Illustrative Math Alignment: Grade 7 Unit 9
Putting it All Together
Lesson 8: Measurement Error (Part 1)
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Solving Equations--Equations with Fractions: Example 4 | Equations with Fractions: Example 4TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 4 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example--Solving Equations--Equations with Fractions: Example 5 | Equations with Fractions: Example 5TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 5 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example--Solving Equations--Equations with Fractions: Example 6 | Equations with Fractions: Example 6TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 6 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example--Solving Equations--Equations with Fractions: Example 7 | Equations with Fractions: Example 7TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 7 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example--Solving Equations--Equations with Fractions: Example 8 | Equations with Fractions: Example 8TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 8 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example--Solving Equations--Equations with Fractions: Example 9 | Equations with Fractions: Example 9TopicEquations DescriptionThis example illustrates solving Equations with Fractions: Example 9 which involves fractions. These equations can be addressed by first removing the fractions by finding a common denominator and multiplying through. This transforms the equation into a standard linear form that can then be solved by isolating the variable. The specific equation in the image shows the importance of maintaining accuracy in operations, and understanding the process is crucial for advancing in algebra. |
Solving Fraction Equations |
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Math Example: Algebra Tiles: Example 1 | Math Example: Algebra Tiles: Example 1TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the addition of 7 and 12 using algebra tiles. Two groups of yellow tiles, one with 7 tiles and another with 12 tiles, are combined to show a total of 19 tiles. This visual representation helps students understand the concept of addition with positive integers. |
Numerical Expressions |
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Math Example: Algebra Tiles: Example 10 | Math Example: Algebra Tiles: Example 10TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the subtraction of 5 from -3 using algebra tiles. The image shows 3 red tiles representing -3, and 5 yellow tiles are added to create zero pairs. After removing the zero pairs, 2 additional red tiles remain, illustrating that -3 - 5 = -8. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 11 | Math Example: Algebra Tiles: Example 11TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the subtraction of -3 from -8 using algebra tiles. The image shows 8 red tiles representing -8, and 3 red tiles are removed to demonstrate the subtraction of -3. The result is 5 red tiles, visually showing that -8 - (-3) = -5. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 12 | Math Example: Algebra Tiles: Example 12TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the subtraction of -6 from -4 using algebra tiles. The image shows 4 red tiles representing -4, and 6 yellow tiles are added to form zero pairs. After removing these pairs, 2 yellow tiles remain, illustrating that -4 - (-6) = 2. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 13 | Math Example: Algebra Tiles: Example 13TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the subtraction of -7 from -7 using algebra tiles. The image shows 7 red tiles representing -7, and 7 red tiles are removed to demonstrate the subtraction of -7. The result is zero tiles remaining, visually showing that -7 - (-7) = 0. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 14 | Math Example: Algebra Tiles: Example 14TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x + 3 = 5 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By creating zero pairs and isolating the variable, the solution x = 2 is visually represented. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 15 | Math Example: Algebra Tiles: Example 15TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x + 4 = 2 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By manipulating the tiles and creating zero pairs, the solution x = -2 is visually demonstrated. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 16 | Math Example: Algebra Tiles: Example 16TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x + 5 = 5 using algebra tiles. The image shows green tiles representing the variable x, and yellow tiles representing positive integers. By manipulating the tiles, students can visually see that x = 0. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 17 | Math Example: Algebra Tiles: Example 17TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x + (-2) = 5 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By strategically moving pieces and creating zero pairs, students can visually determine that x = 7. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 18 | Math Example: Algebra Tiles: Example 18TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x + 3 = -2 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By manipulating the tiles and creating zero pairs, students can visually see that x = -5. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 19 | Math Example: Algebra Tiles: Example 19TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x + (-4) = -1 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By manipulating the tiles and creating zero pairs, students can visually determine that x = 3. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 2 | Math Example: Algebra Tiles: Example 2TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the addition of 6 and -3 using algebra tiles. It shows 6 yellow tiles representing positive integers and 3 red tiles representing negative integers. After removing zero pairs (one yellow tile cancels out one red tile), the result is 3 yellow tiles, demonstrating that 6 + (-3) = 3. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 20 | Math Example: Algebra Tiles: Example 20TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x + (-2) = -6 using algebra tiles. The image shows green tiles representing the variable x, yellow tiles representing positive integers, and red tiles representing negative integers. By manipulating the tiles and creating zero pairs, students can visually see that x = -4. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 21 | Math Example: Algebra Tiles: Example 21TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x+(-5) = -5 using algebra tiles. The image depicts green tiles representing the variable x, red tiles representing negative integers, and yellow tiles representing positive integers. By manipulating these tiles, students can visually see that x = 0. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 22 | Math Example: Algebra Tiles: Example 22
This is part of a collection of math examples that use algebra tiles. This includes modeling integers, sums, differences, and equations. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 23 | Math Example: Algebra Tiles: Example 23TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation 3x + 3 = x + 1 using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. After removing common terms and adding red squares to balance the equation, students can visually see that x = -1. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 24 | Math Example: Algebra Tiles: Example 24TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation 3x + 2 = x + 2 using algebra tiles. The image shows green bars representing the variable x and yellow squares representing constants. After removing common terms from both sides, students can visually see that 2x = 0, leading to the solution x = 0. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 25 | Math Example: Algebra Tiles: Example 25TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation 4x + (-2) = x + 3 using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually determine the solution. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 26 | Math Example: Algebra Tiles: Example 26TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation 3x + 4 = x + (-2) using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually determine the solution. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 27 | Math Example: Algebra Tiles: Example 27TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation 4x + (-3) = x + (-2) using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually determine the solution. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 28 | Math Example: Algebra Tiles: Example 28TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation 3x + (-2) = x + (-5) using algebra tiles. The image shows green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually determine that x = -2/3. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 29 | Math Example: Algebra Tiles: Example 29TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation 4x + (-4) = x + (-4) using algebra tiles. The image depicts green bars representing the variable x, yellow squares representing positive constants, and red squares representing negative constants. By eliminating common terms and zero pairs, students can visually see that x = 0. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 3 | Math Example: Algebra Tiles: Example 3TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the addition of 5 and -8 using algebra tiles. It shows 5 yellow tiles representing positive integers and 8 red tiles representing negative integers. After removing zero pairs, the result is 3 red tiles, illustrating that 5 + (-8) = -3. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 30 | Math Example: Algebra Tiles: Example 30TopicNumerical and Algebraic Expressions DescriptionThis example shows a quadratic equation x2 + 2x - 1 = 0 being solved using algebra tiles. The image illustrates factoring by completing the square and solving for x. This visual representation helps students understand the process of solving quadratic equations. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 31 | Math Example: Algebra Tiles: Example 31TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the quadratic equation x2 + 2x + 1 = 0 using algebra tiles. The image shows factoring as (x + 1)2 = 0 and solving for x, resulting in the solution x = -1. This visual representation helps students understand perfect square trinomials and their solutions. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 32 | Math Example: Algebra Tiles: Example 32TopicNumerical and Algebraic Expressions DescriptionThis example presents solving the quadratic equation x2 - 3x + 2 = 0 using algebra tiles, showing a different approach with negative tiles. It factors as (x - 2)(x - 1) = 0, leading to solutions x = 2 and x = 1. This visual representation helps students understand factoring and solving quadratic equations with two solutions. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 33 | Math Example: Algebra Tiles: Example 33TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the quadratic equation x2 - 3x + 2 = 0 using algebra tiles. It illustrates completing the square and factoring into (x - 2)(x - 1) = 0, followed by solving for x to get solutions x = 1 and x = 2. This visual representation helps students understand the process of completing the square and its relation to factoring. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 34 | Math Example: Algebra Tiles: Example 34TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x - 3 = 5 using algebra tiles. It shows modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand the process of solving linear equations with one variable. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 35 | Math Example: Algebra Tiles: Example 35TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x - 2 = -3 with algebra tiles. The image shows the steps of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand how to solve equations with negative numbers. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 36 | Math Example: Algebra Tiles: Example 36TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x - 2 = -2 using algebra tiles. The image shows a step-by-step solution, including modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations where the solution is zero. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 37 | Math Example: Algebra Tiles: Example 37TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x - (-2) = 4 using algebra tiles. The image shows a step-by-step solution, including modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 38 | Math Example: Algebra Tiles: Example 38TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates solving the equation x - (-4) = 2 with algebra tiles. The image shows the process of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers and their solutions. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 39 | Math Example: Algebra Tiles: Example 39TopicNumerical and Algebraic Expressions DescriptionThis example illustrates solving the equation x - (-3) = 3 using algebra tiles. The image shows the steps of modeling the variable, adding zero pairs, modeling the equation, and solving it. This visual representation helps students understand equations involving subtraction of negative numbers and their solutions. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 4 | Math Example: Algebra Tiles: Example 4TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the addition of 7 and -7 using algebra tiles. It shows 7 yellow tiles representing positive integers and 7 red tiles representing negative integers. When combined, these tiles form zero pairs, resulting in a sum of zero. This demonstrates that 7 + (-7) = 0, visually representing the concept of additive inverses. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 5 | Math Example: Algebra Tiles: Example 5TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the addition of two negative numbers, -6 and -8, using algebra tiles. The image shows 6 red tiles representing -6 and 8 red tiles representing -8. When combined, these tiles result in a total of 14 red tiles, illustrating that -6 + (-8) = -14. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 6 | Math Example: Algebra Tiles: Example 6TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the subtraction of 5 from 14 using algebra tiles. The image shows 14 yellow tiles representing the initial value, and then 5 tiles are removed, leaving 9 yellow tiles. This visually demonstrates that 14 - 5 = 9. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 7 | Math Example: Algebra Tiles: Example 7TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the subtraction of 10 from 8 using algebra tiles. The image shows 8 yellow tiles representing the initial value, and two red tiles next to them. To subtract 10, zero pairs are added as necessary, resulting in a final answer of -2, represented by two red tiles. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 8 | Math Example: Algebra Tiles: Example 8TopicNumerical and Algebraic Expressions DescriptionThis example demonstrates the subtraction of 16 from itself using algebra tiles. The image shows 16 yellow tiles arranged in two rows of eight. Below this, the same 16 tiles are shown with a subtraction sign, illustrating the process of removing all tiles to reach zero. |
Algebra Tiles--Expressions and Equations |
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Math Example: Algebra Tiles: Example 9 | Math Example: Algebra Tiles: Example 9TopicNumerical and Algebraic Expressions DescriptionThis example illustrates the subtraction of a negative number, specifically 8 - (-3), using algebra tiles. The image shows 8 yellow tiles representing the positive 8, and three red tiles are added to represent the subtraction of -3. This visual representation demonstrates that subtracting a negative number is equivalent to adding its positive counterpart, resulting in a total of 11 yellow tiles. |
Algebra Tiles--Expressions and Equations |
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MATH EXAMPLES--Teacher's Guide: Algebra Tiles | MATH EXAMPLES--Teacher's Guide: Algebra Tiles
What Are Algebra Tiles?Numerical Models |
Algebra Tiles--Expressions and Equations |
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Math in the News: Issue 101--Comet Landing | Math in the News: Issue 101--Comet Landing
November 2014. In this issue of Math in the News we examine the historic landing of a spacecraft on an asteroid in space. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Quadratic Functions |
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Math in the News: Issue 112--Back-to-School Purchases | Math in the News: Issue 112--Back-to-School Purchases
September 2016. In this issue of Math in the News, we look at back-to-school purchases and the impact that different tax rates have on the total cost. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 117--Box Office Hits and Misses | Math in the News: Issue 117 | Box Office Hits and Misses
December 2022. In this issue of Math in the News we look at box office hits and misses from Disney. The House of Blockbosters every now and then misfires. It's useful to analyze box office data to see what we can learn from the hits and misses. —PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.Note: The download is a PPT file. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 121--NFL Concussion Statistics | Math in the News: Issue 121 | NFL Concussion Statistics
February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions. —PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.Note: The download is a PPT file. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents |
