview


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Screenshot of Solving Using Trend Lines

Solving Using Trend Lines

Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview


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Screenshot of Trends in Scatter Plots

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview


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SP.1.3: : make predictions based on information and data

Screenshot of Estimating Population Size

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


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Screenshot of Polling: Neighborhood

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


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Screenshot of Solving Using Trend Lines

Solving Using Trend Lines

Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Trends in Scatter Plots

Trends in Scatter Plots

Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview


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SP.1.4: : develop and communicate appropriate conclusions and discuss the reasonableness of data and results

Screenshot of Polling: City

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


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Screenshot of Populations and Samples

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


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Screenshot of Reaction Time 1 (Graphs and Statistics)

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Reaction Time 2 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview


Lesson Info
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Screenshot of Real-Time Histogram

Real-Time Histogram

Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected. 5 Minute Preview


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Screenshot of Sight vs. Sound Reactions

Sight vs. Sound Reactions

Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user. 5 Minute Preview


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SP.1.5: : gather, organize and display information and data, using a variety of organizers/methods; e.g., journals, diagrams, charts, lists, graphs, spreadsheets, rank ordering and/or frequency charts

Screenshot of Box-and-Whisker Plots

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


Lesson Info
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Screenshot of Correlation

Correlation

Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Describing Data Using Statistics

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Graphing Skills

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


Lesson Info
Launch Gizmo
Screenshot of Histograms

Histograms

Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Reaction Time 1 (Graphs and Statistics)

Reaction Time 1 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Reaction Time 2 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview


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SP.1.6: : examine and discuss the results of simple probability experiments/experiences

Screenshot of Geometric 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


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Screenshot of Probability Simulations

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


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Screenshot of Spin the Big Wheel! (Probability)

Spin the Big Wheel! (Probability)

Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview


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Screenshot of Theoretical and Experimental 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


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SP.1.7: : demonstrate and/or discuss that different outcomes may occur when repeating the same experiment and/or everyday activity

Screenshot of Probability Simulations

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


Lesson Info
Launch Gizmo
Screenshot of Spin the Big Wheel! (Probability)

Spin the Big Wheel! (Probability)

Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Theoretical and Experimental 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


Lesson Info
Launch Gizmo

Correlation last revised: 11/11/2022

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.

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Each STEM Case uses realtime reporting to show live student results.
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.

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