lesson 10 homework 4.1 answer key

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Eureka Math Grade 4 Module 1 Lesson 10 Answer Key

Engage ny eureka math 4th grade module 1 lesson 10 answer key, eureka math grade 4 module 1 lesson 10 sprint answer key.

Question 1. 21,000 ≈ Answer: 21,000 ≈ 20,000

Question 2. 31,000 ≈ Answer: 31,000 ≈ 30,000

Question 3. 41,000 ≈ Answer: 41,000 ≈ 40,000

Question 4. 541,000 ≈ Answer: 541,000 ≈ 540,000

Question 5. 49,000 ≈ Answer: 49,000 ≈ 50,000

Question 6. 59,000 ≈ Answer: 59,000 ≈  60,000

Question 7. 69,000 ≈ Answer: 69,000 ≈  70,000

Question 8. 369,000 ≈ Answer: 369,000 ≈ 370,000

Question 9. 62,000 ≈ Answer: 62,000 ≈  60,000

Question 10. 712,000 ≈ Answer: 712,000 ≈ 710,000

Question 11. 28,000 ≈ Answer: 28,000 ≈ 30,000

Question 12. 37,000 ≈ Answer: 37,000 ≈  40,000

Question 13. 137,000 ≈ Answer: 137,000 ≈ 140,000

Question 14. 44,000 ≈ Answer: 44,000 ≈ 40,000

Question 15. 56,000 ≈ Answer: 56,000 ≈  60,000

Question 16. 456,000 ≈ Answer: 456,000 ≈ 460,000

Question 17. 15,000 ≈ Answer: 15,000 ≈  20,000

Question 18. 25,000 ≈ Answer: 25,000 ≈ 30,000

Question 19. 35,000 ≈ Answer: 35,000 ≈ 40,000

Question 20. 235,000 ≈ Answer: 235,000 ≈ 240,000

Question 21. 75,000 ≈ Answer: 75,000 ≈ 80,000

Question 22. 175,000 ≈ Answer: 175,000 ≈ 180,000

Question 23. 185,000 ≈ Answer: 185,000 ≈ 190,000

Question 24. 85,000 ≈ Answer: 85,000 ≈ 90,000

Question 25. 95,000 ≈ Answer: 95,000 ≈ 100,000

Question 26. 97,000 ≈ Answer: 97,000 ≈ 100,000

Question 27. 98,000 ≈ Answer: 98,000 ≈  100,000

Question 28. 198,000 ≈ Answer: 198,000 ≈ 200,000

Question 29. 798,000 ≈ Answer: 798,000 ≈ 800,000

Question 30. 31,200 ≈ Answer: 31,200 ≈ 30,000

Question 31. 49,300 ≈ Answer: 49,300 ≈  50,000

Question 32. 649,300 ≈ Answer: 649,300 ≈  650,000

Question 33. 64,520 ≈ Answer: 64,520 ≈ 60,000

Question 34. 164,520 ≈ Answer: 164,520 ≈ 160,000

Question 35. 17,742 ≈ Answer: 17,742 ≈ 20,000

Question 36. 917,742 ≈ Answer: 917,742 ≈ 920,000

Question 37. 38,396 ≈ Answer: 38,396 ≈ 40,000

Question 38. 64,501 ≈ Answer: 64,501 ≈  60,000

Question 39. 703,280 ≈ Answer: 703,280 ≈ 700,000

Question 40. 239,500 ≈ Answer: 239,500 ≈ 240,000

Question 41. 708,170 ≈ Answer: 708,170 ≈ 710,000

Question 42. 188,631 ≈ Answer: 188,631 ≈ 190,000

Question 43. 777,499 ≈ Answer: 777,499 ≈ 780,000

Question 44. 444,919 ≈ Answer: 444,919 ≈ 440,000

Question 1. 11,000 ≈ Answer: 11,000 ≈ 10,000

Question 2. 21,000 ≈ Answer: 21,000 ≈ 20,000

Question 3. 31,000 ≈ Answer: 31,000 ≈ 30,000

Question 4. 531,000 ≈ Answer: 531,000 ≈ 530,000

Question 5. 39,000 ≈ Answer: 39,000 ≈  40,000

Question 6. 49,000 ≈ Answer: 49,000 ≈ 50,000

Question 7. 59,000 ≈ Answer: 59,000 ≈  60,000

Question 8. 359,000 ≈ Answer: 359,000 ≈ 360,000

Question 9. 52,000 ≈ Answer: 52,000 ≈ 50,000

Question 10. 612,000 ≈ Answer: 612,000 ≈ 610,000

Question 11. 18,000 ≈ Answer: 18,000 ≈ 20,000

Question 12. 27,000 ≈ Answer: 27,000 ≈ 30,000

Question 13. 127,000 ≈ Answer: 127,000 ≈ 130,000

Question 14. 34,000 ≈ Answer: 34,000 ≈ 30,000

Question 15. 46,000 ≈ Answer: 46,000 ≈ 50,000

Question 16. 346,000 ≈ Answer: 346,000 ≈  350,000

Question 17. 25,000 ≈ Answer: 25,000 ≈ 30,000

Question 18. 35,000 ≈ Answer: 35,000 ≈ 40,000

Question 19. 45,000 ≈ Answer: 45,000 ≈ 50,000

Question 20. 245,000 ≈ Answer: 245,000 ≈ 250,000

Question 21. 65,000 ≈ Answer: 65,000 ≈  70,000

Question 22. 165,000 ≈ Answer: 165,000 ≈ 170,000

Question 24. 85,000 ≈ Answer: 85,000 ≈  90,000

Question 26. 96,000 ≈ Answer: 96,000 ≈ 100,000

Question 27. 99,000 ≈ Answer: 99,000 ≈ 100,000

Question 28. 199,000 ≈ Answer: 199,000 ≈ 200,000

Question 29. 799,000 ≈ Answer: 799,000 ≈  800,000

Question 30. 21,200 ≈ Answer: 21,200 ≈ 20,000

Question 31. 39,300 ≈ Answer: 39,300 ≈  40,000

Question 32. 639,300 ≈ Answer: 639,300 ≈ 640,000

Question 33. 54,520 ≈ Answer: 54,520 ≈ 50,000

Question 34. 154,520 ≈ Answer: 154,520 ≈ 150,000

Question 35. 27,742 ≈ Answer: 27,742 ≈ 30,000

Question 36. 927,742 ≈ Answer: 927,742 ≈ 930,000

Question 37. 28,396 ≈ Answer: 28,396 ≈  30,000

Question 38. 54,501 ≈ Answer: 54,501 ≈  50,000

Question 39. 603,280 ≈ Answer: 603,280 ≈ 600,000

Question 40. 139,500 ≈ Answer: 139,500 ≈ 140,000

Question 41. 608,170 ≈ Answer: 608,170 ≈ 610,000

Question 42. 177,631 ≈ Answer: 177,631 ≈ 180,000

Question 43. 888,499 ≈ Answer: 888,499 ≈ 890,000

Question 44. 444,909 ≈ Answer: 444,909 ≈ 440,000

Eureka Math Grade 4 Module 1 Lesson 10 Problem Set Answer Key

Question 4. Opening day at the New York State Fair in 2012 had an attendance of 46,753. Decide which place value to round 46,753 to if you were writing a newspaper article. Round the number and explain why it is an appropriate unit to round the attendance to. Answer: Opening day at the New York State Fair in 2012 had an attendance of 46,753 if i were writing a newspaper article i would round the number to the highest place value of the given number 46,753 The highest place value of 46,753 is ten thousand. So, I would round it to 50,000 and write it in the newspaper article.

Eureka Math Grade 4 Module 1 Lesson 10 Exit Ticket Answer Key

Question 2. A company developed a student survey so that students could share their thoughts about school. In 2011, 78,234 students across the United States were administered the survey. In 2012, the company planned to administer the survey to 10 times as many students as were surveyed in 2011. About how many surveys should the company have printed in 2012? Explain how you found your answer. Answer: Number of students across the United States who administered the survey in 2011 are = 78,234 78,234 i s rounded to nearest ten thousand 80,000 In 2012 The company planned to administer the survey to 10 times as many students as were surveyed in 2011 10 × 80,000  =  800,000.

Eureka Math Grade 4 Module 1 Lesson 10 Homework Answer Key

c. In 2010, 28,357 of the finishers were men, and 14,072 of the finishers were women. About how many more men finished the race than women? To determine your answer, did you round to the nearest ten thousand or thousand? Explain. Answer: Number of men who finished the race in 2010 = 28,357 Number of women who finished the race in 2010 = 14,072 28,357 ~ 30,000 14,072 ~ 10,000 30,000 – 10,000 = 20,000 more men finished the race than women. Rounded the number to the nearest ten thousands. I used this place because i could use mental math.

Eureka Math Grade 4 Module 1 Answer Key

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( 3 , 2 ) ( 3 , 2 )

( 2 , 3 ) ( 2 , 3 )

( 3 , 4 ) ( 3 , 4 )

( 5 , −4 ) ( 5 , −4 )

no solution

infinitely many solutions

ⓐ no solution, inconsistent, independent ⓑ one solution, consistent, independent

( 6 , 1 ) ( 6 , 1 )

( −3 , 5 ) ( −3 , 5 )

( 2 , 3 2 ) ( 2 , 3 2 )

( − 1 2 , −2 ) ( − 1 2 , −2 )

( 2 , −1 ) ( 2 , −1 )

( −2 , 3 ) ( −2 , 3 )

( 1 , 3 ) ( 1 , 3 )

( 4 , −3 ) ( 4 , −3 )

( 6 , 2 ) ( 6 , 2 )

( 1 , −2 ) ( 1 , −2 )

ⓐ Since both equations are in standard form, using elimination will be most convenient. ⓑ Since one equation is already solved for x , using substitution will be most convenient.

ⓐ Since one equation is already solved for y , using substitution will be most convenient. ⓑ Since both equations are in standard form, using elimination will be most convenient.

160 policies

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

The angle measures are 55 and 35.

The angle measures are 5 and 85.

The angle measures are 42 and 138.

The angle measures are 66 and 114.

The length is 60 feet and the width is 35 feet.

The length is 60 feet and the width is 38 feet.

It will take Clark 4 hours to catch Mitchell.

It will take Sally 1 1 2 1 1 2 hours to catch up to Charlie.

The rate of the boat is 11 mph and the rate of the current is 1 mph.

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

The speed of the jet is 235 mph and the speed of the wind is 30 mph.

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

206 adults, 347 children

42 adults, 105 children

13 dimes and 29 quarters

19 quarters and 51 nickels

3 pounds peanuts and 2 pounds cashews

10 pounds of beans, 10 pounds of ground beef

120 ml of 25% solution and 30 ml of 50% solution

125 ml of 10% solution and 125 ml of 40% solution

$42,000 in the stock fund and $8000 in the savings account

$1750 at 11% and $5250 at 13%

Bank $4,000; Federal $14,000

$41,200 at 4.5%, $24,000 at 7.2%

ⓐ C ( x ) = 15 x + 25 , 500 C ( x ) = 15 x + 25 , 500

ⓑ R ( x ) = 32 x R ( x ) = 32 x

ⓓ 1,500 1,500 ; when 1,500 benches are sold, the cost and revenue will be both 48,000

ⓐ C ( x ) = 120 x + 150,000 C ( x ) = 120 x + 150,000

ⓑ R ( x ) = 170 x R ( x ) = 170 x

ⓓ 3,000 3,000 ; when 3,000 benches are sold, the revenue and costs are both $510,000

( 2 , −1 , 3 ) ( 2 , −1 , 3 )

( −2 , 3 , 4 ) ( −2 , 3 , 4 )

( −3 , 4 , −2 ) ( −3 , 4 , −2 )

( −2 , 3 , −1 ) ( −2 , 3 , −1 )

infinitely many solutions ( x , 3 , z ) ( x , 3 , z ) where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

The fine arts department sold 75 adult tickets, 200 student tickets, and 75 child tickets.

The soccer team sold 200 adult tickets, 300 student tickets, and 100 child tickets.

ⓐ [ 3 8 −3 2 5 −3 ] [ 3 8 −3 2 5 −3 ] ⓑ [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ] [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ]

ⓐ [ 11 9 −5 7 5 −1 ] [ 11 9 −5 7 5 −1 ] ⓑ [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ] [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ]

{ x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0 { x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0

{ x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3 { x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3

ⓐ [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] ⓑ [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] ⓒ [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ] [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ]

ⓐ [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] ⓑ [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] ⓒ [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ] [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ]

[ 1 −1 2 0 −3 −4 ] [ 1 −1 2 0 −3 −4 ]

[ 1 −1 3 0 −5 8 ] [ 1 −1 3 0 −5 8 ]

The solution is ( 4 , −1 ) . ( 4 , −1 ) .

The solution is ( −2 , 0 ) . ( −2 , 0 ) .

( 6 , −1 , −3 ) ( 6 , −1 , −3 )

( 5 , 7 , 4 ) ( 5 , 7 , 4 )

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number.

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number.

ⓐ −14 ; −14 ; ⓑ −28 −28

ⓐ 2 ⓑ −15 −15

ⓐ 3 ⓑ 11 ⓒ 2

ⓐ −3 −3 ⓑ 2 ⓒ 3

( − 15 7 , 24 7 ) ( − 15 7 , 24 7 )

( −2 , 0 ) ( −2 , 0 )

( −9 , 3 , −1 ) ( −9 , 3 , −1 )

( −6 , 3 , −2 ) ( −6 , 3 , −2 )

infinite solutions

The solution is the grey region.

No solution.

ⓐ { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 ⓑ

ⓐ { a ≥ p + 5 a + 2 p ≤ 400 { a ≥ p + 5 a + 2 p ≤ 400 ⓑ

ⓐ { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 ⓑ

ⓐ { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 ⓑ

Section 4.1 Exercises

( 0 , 2 ) ( 0 , 2 )

( 2 , 4 ) ( 2 , 4 )

( −2 , 2 ) ( −2 , 2 )

( 3 , 3 ) ( 3 , 3 )

( 6 , −4 ) ( 6 , −4 )

No solutions, inconsistent, independent

1 point, consistent and independent

infinite solutions, consistent, dependent

( 1 , −4 ) ( 1 , −4 )

( −3 , 2 ) ( −3 , 2 )

( −1 / 2 , 5 / 2 ) ( −1 / 2 , 5 / 2 )

( −5 , 4 ) ( −5 , 4 )

( 0 , 10 ) ( 0 , 10 )

( 4 , −2 ) ( 4 , −2 )

( 4 , 0 ) ( 4 , 0 )

( 4 , 5 ) ( 4 , 5 )

( 7 , 12 ) ( 7 , 12 )

( −3 , −5 ) ( −3 , −5 )

( 2 , −3 ) ( 2 , −3 )

( −11 , 2 ) ( −11 , 2 )

( 6 / −9 , 24 / 7 ) ( 6 / −9 , 24 / 7 )

infinitely many

ⓐ substitution ⓑ elimination

ⓐ elimination ⓑ substituion

Answers will vary.

Section 4.2 Exercises

−7 −7 and −19 −19

22 and −67 −67

Eighty cable packages would need to be sold to make the total pay the same.

Mitchell would need to sell 120 stoves for the companies to be equal.

8 and 40 gallons

1000 calories playing basketball and 400 calories canoeing

Oranges cost $2 per pound and bananas cost $1 per pound

Package of paper $4, stapler $7

Hot dog 150 calories, cup of cottage cheese 220 calories

Owen will need 80 quarts of water and 20 quarts of concentrate to make 100 quarts of lemonade.

53.5 53.5 degrees and 36.5 36.5 degrees

16 degrees and 74 degrees

134 degrees and 46 degrees

37 degrees and 143 degrees

16 ° 16 ° and 74 ° 74 °

45 ° 45 ° and 45 ° 45 °

Width is 41 feet and length is 118 feet.

Width is 10 feet and length is 40 feet.

1.5 1.5 hour

Boat rate is 16 mph and current rate is 4 mph.

Boat rate is 18 mph and current rate is 2 mph.

Jet rate is 265 mph and wind speed is 22 mph.

Jet rate is 415 mph and wind speed is 25 mph.

Section 4.3 Exercises

110 adult tickets, 190 child tickets

6 good seats, 10 cheap seats

92 adult tickets, 220 children tickets

13 nickels, 3 dimes

42 dimes, 8 quarters

17 $10 bills, 37 $20 bills

80 pounds nuts and 40 pounds raisins

9 pounds of Chicory coffee, 3 pounds of Jamaican Blue Mountain coffee

10 bags of M&M’s, 15 bags of Reese’s Pieces

7.5 7.5 liters of each solution

80 liters of the 25% solution and 40 liters of the 10% solution

240 liters of the 90% solution and 120 liters of the 75% solution

$1600 at 8%, 960 at 6%

$28,000 at 9%, $36,000 at 5.5 % 5.5 %

$8500 CD, $1500 savings account

$55,000 on loan at 6% and $30,000 on loan at 4.5 % 4.5 %

ⓐ C ( x ) = 5 x + 6500 C ( x ) = 5 x + 6500

ⓑ R ( x ) = 10 x R ( x ) = 10 x

ⓓ 1,500; when 1,500 water bottles are sold, the cost and the revenue equal $15,000

Section 4.4 Exercises

( 4 , 5 , 2 ) ( 4 , 5 , 2 )

( 7 , 12 , −2 ) ( 7 , 12 , −2 )

( −3 , −5 , 4 ) ( −3 , −5 , 4 )

( 2 , −3 , −2 ) ( 2 , −3 , −2 )

( 6 , −9 , −3 ) ( 6 , −9 , −3 )

( 3 , −4 , −2 ) ( 3 , −4 , −2 )

( −3 , 2 , 3 ) ( −3 , 2 , 3 )

( −2 , 0 , −3 ) ( −2 , 0 , −3 )

x = 203 16 ; y = –25 16 ; z = –231 16 ; x = 203 16 ; y = –25 16 ; z = –231 16 ;

( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

$20, $5, $10

Section 4.5 Exercises

ⓐ [ 2 4 −5 3 −2 2 ] [ 2 4 −5 3 −2 2 ] ⓑ [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ] [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ]

ⓐ [ 2 −5 −3 4 −3 −1 ] [ 2 −5 −3 4 −3 −1 ] ⓑ [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ] [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ]

{ 2 x − 4 y = −2 3 x − 3 y = −1 { 2 x − 4 y = −2 3 x − 3 y = −1

{ 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2 { 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2

ⓐ [ 3 2 1 4 −6 −3 ] [ 3 2 1 4 −6 −3 ] ⓑ [ 12 8 4 4 −6 −3 ] [ 12 8 4 4 −6 −3 ] ⓒ [ 12 8 4 24 −10 −5 ] [ 12 8 4 24 −10 −5 ]

ⓐ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓑ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓒ [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ] [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ]

[ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ] [ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ]

( 1 , −1 ) ( 1 , −1 )

( −2 , 5 , 2 ) ( −2 , 5 , 2 )

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 1 2 z + 4 ; y = 1 2 z − 6 ; z x = 1 2 z + 4 ; y = 1 2 z − 6 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

Section 4.6 Exercises

ⓐ 6 ⓑ −14 −14 ⓒ −6 −6

ⓐ 9 ⓑ −3 −3 ⓒ 8

( 7 , 6 ) ( 7 , 6 )

( −9 , 3 ) ( −9 , 3 )

inconsistent

Section 4.7 Exercises

ⓐ false ⓑ true

ⓐ { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 ⓑ

ⓐ { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c ⓑ

ⓐ { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 ⓑ

ⓐ { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 ⓑ

Review Exercises

( 3 , −1 ) ( 3 , −1 )

one solution, consistent system, independent equations

( 3 , 1 ) ( 3 , 1 )

( 4 , −1 ) ( 4 , −1 )

elimination

50 irises and 150 tulips

10 calories jogging and 10 calories cycling

35 ° 35 ° and 55 ° 55 °

the length is 450 feet, the width is 264 feet

1 2 1 2 an hour

the rate of the jet is 395 mph, the rate of the wind is 7 mph

41 dimes and 11 pennies

46 2 3 46 2 3 liters of 30% solution, 23 1 3 23 1 3 liters of 60% solution

$29,000 for the federal loan, $14,000 for the private loan

( −3 , 2 , −4 ) ( −3 , 2 , −4 )

[ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ] [ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ]

{ x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3 { x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3

ⓐ [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] ⓑ [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] ⓒ [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ] [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ]

( −2 , 5 , −2 ) ( −2 , 5 , −2 )

ⓐ { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 ⓑ

Practice Test

( 2 , 1 ) ( 2 , 1 )

( 2 , −2 , 1 ) ( 2 , −2 , 1 )

15 liters of 1% solution, 5 liters of 5% solution

The candy cost $20; the cookies cost $5; and the popcorn cost $10.

ⓐ { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C ⓑ

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Lesson 4.1.1, lesson 4.1.2, lesson 4.2.1, lesson 4.2.2, lesson 4.2.3, lesson 4.2.4, lesson 4.3.1, lesson 4.3.2, lesson 4.3.3.

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Texas Go Math Grade 1 Lesson 4.1 Answer Key Use Pictures to Add To

Refer to our  Texas Go Math Grade 1 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 1 Lesson 4.1 Answer Key Use Pictures to Add To.

Essential Question How con you use pictures to show adding to, or joining? Explanation: By counting the pictures we can add the pictures.

Explore Draw to show adding to, or joining Write how many there are.

3 + 3 = 6 lady bugs

For The Teacher

• Read the following problem. Have children draw a picture to show the problem. There are 3 ladybugs on a leaf. 2 more ladybugs join them. How many ladybugs are there?

Math Talk Mathematical Processes How does your drawing show the problem? Explain.

Model and Draw

Share and Show

Write how many.

Problem Solving

Write or draw to solve.

Daily Assessment Task

Choose the correct answer.

Question 9. Representations There are 4 ducks in the pond. 2 more ducks join them. How many ducks are ¡n the pond now? (A) 2 (B) 6 (C) 4 Answer: B Explanation: 4 + 2 = 6 6 ducks are ¡n the pond now

Question 10. Gavin sees 2 turtles on a log. Then he sees 6 more turtles join them. How many turtles are on the log now? (A) 6 (B) 8 (C) 2 Answer:  B Explanation: 2 + 6 = 8 8 turtles are on the log now

Take Home Activity

• Have your child use stuffed animals or other toys to show 3 animals. Then odd to the group showing 2 more animals. Ask how many animals there are, Repeat for other combinations of animals with totals up to 10.

Texas Go Math Grade 1 Lesson 4.1 Homework and Practice Answer Key

Question 2. 4 oranges fall off the tree. Then 2 more oranges fall off. How many oranges fall off the tree? ____ oranges Answer: 6 oranges Explanation: 4 + 2 = 6 6 oranges fall off the tree

Question 3. Ava and Emma eat 5 strawberries. Emma eats 1 more than Ava. Ava eats 2 strawberries. How many strawberries does Emma eat? ___ strawberries Answer: 3 strawberries Explanation: 2 + 1 = 3 3 strawberries that Emma eat

Texas Test Prep

Lesson Check

Question 5. There are 6 friends playing kickball. 3 more friends join them. How many friends are playing kickball? (A) 8 (B) 3 (C) 9 Answer: C Explanation: 6 + 3 = 9 9 friends are playing kickball

Question 6. How many soccer balls are there? 3 soccer balls and 5 more soccer balls. (A) 2 soccer balls (B) 8 soccer balls (C) 7 soccer balls Answer: B Explanation: 3 + 5  = 8 8 soccer balls.

Question 7. Multi-Step Matt is playing with 4 friends. 5 friends join them. Then 3 more friends join them. How many friends is Matt playing with? (A) 12 (B) 8 (C) 13 Answer: A Explanation: 4 + 5  + 3 = 12 12 friends is Matt playing with

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