lesson 3 homework 1.3 answer key

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Into Math Grade 8 Module 1 Lesson 3 Answer Key Explore Reflections

We included H MH Into Math Grade 8 Answer Key PDF Module 1 Lesson 3 Explore Reflections to make students experts in learning maths.

HMH Into Math Grade 8 Module 1 Lesson 3 Answer Key Explore Reflections

Spark Your Learning

Build Understanding

Connect to Vocabulary A reflection is a transformation of a figure that flips the figure across a given line, called the line of reflection, so that each point on the preimage is the same distance from the line of reflection as the corresponding point on the image.

B. Use a ruler to measure the length of a line segment in the preimage. Then measure the length of the corresponding line segment in the image. What do you notice about the lengths of the two segments? Answer: No change in lengths, Explanation: The length of a line segment in the preimage and corresponding line segment in the image. We notice that the lengths of the two segments are same, with no change.

C. Use a protractor to measure an angle in the preimage and the corresponding angle in the image. What do you notice? Answer: No change in the angles, Explanation: We observe that there is no change in the angles of a line segment in the preimage of letter N, and corresponding line segment of letter N in the image. We notice that the lengths of the two angles segments are same angles, no change.

D. What can you conclude about the way reflecting a figure affects side length, angle measure, and parallel line segments? Answer: A reflection on the coordinate plane takes a geometric figure such as a point, line segment, or shape and transforms it into a congruent geometric figure called the image. Explanation: In this explainer, we will focus on three different types of reflection on the coordinate plane: Reflection in the 𝑥-axis Reflection in the 𝑦-axis Reflection about the origin

Explanation: letter N changes the shape of the letter N, but the lengths and angles between the side of the letter N remain same.

Turn and Talk Two students perform a reflection of the same shape. One reflects over a vertical line. The other reflects over a horizontal line. How are their reflections the same? How are they different? Answer: Letter N changes the shape of the letter N, but the lengths and angles between the side of the letter N remain same as shown below.

Step It Out

B. The preimage is upright. Is the image also upright, or has it changed? __________ Answer: Image has changed, Explanation: The image is larger than the preimage. The image and the preimage are congruent, but do not have the same orientation. When the image is on the same side the object and the image distance is positive, then the image is said to be real and inverted. When the image of the object is behind then the image distance is negative, the image is said to be virtual and upright.

Check Understanding

Question 2. The coordinates of the vertices of a square are (-10, -2), (-5, -2), (-5, -7), and (-10, -7). The square is reflected over the y—axis. A. What are the coordinates of the vertices of the image? ______________________ Answer: (-10, -2), (-5, -2), (-5, -7), and (-10, -7) 𝑃(x, y) → 𝑃′(-x, y). (10, -2), (5, -2), (5, -7), and (10, -7) Explanation: A reflection in the 𝑦-axis maps point 𝑃 onto its image point 𝑃′ by changing the sign of the 𝑥-coordinates, and keeping the 𝑦-coordinate as the same. The effect is that the position of 𝑃′ will mirror that of 𝑃, on the opposite side of the 𝑦-axis (which is the line with equation 𝑥=0), and at the same perpendicular distance from the 𝑦-axis as  𝑃. Since the 𝑦-axis acts like a mirror, it is called the line of reflection (or mirror line).

Question 3. In your own words, describe the meaning of a reflection. ______________________ Answer: A reflection is a transformation that flips a figure across a line. Explanation: A reflection is known as a flip which is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, then every point in a figure is equidistant from each corresponding point in another figure.

On Your Own

Use the figures to answer Problems 4—7.

Figure Y is a reflection of Figure X.

Question 5. Angle A measures 115°. What is the measure of the corresponding angle in Figure Y? Answer: 115° Explanation: The measure of the corresponding angle in Figure Y is also 115° no change in lengths and angles in the reflected figure.

Question 6. \(\overline{F E}\) is parallel to \(\overline{B C}\) Are the corresponding sides in Figure Y also parallel? Answer: Yes, Explanation: The measure of the corresponding lengths in Figure Y, \(\overline{F E}\) is parallel to \(\overline{B C}\). Are the corresponding sides in Figure Y also parallel, no change in lengths and angles in the reflected figure.

A. Is Figure P a reflection of Figure N over the y-axis? _______________ Answer: yes, Explanation: figure P is a reflection of figure N over y axis, a reflection in the 𝑦-axis maps point 𝑃 onto its image point N. By changing the sign of the 𝑥-coordinate and keeping the 𝑦-coordinate the same. The effect is that the position of N will mirror that of 𝑃, on the opposite side of the 𝑦-axis.

Question 10. Figure ABCD is a trapezoid in the second quadrant.

C. Is A’B’C’D’ facing the same direction as ABCD? Explain. Answer: yes, Explanation: A’B’C’D’ facing the same direction as ABCD, a reflection in its image ABCD by changing the sign of the 𝑥-coordinate and keeping the 𝑦-coordinate as same. The effect is that the position of A’B’C’D’ will mirror that of ABCD on the opposite side of the 𝑦-axis.

C. If you reflect the square from Part B over a vertical line, does it look any different? If so, what is different? Answer: yes, the difference is the right angle marked corner shifted. Explanation: There is difference in the shape and size of the square over a vertical line, the difference to the right angle corner is shifted in the image with reference to preimage.

I’m in a Learning Mindset!

How does my mindset affect my confidence with performing reflections? Answer: Thinking over the preimage and image changes in the positions of the image, with reference to the preimage and rule given will effect the mind set.

Lesson 1.3 More Practice/Homework

Use the tiger images to answer Problems 1—3.

Question 1. Construct Arguments Could Tiger 2 be an image of Tiger 1 after one reflection? Explain. Tiger 1 Tiger 3 Answer:

B. Both arrows in Figure R are 4 units long. How long are the arrows in Figure R’? Answer: 4 units long. Explanation: P(x, y) is changed to P'(-x, y) the image of Figure R reflected across the y-axis, with reference to y axis or vertical line letter R is reflected, and the lengths are 4 units long in the R’ reflected figure.

E. What are the coordinates of the point at which the arrows intersect in R”? Answer: (-3, 2) and (-7, 6 ) Explanation: The coordinates of the tips of the arrows on R (x, y) are, (-3, 2) and (-7, 6 ).

F. In which directions do the arrows point in Figure R”? Answer: Left and Down direction of arrows. Explanation: With reference to the x axis in the direction of the arrows are Left and Down direction of arrows.

Question 7. Which of the following is a rule that represents what happens to the coordinates of any point on a figure after it is reflected over the x-axis and then the y-axis? A. (x, y) → (x, -y) B. (x, y) → (-x, y) C. (x, y) → (y, x) D. (x, y) → (-x, -y) Answer: Option (A) and Option (B) Explanation: Option (A) (x, y) → (x, -y) the coordinates of any point on a figure after it is reflected over the x-axis. Option (B) (x, y) → (-x, y) the coordinates of any point on a figure after it is reflected over the y-axis.

Spiral Review

Question 8. Albert works at a farmers’ market. He recently sold 18 pieces of fruit, 6 of which were oranges. What is the experimental probability that the next piece of fruit Albert sells will be an orange? Answer: \(\frac{1}{3}\) Explanation: 18 pieces of fruit, 6 of which were oranges. The probability that the next piece of fruit Albert sells will be an orange, \(\frac{6}{18}\) = \(\frac{1}{3}\)

Question 9. What is the surface area of a cube that has edges 3 centimeters long? Answer: 54 cm 2 Explanation: Total surface area of a cube = 2AB + 2BC + 2 CA Cube of edge length 3 cm, the surface area of a cube if its height is 3 cm, Surface area = 18 x 3 = 54 cm 2

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Texas Go Math Grade 3 Lesson 1.3 Answer Key Numbers Through Hundred Thousands

Refer to our Texas Go Math Grade 3 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 3 Lesson 1.3 Answer Key Numbers Through Hundred Thousands.

Essential Question What relationships con you find in the place-value system?

Unlock the Problem

Connect You have learned how to find the value ola digit in a 5-digit number. You can use a pattern to flnd the value of a digit in any number.

What patterns do you see?

• how many ten thousands in all? ___
• how many thousands in all? ___
• how many hundreds in all? ___
• how many ten thousands in all = 6
• how many thousands in all = 0
• how many hundreds in all = 0
• how many hundred thousands in all? ____
• how many ten thousands in all = 0
• how many hundred thousands in all = 0

Share and Show

Math Talk Mathematical Processes Describe the pattern you see in the chart.

Question 1. how many ten thousands in all? ___ Answer: 4

there are 4 ten thousands in all.

Question 2. how many thousands in all? ___ Answer: 0

Go Math Lesson 1.3 Hundred Thousands 3rd Grade Question 3. how many hundreds in all? ___ Answer: 0

Question 4. how many hundred thousands in all? ___ Answer:

There are 7 hundred thousands in all

Question 5. how many thousands in all? ____ Answer:

Question 6. how many tens in all? ____ Answer: 0

Problem Solving

Complete the sentences for 7-8.

The capital of Texas is Austin. In a recent year, there were 790,390 people living in Austin.

Question 7. The digit ___ is in the hundred thousands place and has a value of ___. Answer:

The digit 7 is in the hundred thousands place and has a value of 700,000

Question 8. The digit ___ is in the hundreds place and has a value of ___. Answer:

The digit 3 is in the hundreds place and has a value of 300.

Question 9. Write the number 790,390 in expanded form. Answer:

Expanded form = 700,000 + 90,000+ 300 +90

Go Math Grade 3 Lesson 1.3 Answer Key Question 10. H.O.T. Explain how you can find the number of thousands in 790,390. Answer:

The number of thousands in 790,390 = 0

Because, the digit in thousands place is 0 So, the number of thousands = 0

Problem-Solving

Use the table for 11-14.

Question 11. How many thousands of people live in Boston? Answer:

Total number of people live in Boston = 617,594

The digit in thousand’s place is 7 and its value is 7000.

So, 7 thousands of people lives in Boston.

Question 12. How many ten thousands of people live in Boulder? Answer: 0

Total number of people = 94,673

There is no Ten thousands place.

Question 13. How many hundreds of people live in Tucson? Answer:

Total number of people lives in Tucson = 520,116

The digit in hundred’s place is 1 and its value is 100

So, 1 hundred of people live in Tucson.

Question 14. Reasoning Describe the relationship between the two digit 3s in the population of Tampa. Answer:

Population of Tampa = 335,709

The digit  in the hundred thousands place is 3 and then it’s value is 300,000

The digit in ten thousand’s place is also 3 and its value is 30,000

Go Math Grade 3 Answer Key Lesson 1.3 Hundred Thousands Question 15. The Chicago Cubs baseball team plays its home games at Wrigley Field in Chicago, Illinois. The stadium holds 41,160 people. How many hundreds of people in all can the stadium hold? Answer:

The total number of people  the stadium holds = 41,160

Expanded form = 40,000+1,000+100+60

The digit in hundred’s place is 1 and it’s value is 100

Therefore, 1 hundred of people in all the stadium can hold.

2 hundred thousands+4 ten thousands + 8 thousands + 6 hundreds + . 3 tens +9 ones

Daily Assessment Task

Fill in the bubble for the correct answer choice.

Question 17. A robot can juggle 153,270 rings. ‘Which digit is in the thousands place in the number of rings that the robot can juggle? (A) 5 (B) 1 (C) 2 (D) 3 Answer:

Given, The number of juggle’s a robot can make = 153,270

Expanded form = 100,000+50,000+3,000+200+70

3 is the digit is in the thousands place in the number of rings that the robot can juggle.

Question 18. Otis scored 27,486 points playing a computer game. Which digit is in the ten thousands place of his score? (A) (B) 2 (C) 8 (D) 4 Answer: (B)

The score of Otis = 27,486

Expanded form = 20,000+7000+400+80+6

So, the digit in ten thousand place is 2

Question 19. Multi-Step A store sells single greeting cards, bundles of 10 cards, boxes of 100 cards, and cases of 1,000 cards. A business buys 12,578 cards. How can they buy this exact amount? (A) 12 cases, 15 boxes, 7 bundles, and 8 singles (B) 1 case, 15 boxes, 7 bundles, and 8 singles (C) 12 cases, 5 boxes, 7 bundles, and 8 singles (D) 1 case, 5 boxes, 17 bundles, and 8 singles Answer:

1 bundle = 10 cards

1 box = 100 cards

1 case = 1000 cards

12,578 can be expanded as 12000+500+70+8

12000/1000 = 12 cases

500/100 = 5 boxes

70/10 = 7 bundles

And 8 singles.

Therefore, They can buy the exact amount of as 12 cases, 5 boxes, 7 bundles, and 8 singles

Texas Test Prep

Texas Go Math Grade 3 Pdf Lesson 1.3 Answer Key Question 20. On one day, a theme park in Central Florida had 26572 visitors. How many thousands of people visited the theme park? (A) 26 (B) 2 (C) 265 (D) 65 Answer:

26 thousands of people have visited the theme park.

Texas Go Math Grade 3 Lesson 1.3 Homework and Practice Answer Key

Use the table for 1-3.

Question 1. How many ten thousands of red crayons were made? Answer:

Red crayons = 420,189

Expanded form = 4 hundred thousand. + 2 ten thousands + 1 hundreds +8 tens +9 ones

Therefore, 2 ten thousands of red crayons were made.

Question 2. How many hundreds of purple crayons were made? Answer:

Purple crayons = 148,305

Expanded form :1 hundred thousand. + 4 ten thousands + 8 thousands + 3 hundreds +5 ones

So, 3 hundreds of purple crayons were made.

Question 3. How many thousands of blue crayons were made? Answer:

Blue crayons = 327,412

Expanded form = 3 hundred thousand. + 2 ten thousands + 7 thousands + 4 hundreds +1 tens +2 ones

So, 7 thousands of blue crayons were made.

Go Math Lesson 1.3 3rd Grade Answer Key Question 4. Unscramble the place values. Write the number in standard form. 4 hundreds + 5 tens + 7 ten thousands + 9 ones + 3 thousands + 1 hundred thousand. Answer:

1 hundred thousand. + 7 ten thousands + 3 thousands + 4 hundreds +5 tens +9 ones

Question 5. Unscramble the place values. Write the number in standard form. 3 thousands + 4 ones + 8 hundred thousands + 7 hundreds + 5 ten thousands. Answer:

8 hundred thousands + 5 ten thousands+3 thousands + 7 hundreds + 4 ones

Question 6. Last year, a sticker factory made a total of 528,390 booklets of stickers. How many hundreds of booklets of stickers were made? Answer:

Expanded form = 5 hundred thousand. + 2 ten thousands + 8 thousands + 3 hundreds +9 tens

Therefore, 3 hundred of stickers were made.

Question 7. A trucking company shipped a total of 151,375 boxes of fruit across the county. flow many thousands of boxes of fruit were shipped? Answer:

Expanded form:

1 hundred thousand. + 5 ten thousands + 1 thousands + 3 hundreds +7 tens + 5 ones

So, 1 thousand boxes of fruits were shipped.

Lesson Check

Question 8. Deanna plays a video game and scores 73,492 points. Which digit is in the ten thousands place of her score? (A) 3 (B) 4 (C) 7 (D) 9 Answer:

Expanded form = 70,000 +3,000+400+90+2

The digit in ten thousands place (70,000) = 7

Question 9. A newspaper company prints 15,980 copies in one day. Which digit is in the hundreds place? (A) 8 (B) 9 (C) 5 (D) 1 Answer:

Expanded form= 10,000+5,000+900+80

The digit in hundreds place is 9

3rd Grade Go Math Lesson 1.3 Answer Key Question 10. In one day, 125,683 people fly in and out of an airport in Texas. How many thousands of people fly in and out that day? (A) 5,000 (B) 5,683 (C) 25 (D) 125 Answer:

Expanded form = 100,000 + 20,000+5,000+600+80+3

The value of thousands placed in the given number = 5000

The number of people travelled in and out that day = 5,000

Question 11. In one week, 215,328 people visited the Grand Canyon. How many hundreds of people visit the canyon that week? (A) 300 (B) 53 (C) 2,153 (D) 528 Answer: (A)

Expanded form = 200,000 + 10,000 + 5000 + 300 + 20 +5

The value of the digit 3 in hundred’s place is 300

Therefore, the number of people visited canyon that week = 300

Question 12. Multi-Step A marble factory makes single marbles, then puts them in boxes of 10, cartons of 100, and crates of 1,000. How can the marble factory package 21,650 marbles? (A) 2 crates, 16 cartons, 50 boxes (B) 21 crates, 60 cartons, 5 boxes (C) 21 crates, 6 cartons, 5 boxes (D) 2 crates, 10 cartons, 65 boxes Answer:

Expanded form = 21000 + 600+50

10 marbles = 1 Box

This means, 50 marbles = 5 boxes

100 marbles = 1 cartons

600 marbles = 600/100 = 6 cartons

1,000 marbles = 1 crates

21,000 marbles = 21,000/1000 = 21

21,000 cards = 21 cases.

Therefore 21 crates, 6 cartons, and 5 boxes in this order the company fills marbles.

Practice And Homework Lesson 1.3 Answer Key 3rd Grade Question 13. Multi-Step A company makes baseball cards in packs of 10, boxes of 100, and cases of 1,000. A store orders a total of 15,470 cards. How can the company f111 the order in the exact amount? (A) 1 case, 5 boxes, 47 packs (B) 1 case, 54 boxes, 7 packs (C) 15 cases, 40 boxes, 7 packs (D) 15 cases, 4 boxes, 7 packs Answer: 15 cases, 4 boxes, 7 packs

Explanation:

Expanded form = 15000 + 400+70

10 cards= 1 pack

Which means, 70 cards = 7 packs

100 cards = 1 box

400 cards = 400/100 = 4 boxes

1,000 cards = 1 case

15,000 cards = 15,000/1000 = 15

15,000 cards = 15 cases.

Therefore, 15 cases, 4 boxes, and 7 packs in this order the company filled the order in the exact amount.

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