G6 m3-a-lesson 3-s
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The document describes examples using positive and negative numbers to represent real-world situations involving elevation, temperature, money amounts, and more. It includes exercises asking students to: 1) Write integers to represent a diver below sea level, a sailor at sea level, and a hiker above sea level. 2) Graph integers on a number line to show a hiker and diver's elevations relative to sea level. 3) Identify which of two statements correctly describes submarine depth and a coral reef's elevation in relation to sea level.
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G6 m3-a-lesson 4-s
1. The document discusses opposites of numbers on a number line. Every integer has an opposite that is the same distance from zero but on the opposite side.
2. Examples locate the opposite of numbers such as 8 (-8) and illustrate opposites in contexts like locations along a street (furthest is the opposite direction from the starting point).
3. Exercises have students find and explain opposites of numbers in numerical examples and real-world contexts like temperature, elevation, and financial amounts.
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This document contains notes from lessons on rational numbers from a mathematics module. It includes examples and exercises on locating rational numbers on number lines, including integers and fractions. Key points covered are that rational numbers can be written as fractions, integers and some decimals are rational, and the opposite of a rational number has the same magnitude but opposite sign when graphed on a number line. Sample problems have students graphing rational numbers and their opposites on number lines segmented into units of equal length.
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This document contains notes from mathematics lessons on positive and negative numbers on the number line. Some key points include:
1) Positive and negative numbers can represent real-world concepts like elevation, temperature, and bank account balances in relation to a fixed reference point like sea level or zero degrees.
2) The opposite of any nonzero number has the same magnitude but opposite sign, located an equal distance from zero on the other side of the number line.
3) Zero is its own opposite and serves as a reference point for determining relative positions above or below for elevations, temperatures, and financial amounts.
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This document contains notes from mathematics lessons on positive and negative numbers on the number line. Some key points include:
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This document defines key vocabulary terms related to integers and absolute value. It defines positive numbers as greater than zero, negative numbers as less than zero, and opposites as numbers the same distance from zero but on different sides. Integers are defined as all whole numbers and their opposites. Absolute value is defined as the distance of a number from zero on the number line, with the absolute value symbol being | |. An example of calculating absolute value is given.
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This document provides examples and exercises about calculating the volumes of cubes and rectangular prisms using formulas. It begins with examples of calculating the volume of a cube with sides of 2 1/4 cm and a rectangular prism with a base area of 7/12 ft^2 and height of 1/3 ft. The exercises then involve calculating volumes of cubes and prisms when dimensions are changed, identifying relationships between dimensions and volumes, and writing expressions for volumes.
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This lesson teaches students about calculating the volume of rectangular prisms using two different formulas: 1) length × width × height and 2) area of the base × height. Students work through examples calculating the volume of various rectangular prisms using both formulas. They learn that it does not matter which face is used as the base, as the volume will be the same. The lesson reinforces that volume can be expressed in multiple equivalent ways and emphasizes using the area of the base times the height.
G6 m5-c-lesson 12-s
This document provides examples and problems about calculating the volume of rectangular prisms. It begins by showing different rectangular prisms and having students write expressions for the volume of each using length, width, and height. It explains that the volume can also be written as the area of the base times the height. Students then practice calculating volumes using both methods. Later problems involve calculating volume when given the area of the base and height or vice versa. The goal is for students to understand that the volume of a rectangular prism is the area of its base multiplied by its height.
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1) The document outlines a math lesson plan for a week in May that includes topics on polygons, area, surface area, and volume.
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G6 m5-b-lesson 9-t
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This document provides examples and exercises for plotting polygons on a coordinate plane and calculating their areas. It includes examples of plotting triangles, rectangles, and other polygons given their vertices and calculating their areas. It then gives practice problems for students to plot polygons on their own, name the shapes, determine the areas using formulas, and write expressions to represent the area calculations. The final problems involve finding missing vertices of polygons when given some vertices and the total area.
G6 m5-b-lesson 8-note sheet
1. The document contains a student worksheet with multiple geometry problems. It asks the student to plot points, identify shapes, and calculate areas. The first problem involves plotting points A, B, and C, identifying the triangle shape, and calculating its area.
2. The second problem has the student plot points E, F, and G, name the triangle shape, and calculate its area.
3. The third problem involves plotting points K, L, M, and N, naming the quadrilateral shape, and calculating its total area.
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This document contains notes from a math lesson on volume. It discusses determining the volume of composite figures using decomposition into simpler shapes. Students will practice finding the volume of various objects. The document contains examples of area problems and notes for students to solve.
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1) This lesson teaches students the formulas for calculating the volume of right rectangular prisms and cubes. It provides examples of using the formulas to find the volume when given the length, width, height or area of the base.
2) Students complete exercises that explore how changes to the lengths or heights affect the volume. They discover that if the height is doubled, the volume is also doubled, and if the height is tripled the volume is tripled.
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This lesson teaches students about calculating the volume of rectangular prisms using two different formulas: 1) length × width × height and 2) area of the base × height. Students work through examples calculating the volume of various rectangular prisms using both formulas. They learn that it does not matter which face is used as the base, as the volume will be the same. The lesson reinforces that volume can be expressed in multiple equivalent ways and emphasizes using the area of the base times the height.
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2) On Tuesday, students will work on problem sets for Lesson 9 and 13, which cover finding the perimeter and area of polygons on the coordinate plane.
3) On Thursday, students will work on a Lesson 15 worksheet, and on Friday they are asked to bring in a rectangular prism from home to create a net and label edge lengths.
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Lesson 9 focuses on determining the area and perimeter of polygons on the coordinate plane. Students will find the perimeter of irregular figures by using coordinates to find the length of sides joining points with the same x- or y-coordinate. Students will also find the area enclosed by a polygon by composing or decomposing it into polygons with known area formulas. The lesson provides examples of calculating perimeter and area, as well as exercises for students to practice these skills by decomposing polygons in different ways.
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G6 m3-a-lesson 3-s
- 1. Lesson 3: Real-World Positiveand Negative Numbers and Zero Date: 1/22/15 S.8 8 © 2013 Common Core, Inc. Some rightsreserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 3 Lesson 3: Real-World Positive and Negative Numbers and Zero Classwork Example 1: A Look at SeaLevel The picture below shows three different people participatingin activities at three different elevations. With a partner, discusswhatyou see. What do you think the word elevation means in this situation? I’m hiking, so I’m above sea level.I’m sailing, so I’m at sea level. I’m scuba diving, and I’m below sea level.
- 2. Lesson 3: Real-World Positiveand Negative Numbers and Zero Date: 1/22/15 S.9 9 © 2013 Common Core, Inc. Some rightsreserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 3 Exercises Refer back to Example 1. Use the followinginformation to answer Exercises 1 and 2. The diver is 30 feet below sea level. The sailor isatsea level. The hiker is 2 miles (10,560 feet) above sea level. 1. Write an integer to represent each situation. 2. Use an appropriatescaleto graph each of the followingsituations on the number lineto the right. Also,write an integer to represent both situations. a. A hiker is 15 feet above sea level. b. A diver is 20 feet below sea level. 3. For each statement there are two related statements: i and ii. Determine which related statement is expressed correctly (i and ii), and circleit. Then correct the other related statement so that both parts, i and ii, are stated correctly. a. A submarineis submerged 800 feet below sea level. i. The depth of the submarineis −800 feet below sea level. ii. 800 feet below sea level can be represented by the integer −800. b. The elevation of a coral reef with respect to sea level is given as −250 feet. i. The coral reef is 250 feet below sea level. ii. The depth of the coral reef is −250 feet below sea level.
- 3. Lesson 3: Real-World Positiveand Negative Numbers and Zero Date: 1/22/15 S.10 10 © 2013 Common Core, Inc. Some rightsreserved. commoncore.org This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM 6•3Lesson 3 Problem Set 1. Write an integer to match the followingdescriptions: a. A debit of $40. b. A depositof $225. c. 14,000 feet above sea level. d. A temperature increaseof 40 degrees. e. A withdrawal of $225. f. 14,000 feet below sea level. For questions 2–4, read each statement about a real-world situation and thetwo related statements in parts (a) and (b) carefully. Circlethe correct way to describeeach real-world situation;possibleanswers include either (a), (b), or both (a) and (b). 2. A whaleis 600 feet below the surfaceof the ocean water. a. The depth of the whaleis 600 feet from the water’s surface. b. The whale is −600 feet below the surfaceof the ocean water. 3. The elevation of an iceberg with respect to sea level is given as −125 feet. a. The iceberg is 125 above sea level. b. The iceberg is 125 feet below sea level. 4. Alex’s body temperature decreased by 2℉. a. Alex’s body temperature dropped 2℉. b. The integer −2 represents the change in Alex’s body temperature in degrees Fahrenheit. 5. A creditof $35 and a debit of $40 areapplied to your bank account. a. What is an appropriatescaleto graph a credit of $35 and a debit of $40? Explain your reasoning. b. What integer represents “a creditof $35” if zero represents the original balance? Explain. c. What integer describes “debitof $40” if zero represents the original balance? Explain. d. Based on your scale,describethe location of both integers on the number line. e. What does zero represent in this situation?