College and Career-Ready Standards | Adopted: 2025
This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
NOS: Number and Operation Sense
4.NOS.A: Generalize place value understanding for multi-digit whole numbers.
4.NOS.A.1: Apply and extend place value understanding to multi-digit whole numbers within 1,000,000.
4.NOS.A.2: Explain that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right (e.g., recognize that 700 รท 70 = 10 by applying concepts of place value and division).
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.
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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.
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Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more!
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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.
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4.NOS.B: Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NOS.B.3: Fluently add and subtract multi-digit whole numbers within 1,000,000.
4.NOS.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.
4.NOS.B.6: Divide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders.
4.NOS.C: Gain familiarity with factors and multiples.
4.NOS.C.7: Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotients less than are equal to 10).
4.NOS.C.8: Explain and apply concepts of factors, multiples, and prime and composite numbers for whole numbers in the range of 1-100.
4.NOS.D: Extend understanding of fraction equivalence and ordering.
4.NOS.D.9: Understand and generate equivalent fractions.
4.NOS.D.10: Compare two fractions with different numerators and different denominators, understanding that comparisons are valid only when the two fractions refer to the same whole.
4.NOS.E: Build fractions from unit fractions by applying and extending previous understandings of Operations on whole numbers.
4.NOS.E.11: Apply understanding of a fraction ๐/๐ with ๐ >1 as a sum of unit fractions (1/๐) to decompose a fraction (including fractions greater than 1) into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation. Justify decompositions using visual fraction models and equations (e.g., 3/8 = 1/8 + 1/8 + 1/8 or 3/8 = 1/8 + 2/8 or 2 1/8 = 1 + 1 + 1/8 or 2 1/8 = 8/8 + 8/8 + 1/8).
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.
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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.
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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.
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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.
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4.NOS.E.12: Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract fractions with like denominators.
4.NOS.E.13: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number (๐ ร ๐/๐).
4.NOS.F: Understand decimal notation for fractions and compare decimal fractions.
4.NOS.F.14: Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 to add two fractions with respective denominators of 10 and 100.
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.
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4.NOS.F.15: Use decimal notation for fractions with denominators 10 and 100 (e.g., rewrite 0.62 as 62/100 or describe a length as 0.62 meters or locate 0.62 on a number line).
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.
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4.NOS.F.16: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, (e.g. using a visual model).
Comparing and Ordering Decimals
Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line.
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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?
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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.
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4.AT.A: Represent and solve problems involving multiplication and division.
4.AT.A.1: Interpret a multiplication situation as a comparison (e.g., interpret 35 = 5 ร 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.
Critter Count (Modeling Multiplication)
Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the critters either on leaves or as a rectangular array.
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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.
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4.AT.A.2: Multiply or divide to solve multiplicative comparison problems in context by using drawings and equations with a symbol for the unknown number to represent the problem.
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.
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Use groups of critters on leaves to model multiplication as repeated addition. Change the expression to change the number of groups or the number of critters per group. Display the critters either on leaves or as a rectangular array.
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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.
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4.GR.A: Solve problems involving measurement conversion, area, and perimeter.
4.GR.A.1: Apply the relationship between measurement units within a given measurement system (customary: in, ft, yd, oz, lb, sec, min, hr; metric: cm, m, km, g, kg, mL, L) to convert measurements from a larger unit to smaller unit.
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.
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Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more!
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4.GR.A.2: Use the four operations to solve problems in context involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving common fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.
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.
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Launch clowns from a circus cannon and try to hit the target. Drag digit cards on the control panel to set the launch distance and choose an appropriate unit of distance. After practicing your clown-launching skills on a number line, move on to the Big Top, Football Field, School Buses, the Golden Gate Bridge, and more!
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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.
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4.GR.A.3: Apply the area and perimeter formulas for rectangles in context, including rectangles with missing dimensions.
Fido's Flower Bed (Perimeter and Area)
Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas.
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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.
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4.GR.A.4: Relate the area of a triangle to the area of a rectangle using decomposition and visual models. Derive and apply the formula to solve problems in contexts involving triangles positioned within or formed from the decomposition of rectangles.
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.
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4.GR.B: Understand concepts of angle and measure angles.
4.GR.B.7: Explain that when an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in context (e.g., by using an equation with a symbol for the unknown angle measure).
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
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4.GR.C: Draw and identify lines and angles and classify shapes by properties of their lines and angles.
4.GR.C.8: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
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.
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4.GR.C.9: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category and identify right triangles.
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.
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4.DS.A.1: Ask and answer questions by collecting, organizing and summarizing data, recognizing the importance of context when analyzing data.
Correlation last revised: 7/9/2026
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.
