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- Mathematics: 4th Grade
Illinois - Mathematics: 4th Grade
Learning Standards | Adopted: 2010
Math.Content.4.OA: : Operations and Algebraic Thinking
Math.Content.4.OA.A: : Use the four operations with whole numbers to solve problems.
Math.Content.4.OA.A.1: : Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 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.
![Screenshot of Critter Count (Modeling Multiplication)](/Assets/img/blank.gif)
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. 5 Minute Preview
Math.Content.4.OA.A.2: : Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
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
![Screenshot of Critter Count (Modeling Multiplication)](/Assets/img/blank.gif)
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. 5 Minute Preview
![Screenshot of No Alien Left Behind (Division with Remainders)](/Assets/img/blank.gif)
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
Math.Content.4.OA.A.3: : Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
![Screenshot of Cargo Captain (Multi-digit Subtraction)](/Assets/img/blank.gif)
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
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
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
![Screenshot of Critter Count (Modeling Multiplication)](/Assets/img/blank.gif)
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. 5 Minute Preview
![Screenshot of No Alien Left Behind (Division with Remainders)](/Assets/img/blank.gif)
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
![Screenshot of Number Line Frog Hop (Addition and Subtraction)](/Assets/img/blank.gif)
Number Line Frog Hop (Addition and Subtraction)
Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview
Math.Content.4.OA.B: : Gain familiarity with factors and multiples.
Math.Content.4.OA.B.4: : Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
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
![Screenshot of Factor Trees (Factoring Numbers)](/Assets/img/blank.gif)
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
![Screenshot of Finding Factors with Area Models](/Assets/img/blank.gif)
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
Math.Content.4.OA.C: : Generate and analyze patterns.
Math.Content.4.OA.C.5: : Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
![Screenshot of Finding Patterns](/Assets/img/blank.gif)
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
![Screenshot of Function Machines 1 (Functions and Tables)](/Assets/img/blank.gif)
Function Machines 1 (Functions and Tables)
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
![Screenshot of Function Machines 2 (Functions, Tables, and Graphs)](/Assets/img/blank.gif)
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
![Screenshot of Pattern Flip (Patterns)](/Assets/img/blank.gif)
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
Math.Content.4.NBT: : Number and Operations in Base Ten
Math.Content.4.NBT.A: : Generalize place value understanding for multi-digit whole numbers.
Math.Content.4.NBT.A.1: : Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
![Screenshot of Cannonball Clowns (Number Line Estimation)](/Assets/img/blank.gif)
Cannonball Clowns (Number Line Estimation)
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! 5 Minute Preview
![Screenshot of Cargo Captain (Multi-digit Subtraction)](/Assets/img/blank.gif)
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
![Screenshot of Modeling Whole Numbers and Decimals (Base-10 Blocks)](/Assets/img/blank.gif)
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
![Screenshot of Whole Numbers with Base-10 Blocks](/Assets/img/blank.gif)
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
Math.Content.4.NBT.A.2: : Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
![Screenshot of Cannonball Clowns (Number Line Estimation)](/Assets/img/blank.gif)
Cannonball Clowns (Number Line Estimation)
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! 5 Minute Preview
![Screenshot of Modeling Whole Numbers and Decimals (Base-10 Blocks)](/Assets/img/blank.gif)
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
Math.Content.4.NBT.A.3: : Use place value understanding to round multi-digit whole numbers to any place.
![Screenshot of Rounding Whole Numbers (Number Line)](/Assets/img/blank.gif)
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
Math.Content.4.NBT.B: : Use place value understanding and properties of operations to perform multi-digit arithmetic.
Math.Content.4.NBT.B.4: : Fluently add and subtract multi-digit whole numbers using the standard algorithm.
![Screenshot of Adding Whole Numbers and Decimals (Base-10 Blocks)](/Assets/img/blank.gif)
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
![Screenshot of Cargo Captain (Multi-digit Subtraction)](/Assets/img/blank.gif)
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
![Screenshot of Number Line Frog Hop (Addition and Subtraction)](/Assets/img/blank.gif)
Number Line Frog Hop (Addition and Subtraction)
Live a frog's life as you hop along a number line in search of flies. Learn how addition and subtraction can be represented as movement along a number line. Fred the frog may even help you get better at adding and subtracting two-digit numbers in your head by decomposing them into tens and ones. 5 Minute Preview
![Screenshot of Subtracting Whole Numbers and Decimals (Base-10 Blocks)](/Assets/img/blank.gif)
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
![Screenshot of Target Sum Card Game (Multi-digit Addition)](/Assets/img/blank.gif)
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
![Screenshot of Whole Numbers with Base-10 Blocks](/Assets/img/blank.gif)
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
Math.Content.4.NBT.B.5: : Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
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
![Screenshot of Critter Count (Modeling Multiplication)](/Assets/img/blank.gif)
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. 5 Minute Preview
Math.Content.4.NBT.B.6: : Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
![Screenshot of Factor Trees (Factoring Numbers)](/Assets/img/blank.gif)
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
![Screenshot of No Alien Left Behind (Division with Remainders)](/Assets/img/blank.gif)
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
Math.Content.4.NF: : Number and Operations—Fractions
Math.Content.4.NF.A: : Extend understanding of fraction equivalence and ordering.
Math.Content.4.NF.A.1: : Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
![Screenshot of Equivalent Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 1 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Garden (Comparing Fractions)](/Assets/img/blank.gif)
Fraction Garden (Comparing Fractions)
Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview
![Screenshot of Fractions Greater than One (Fraction Tiles)](/Assets/img/blank.gif)
Fractions Greater than One (Fraction Tiles)
Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
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
![Screenshot of Toy Factory (Set Models of Fractions)](/Assets/img/blank.gif)
Toy Factory (Set Models of Fractions)
Create a set of stuffed animals: monkeys, giraffes, and rabbits. Toys can be painted red, green, or blue. Describe the makeup of the set (animals or colors) with fractions. Arrange the toys into groups to simplify the fractions. 5 Minute Preview
Math.Content.4.NF.A.2: : Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
![Screenshot of Equivalent Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 1 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Garden (Comparing Fractions)](/Assets/img/blank.gif)
Fraction Garden (Comparing Fractions)
Plant flowers in two gardens to help develop fraction sense. The two gardens act as number lines, from 0 to 1. Use the flowers in the gardens to compare fractions and to explore equivalent fractions. Chalk marks can be drawn to divide the garden into equal sections. 5 Minute Preview
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.B: : Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Math.Content.4.NF.B.3: : Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Math.Content.4.NF.B.3.a: : Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
![Screenshot of Adding Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fractions Greater than One (Fraction Tiles)](/Assets/img/blank.gif)
Fractions Greater than One (Fraction Tiles)
Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.B.3.b: : Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
![Screenshot of Adding Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Equivalent Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 1 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
Math.Content.4.NF.B.3.c: : Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
![Screenshot of Fractions Greater than One (Fraction Tiles)](/Assets/img/blank.gif)
Fractions Greater than One (Fraction Tiles)
Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview
![Screenshot of Improper Fractions and Mixed Numbers](/Assets/img/blank.gif)
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
Math.Content.4.NF.B.3.d: : Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
![Screenshot of Adding Fractions (Fraction Tiles)](/Assets/img/blank.gif)
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
![Screenshot of Fractions Greater than One (Fraction Tiles)](/Assets/img/blank.gif)
Fractions Greater than One (Fraction Tiles)
Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview
![Screenshot of Improper Fractions and Mixed Numbers](/Assets/img/blank.gif)
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
Math.Content.4.NF.B.4: : Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Math.Content.4.NF.B.4.a: : Understand a fraction a/b as a multiple of 1/b.
![Screenshot of Fraction Artist 1 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.B.4.b: : Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
![Screenshot of Fraction Artist 1 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Fraction Artist 2 (Area Models of Fractions)](/Assets/img/blank.gif)
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
![Screenshot of Modeling Fractions (Area Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.C: : Understand decimal notation for fractions, and compare decimal fractions.
Math.Content.4.NF.C.5: : Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.C.6: : Use decimal notation for fractions with denominators 10 or 100.
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
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
Math.Content.4.NF.C.7: : 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 >, =, or <, and justify the conclusions, e.g., by using a visual model.
![Screenshot of Fraction, Decimal, Percent (Area and Grid Models)](/Assets/img/blank.gif)
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
![Screenshot of Modeling Decimals (Area and Grid Models)](/Assets/img/blank.gif)
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
![Screenshot of Treasure Hunter (Decimals on the Number Line)](/Assets/img/blank.gif)
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
Math.Content.4.MD: : Measurement and Data
Math.Content.4.MD.A: : Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
Math.Content.4.MD.A.1: : Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.
![Screenshot of Cannonball Clowns (Number Line Estimation)](/Assets/img/blank.gif)
Cannonball Clowns (Number Line Estimation)
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! 5 Minute Preview
![Screenshot of Elapsed Time](/Assets/img/blank.gif)
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
Math.Content.4.MD.A.2: : Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
![Screenshot of Cannonball Clowns (Number Line Estimation)](/Assets/img/blank.gif)
Cannonball Clowns (Number Line Estimation)
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! 5 Minute Preview
![Screenshot of Elapsed Time](/Assets/img/blank.gif)
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
![Screenshot of Road Trip (Problem Solving)](/Assets/img/blank.gif)
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
Math.Content.4.MD.A.3: : Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
![Screenshot of Chocomatic (Multiplication, Arrays, and Area)](/Assets/img/blank.gif)
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
![Screenshot of Fido's Flower Bed (Perimeter and Area)](/Assets/img/blank.gif)
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. 5 Minute Preview
Math.Content.4.MD.C: : Geometric measurement: understand concepts of angle and measure angles.
Math.Content.4.MD.C.7: : Recognize angle measure as additive. When an angle is decomposed into non-overlapping 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 real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
Math.Content.4.G: : Geometry
Math.Content.4.G.A: : Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Math.Content.4.G.A.1: : Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
![Screenshot of Classifying Quadrilaterals](/Assets/img/blank.gif)
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
![Screenshot of Classifying Triangles](/Assets/img/blank.gif)
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
Math.Content.4.G.A.2: : 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.
![Screenshot of Classifying Quadrilaterals](/Assets/img/blank.gif)
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
![Screenshot of Classifying Triangles](/Assets/img/blank.gif)
Classifying Triangles
Place constraints on a triangle and determine what classifications must apply to the triangle. 5 Minute Preview
Math.Content.4.G.A.3: : Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
![Screenshot of Holiday Snowflake Designer](/Assets/img/blank.gif)
Holiday Snowflake Designer
Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper. 5 Minute Preview
![Screenshot of Quilting Bee (Symmetry)](/Assets/img/blank.gif)
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
Correlation last revised: 8/22/2022
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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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
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Start teaching with 20-40 Free Gizmos. See the full list.
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