Monday, December 4, 2023

## Lesson 88 Solve Problems Involving Surface Area

7-5 EnVision Grade 6 Pearson Realize Solids and Nets

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Alaya will paint the outside of a box in three different colors. Decide how she could paint the box. What is the total area that each color will cover?I can find the area and surface area of 2-dimensional composite shapes and 3-dimensional prisms.Answer:Alaya will paint the outside of a box in three different colorsNow,We can observe that the given figure is a Cuboid which has 6 facesNow,The different ways that Alaya can paint are:a. She can paint all the faces of the box with the same colorb. She can paint the faces of the box with alternative colors i.e., 1 face is colored with 1 color, 2nd face is colored with 1 color, etc.Now,The total surface area of a cuboid = 2 Where,l is the length of the cuboidw is the width of the cuboidh is the height of the cuboidNow,The length of the cuboid is 32 in.The width of the cuboid is 16 in.The height of the cuboid is 14 in.So,A = 2 = 2 The different ways that Alaya can paint are:a. She can paint all the faces of the box with the same colorb. She can paint the faces of the box with alternative colors i.e., 1 face is colored with 1 color, 2nd face is colored with 1 color, etc.The total area covered by each color is: 394.66 in.²

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KEY CONCEPT

The area of a two-dimensional composite figure is the sum of the areas of all the shapes that compose it. The surface area of a three-dimensional composite figure is the sum of the areas of all its faces.Two-dimensional composite figure

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• ## Lesson 85 Solve Problems Involving Circumference Of A Circle

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The distance around a circle and the distance across a circle are related.I can solve problems involving radius, diameter, and circumference of circles.

A. Use string to measure the distance across each circle. How many of these lengths does it take to go completely around the circle?Answer:The distance around the circle is: CircumferenceThe distance across the circle is: DiameterNow,The complete length to go completely around the circle is given as:Circumference = dThe total length does it take to go completely around the circle = dWhered is the diameter

B. Use the string and a ruler to measure the distance across the circle and the distance around the circle. Complete the table. Round each measurement to the nearest quarter inch.Answer:

C. What do you notice about the ratio of the distance around the circle to the distance across the circle for each circle?Answer:From the given table,We can observe that the ratio of the circumference and the diameter is constant for all the circlesHence, from the above,We can conclude that the ratio of the distance around the circle to the distance across the circle for each circle is constant

The side of the square is: 1.5 unitsNow,The area of the square = Side²So,The area of the square = ²= 2.25 units²We can conclude that the area of the square is: 2.25 units²

KEY CONCEPTThe parts of a circle and their relationships are summarized in the diagram below.

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7 Topic 1 statement is true: If a customer chooses a meal that has a banana, then the customer also has a cheese sandwich. Part B If a customer chooses a meal that has yogurt, then the customer does not have an apple. Proof: Assume the customer has an apple. Then the customer must have chosen the meal that has the cheese sandwich, carrot sticks, and apple. Therefore the customer does not have yogurt. This proves the contrapositive, so the original statement is true: If a customer chooses a meal that has yogurt, then the customer does not have an apple. Topic Review. postulate 4. biconditional 6. theorem 8. deductive reasoning U V 0.. 5 4. 5 6. 8. 15, , 41 L. and 14 4 and 16 6 and 18 8 and 0 4. \$ Conditional: If it is Saturday, then Kona jogs 5 miles. Converse: If Kona jogs 5 miles, then it is Saturday. Inverse: If it is not Saturday, then Kona does not jog 5 miles. Contrapositive: If Kona does not jog 5 miles, then it is not Saturday. 8. True simplifying the inequality gives, and any number less than is also less than Pudding is available if and only if it is a Tuesday. 4. If it is a sunny day, the lines for each ride are long. 44. x = 8 78 Statements Reasons 1. m TUV = Given. m TUW + m WUV = m TUV. Angle Addition Postulate. y + 4 = 90. Substitution Property 4. y = Subtraction Property 5. 4x = y 5. Vertical Angle Theorem 6. 4x = Substitution Property 7. x = 1 7. Simplify. envision Geometry 7 Selected Answers

## Lesson 89 Solve Problems Involving Volume

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Volunteers at a food pantry pack boxes of soup into crates. How many boxes of soup will fill each crate? Show your work.I can use the area of the base of a three-dimensional figure to find its volume.Answer:Volunteers at a food pantry pack boxes of soup into cratesNow,We can observe that the boxes and crates are in the form of a cuboidNow,The volume of a cuboid = Length × Width × HeightSo,The volume of the box = 4 × 2 × 6= 48 in.³The volume of the crate = 12 × 18 × 12= 2,592 in.³So,The number of boxes of soup that will fill each crate = \= \= 54 boxesHence, from the above,We can conclude that the number of boxes of soup that will fill each crate is: 54 boxes

Look for Relationships How can you layer the soup boxes to cover the bottom of the crate?Answer:The given figure in part is:Now,From the given figure in part ,We can observe thatWe have to layer the soup boxes in the horizontal position to cover the bottom of the crate

Focus on math practicesReasoning A supplier donated crates to the food pantry that are 15 inches long, instead of 18 inches long. All other dimensions are the same. What is the greatest number of boxes of soup that will fit in the donated crates? How will the volume of the soup vary from the total volume of the crate?Answer:It is given thatA supplier donated crates to the food pantry that are 15 inches long, instead of 18 inches long. All other dimensions are the sameNow,

KEY CONCEPT

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Mr. Biden lobs a big, slow haymaker at his longtime frenemy Mitch McConnell, saying the Republican leader’s goal is to “make sure there is nothing I do that looks good.” He then claims that five Republican senators have told him they would support his bills if they weren’t afraid of attracting primary challenges from Trump backers but he declines to name them.

New York Times

## Lesson 87 Describe Cross Sections

16-4 EXTRA PRACTICE, EnVision Math 2.0, 5th Grade

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How could Mrs. Mendoza divide the ream of paper equally between two art classes? She has a paper cutter to slice the paper if needed. What will the dimensions for each sheet of paper be once she has divided the ream? How many sheets will each class receive?

I can determine what the cross-section looks like when a 3D figure is sliced.Answer:Mrs. Mendoza has a paper cutter to slice the paper.Now,The number of sheets each class will receive is: 250The dimensions of each sheet of paper once Mrs. Mendoza divided the ream is:Length: 8\ inchesWidth: 11 inches

Focus on math practicesUse Structure How would the number of sheets of paper each class receives change if Mrs. Mendoza started with 300 sheets?Answer:It is given thatMrs. Mendoza has 500 sheets of paper and she divided the sheets equally between the two classesNow,If Mrs. Mendoza started with 300 sheets of paper, thenThe number of sheets divided by Mrs. Mendoza equally between the two classes = \= 150Hence, from the above,We can conclude that the number of sheets each class receives when Mrs. Mendoza started with 300 sheets is: 150

KEY CONCEPT

A cross section is the two-dimensional shape exposed when a three-dimensional figure is sliced. The shape and dimensions of a cross section in a rectangular prism are the same as the faces that are parallel to the slice.

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## Lesson 84 Solve Problems Using Angle Relationships

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The intersecting skis form four angles.

I can solve problems involving angle relationships.

A. List all the pairs of angles that share a ray.Answer:It is given that the intersecting skis form four angles.Now,The representation of the intersecting skies and the angles made by intersection are:Hence, from the above figure,We can conclude that the angles that share a ray are:1, 2, 3, and 4

B. Suppose the measure of Z1 increases. What happens to the size of 2? 3?Answer:From the given figure,We can observe that 1 and 2 are on the same side and they are known as Adjacent anglesWe can observe that 1 and 3 are on the opposite sides of the ray and they are known as Vertical anglesNow,The sum of the adjacent angles is 180°The angle measures of the vertical angles are the sameHence, from the above,When the value of 1 increases, the value of 2 automatically decreasesWhen the value of 1 increases, the value of 3 also increases

C. How does the sum of the measures of 1 and 2 change when one ski moves? Explain.Answer:From the given figure,We can observe that 1 and 2 lies on the same side of the ski and they are known as Adjacent angles Supplementary anglesNow,The sum of the angle measures of adjacent angles is 180°Hence, from the above,We can conclude that the sum of the measures of 1 and 2 always remains constant even when one ski moves

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Use the diagram below for 4-6.Answer:

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## Lesson 82 Draw Geometric Figures

Solve & Discuss It!

Students in the Art Club are designing a flag with the schools mascot and emblem. The flag has four sides, with two sides that are twice as long as the other two sides. What shape could the flag be, and what dimensions could it have? Make and label a scale drawing as part of your answer.I can draw figures with given conditions.Answer:It is given thatStudents in the Art Club are designing a flag with the schools mascot and emblem. The flag has four sides, with two sides that are twice as long as the other two sides.Now,A Quadrilateral is only a geometrical figure which has 4 sidesNow,Let the length of the two sides be x cmLet the length of the other two sides be 2x cmWhere,x = 1, 2, 3,.., nNow,Let the value of x be 2Hence,The representations of the flag are:

Make Sense and Persevere: Is there more than one shape that could represent the flag?Answer:Yes, there is more than one shape that could represent the flagNow,The representations of the flag are:Hence,The different shapes of the flags are: Rectangle, Parallelogram, and Trapezium, and a Quadrilateral

Essential QuestionHow can a shape that meets given conditions be drawn?Answer:Use the conditions that are given to draw a shape and based on that shape, determine the name of the shape and its dimensions

Convince Me! Could you have drawn more than one shape that fits the given conditions? Explain.Answer:No, we cant draw any shape other than the square that fits the above conditions

## Lesson 81 Solve Problems Involving Scale Drawings

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Calvin made a scale model of the plane shown.

I can use the key in a scale drawing to find missing measures.

A. How can you represent the relationship between the model of the plane and the actual plane?Answer:The given figure is:Now,The representation of the relationship between the model of the plane and the actual plane is:The actual diagram is an enlarged diagram of the scale diagramSo,The scale factor = \= \Hence, from the above,We can conclude that the actual diagram is 16 times larger than the scale diagram

B. What do you notice about the relationship between the model of the plane and the actual plane?Answer:We know that,The relationship between the model of the plane and the actual plane can be given by a Scale factorSo,The scale factor = \= \We can conclude that the actual diagram is 16 times larger than the scale diagram

Focus on math practicesLook for Relationships If the model and the actual plane are to scale, what do you know about the relationship between all the other parts of the model and the actual plane, aside from the total length?Answer:If the model and the actual plane are to scale, thenAll the other parts of the model and the actual plane, aside from the total length are also scaled

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The scale of the enlarged map = \= 15We can conclude that the scale of the enlarged map is: 1inch = 15 miles

Practice & Problem Solving

The actual distance between the houses is: 10.8 miles

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## Lesson 83 Draw Triangles With Given Conditions

Solve & Discuss It!

Kane has 4 pieces of wood available to build a triangle-shaped garden. Which pieces of wood can he use?I can draw triangles when given information about their side lengths and angle measures.Answer:Kane has 4 pieces of wood available to build a triangle-shaped garden.Now,We know that,To build a Triangle,The sum of the lengths of the two shortest sides must be greater than the length of the third sideNow,The given pieces of wood are:a. 2 feet b, 3 feet c. 4 feet d. 5 feetSo,The possible combination of pieces of wood is:a. b. c. d. Now,The possible combination of pieces of wood that allow to form a triangle-shaped garden is:a. 2 + 3 !> 5b. 2 + 3 > 4d. 2 + 4 > 5Hence, from the above,We can conclude that the possible combinations of the pieces of wood that form a Triangle-shaped garden are:a. b. c.

Make Sense and Persevere Try all possible combinations of three pieces of wood.Answer:We know that,To build a Triangle,The sum of the lengths of the two shortest sides must be greater than the length of the third sideNow,The given pieces of wood from part are:a. 2 feet b, 3 feet c. 4 feet d. 5 feetSo,The possible combination of pieces of wood to form a triangle-shaped garden is:a. b. c. d. Now,The possible combination of pieces of wood that allow to form a triangle-shaped garden is:a. 2 + 3 !> 5b. 2 + 3 > 4d. 2 + 4 > 5Hence, from the above,We can conclude that the possible combinations of the pieces of wood that form a Triangle-shaped garden are:a. b. c.