## Big Ideas Math Book 2nd Grade Answer Key Chapter 12 Solve Length Problems

### Solve Length Problems Vocabulary

**Organize It**

Use the review words to complete the graphic organizer.

Answer :

Explanation :

Bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems.

**Define It**

Match the review word to its model.

Answer :

### Lesson 12.1 Use a Number Line to Add and Subtract Lengths

**Explore and Grow**

Your goldfish is 4 centimetres long. It grows 6 more centimetres. Use the number line and your ruler to show how long the goldfish is now.

Answer :

Length of the gold fish = 4 centimetres

Increased length of gold fish = 6 centimetres

Length of gold fish now = 4 + 6 = 10 centimetres .

Explanation:

Draw an arrow from 0 to 4 to represent 4. Then draw an arrow 6 units to the right representing adding +6.

So, 4 + 6 =0

What is the same about your ruler and the number line? What is different?

_________________________

_________________________

_________________________

_________________________

Answer:

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

Ruler a straight strip, typically marked at regular intervals and used to draw straight lines or measure distances.

**Show and Grow**

Question 1.

You swim 15 meters and take a break. Then you swim 10 meters. How many meters do you swim?

Answer:

Distance covered while swimming = 15 meters

Distance covered while swimming after break = 10 metresters .

Therefore, 25 meters traveled in swimming

Explanation :

Draw an arrow from 0 to 10 to represent 10. Then draw an arrow 15 units to the right representing adding +15.

So, 10 + 15 = 25

Question 2.

A ribbon is 16 yards long. You cut off 7 yards. How long is the ribbon now?

Answer:

Length of the ribbon = 16 yards

Decreased in the length of the ribbon = 7 yards

Length of the ribbon now = 16 – 7 = 9 yards .

Explanation :

Draw an arrow from 0 to 16 to represent 16. Then draw an arrow 7 units to the left representing Subtracting -7.

So, 16 – 7 = 9

**Apply and Grow: Practice**

Question 3.

A snake is 24 inches long. It sheds 14 inches of its skin. How much skin does it not shed?

Answer:

Length of the snake = 24

Length of snake sheds = 14

Length of the snake didn’t shed = Total Length – shed length = 24 – 14 = 10 inches

Explanation :

Draw an arrow from 0 to 24 to represent 24. Then draw an arrow 14 units to the left representing Subtracting 10

So, 24 – 14 = 10 inches .

Question 4.

A photo is 15 centimetres long. You cut off 3 centimetres from the left and 3 centimetres from the right. How long is the photo now?

Answer:

Length of the photo = 15 centimetres

Length of the photo cut from left = 3 centimetres

Length of the photo cut from right = 3 centimetres

Length of the photo now = 15 – 3 – 3 = 15 – 6 = 9 centimetres

Question 5.

**Structure**

Write an equation that matches the number line.

Answer:

Explanation :

Draw an arrow from 0 to 11 to represent 11. Then draw an arrow 6 units to the right representing adding 6 and draw an arrow 3 units to the left representing subtracting 3 .

So, 11 + 6 – 3 = 14 .

**Think and Grow: Modeling Real Life**

You want to make a bracelet that is 6 inches long. You make 4 inches before lunch. You make 2 inches after lunch. Did you finish the bracelet?

Model:

Did you finish? Yes No

Answer:

Length of the bracelet = 6 inches

Length of the bracelet made before lunch = 4 inches.

Length of the bracelet made after lunch = 2 inches.

Total Length of the bracelet made = 4 + 2 = 6 inches .

Yes , it is finished

Explanation :

Draw an arrow from 0 to 4 to represent 4. Then draw an arrow 2 units to the right representing adding 2

So, 4 + 2 = 6 inches .

**Show and Grow**

Question 6.

You are painting a fence that is 24 feet long. You paint 10 feet on Saturday. You paint 13 feet on Sunday. Did you finish painting the fence?

Answer:

Length of the total fencing = 24 feet

Length of the fence painted on Saturday = 10 feet

Length of the fence painted on Sunday = 13 feet

Total length of the fencing painted = 10 + 13 = 23 feet.

No painting of fencing is not finished as it is painted 23 feet . still 1 feet left to paint ( 24 – 23 = 1 feet )

Explanation :

Draw an arrow from 0 to 10 to represent 10. Then draw an arrow 13 units to the right representing adding 13

So, 10 + 13 = 23 feet .

Question 7.

**DIG DEEPER!**

You throw a disc 9 meters. On your second throw, the disc travels 3 meters more than your ﬁrst throw. How many meters did the disc travel in all?

______ meters

Answer:

Length of the first disc thrown = 9 metres

Length of the disc travels in second throw = 3 meters more than your ﬁrst throw = 9 + 3 = 12

Total length the disc travels in first and second throw = 9 + 12 = 21 meters .

Explanation :

Draw an arrow from 0 to 9 to represent 9. Then draw an arrow 12 units to the right representing adding 12

So, 9 + 12 = 21 meters .

### Use a Number Line to Add and Subtract Lengths Homework & Practice 12.1

Question 1.

You kick a ball 13 yards. Your friend kicks it back 9 yards. How far is the ball from you now?

Answer:

Distance traveled by ball when i kicked the ball = 13 yards

Distance traveled by ball when my friend kicked the ball = 9 yards back ward = -9 yards.

Distance of ball from me now = 13 yards – 9 yards = 4 yards.

Explanation :

Draw an arrow from 0 to 13 to represent 13. Then draw an arrow 9 units to the left representing Subtracting 9

So, 13- 9 = 4 yards .

Question 2.

Your shoelace is 20 inches long. Your friend’s is 4 inches longer than yours. How long is your friend’s shoelace?

Answer:

Length of my shoelace = 20 inches

Length of my friend’s shoelace = 4 inches longer than me = 4 + 20 = 24 inches.

Explanation :

Draw an arrow from 0 to 20 to represent 20. Then draw an arrow 4 units to the right representing adding 4

So, 20 + 4 = 24 inches .

Question 3.

**Structure**

One power cord is 7 feet long. Another power cord is 5 feet long. Use the number line to find the combined length of the power cords.

Answer:

Length of power cord = 7 feet

Length of another power cord = 5 feet

Total length of both cords = 7 + 5 = 12 feet

Explanation :

Draw an arrow from 0 to 7 to represent 7. Then draw an arrow 5 units to the right representing adding 5

So, 7 + 5 =12 feets .

Question 4.

**Modeling Real Life**

A worker needs to pave a bike path that is 25 feet long. He completes 13 feet on Monday and 11 feet on Tuesday. Did he complete the paving?

Answer:

Length of the bike path = 25 feet

length paved on Monday = 13 feet

Length paved on Tuesday = 11 feet

Total length paved on Monday and Tuesday = 13 + 11 = 24 feet

1 feet is less to complete the length of bike path . So, Paving is not completed .

Explanation :

Draw an arrow from 0 to 13 to represent 13. Then draw an arrow 11 units to the right representing adding 11

So, 13+ 11 = 24 feets .

Question 5.

**DIG DEEPER!**

You throw a baseball 5 yards. On your second throw, the baseball travels 2 yards more than your ﬁrst throw. How many yards did the baseball travel in all?

_______ yards

Answer:

Distance traveled by a base ball = 5 yards

Distance traveled by a base ball in second throw = 2 yards more than your ﬁrst throw = 5 + 2 = 7 yards .

Explanation :

Draw an arrow from 0 to 5 to represent 5. Then draw an arrow +2 units to the right representing adding 2

So, 5 + 2 = 7 yards .

**Review & Refresh**

**Compare**

Question 6.

Answer:

210 = 200 + 10

Question 7.

Answer:

532 = 500 + 20 + 3

### Lesson 12.2 Problem Solving: Length

**Explore and Grow**

How much longer is the red ribbon than the blue ribbon?

______ inches

Answer:

**Show and Grow**

Question 1.

An orange fish is 10 centimeters long. A yellow fish is 35 centimeters long. A red fish is 19 centimeters long. How much longer is the yellow fish than the red fish?

Answer:

Length of Orange fish = 10 centimeters

Length of Yellow fish = 35 centimeters

Length of red fish = 19 centimeters

length of yellow fish is how much longer than the red fish = 35 – 19 = 16 centimeters

**Apply and Grow: Practice**

Question 2.

A green scarf is 60 inches long. An orange scarf is 45 inches long. A red scarf is 36 inches long. How much longer is the green scarf than the red scarf?

______ inches

Answer:

Length of green scarf = 60 inches

Length of Orange scarf = 45 inches .

Length of Red scarf = 36 inches .

Length of green scarf is how much longer than red scarf = 60 – 36 = 24 inches .

Question 3.

**DIG DEEPER!**

A pink ribbon is 90 centimeters long. A purple ribbon is 35 centimeters long. A blue ribbon is46 centimeters long. How much longer is the pink ribbon than the total length of the purple and blue ribbons?

_______ centimeters

Answer:

Length of pink ribbon = 90 centimeters

Length of purple ribbon = 35 centimeters

Length of blue ribbon = 46 centimeters

The total length of the purple and blue ribbons = 35 + 46 = 81 centimeters.

Length of pink ribbon is how much longer than the total length of the purple and blue ribbons = 90 – 81 = 9 centimeters

Question 4.

**Structure**

How much taller is Student 3 than the shortest student?

________ inches

Answer:

Taller student is student 3 = 53 inches .

Shorter student is student 2 = 48 inches .

Taller Student is how much taller than shorter student = 53 – 48 = 5 inches .

**Think and Grow: Modeling Real Life**

You hop 27 inches and then 24 inches. Your friend hops 3 inches less than you. How far does your friend hop?

Think: What do you know? What do you need to find?

Model:

_______ inches

Answer:

Length hoped by me is 27 and 24 inches = 27 + 24 = 51 inches

Length hoped by my friend = 3 inches less than me = 51 – 3 = 48 inches .

**Show and Grow**

Question 5.

You throw a ball 36 feet and then 41 feet. Your friend throws a ball 5 feet farther than you. How far does your friend throw the ball?

______ feet

Answer:

Distance traveled by ball in first throw = 36 feet

Distance traveled by ball in Second throw = 41 feet

Total Distance traveled by balls = 36 + 41 = 77 feet

Distance traveled by ball when my friend throws = 5 feet farther than me = 77 + 5 = 82 feet .

Question 6.

**DIG DEEPER!**

A black horse runs 53 meters and then 45 meters. A brown horse runs 62 meters and then 31 meters. Which horse ran the longer distance in all? How many more meters did the horse run?

Black horse Brown horse

_________ more meters

Answer:

Distance traveled by black horse is 53 meters and then 45 meters. = 53 + 45 = 98 meters

Distance traveled by Brown horse is 62 meters and then 31 meters = 62 + 31 = 93 meters

Black Horse runs longer distance than brown horse

Black horse travels 98 – 93 = 5 meters more than brown horse .

### Problem Solving: Length Homework & Practice 12.2

Question 1.

The distance to the principal’s office is 24 yards. The distance to the bathroom is 15 yards. The distance to your teacher’s desk is 2 yards. How much farther away is the principal’s office than the bathroom?

_______ yards

Answer:

The distance to the principal’s office = 24 yards

The distance to the bathroom = 15 yards

The distance to your teacher’s desk = 2 yards

The principal’s office is 9 yards farther away than the bathroom .

Question 2.

**YOU BE THE TEACHER**

You launch a rocket 63 meters. Your friend launches it 28 meters, and your cousin launches it 86meters. Your cousin says that he launches the rocket 58 meters farther than you. Is he correct? Explain.

Answer:

Distance traveled by my rocket = 63 meters

Distance traveled by my friend rocket = 28 meters

Distance traveled by my cousin’s rocket = 86 meters

Distance differences between my rocket and my cousins rocket = 86 – 63 = 23 meters .

My Rockets is 23 meters farther than my cousin rocket not 58 meters.

So above statement is wrong .

Explanation :

Distance differences between my rocket and my cousins rocket = 86 – 63 = 23 meters .

My Rockets is 23 meters farther than my cousin rocket not 58 meters.

Question 3.

**Modeling Real Life**

You create a drawing that is 15 centimeters long and then add on 7 more centimeters. Your friend creates a drawing that is 3 centimeters longer than yours. How long is your friend’s drawing?

_______ centimeters

Answer:

Length of my Drawing = 15 centimeters

Length of my drawing after adding 7 centimeters = 15 + 7 = 22 centimeters

Length of my Friends drawing = 3 centimeters longer than my drawing = 22 + 3 = 25 centimeters

Therefore length of my friend’s drawing = 25 centimeters .

Question 4.

**DIG DEEPER!**

A frog hops 36 inches and then 22 inches. A toad hops 14 inches and then 43 inches. Which animal hopped the longer distance in all? How many more inches did the animal hop?

Frog Toad

________ more inches

Answer:

Distance hopped by frog is 36 inches and then 22 inches. = 36 + 22 = 58 inches .

Distance hopped by toad is 14 inches and then 43 inches = 14 + 43 = 57 inches .

Frog hopped more distance than toad

Difference of distance hopped by frog and toad = 58 – 57 = 1 inch .

**Review & Refresh **

Question 5.

635 + 10 = ______

635 + 100 = _____

Answer:

635 + 10 = 645

635 + 100 = 735

Explanation :

The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten

The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

Question 6.

824 + _____ = 924

824 + _____ = 834

Answer:

824 + 100 = 924

824 + 10 = 834

Explanation :

The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten

The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

Question 7.

309 + _____ = 409

309 + _____ = 319

Answer:

309 + 100 = 409

309 + 10 = 319

Explanation :

The ones digit remains the same when you add ten. The tens digit increases by 1 every time you add ten

The ones digit remains the same and the tens digit remains the same when you add hundred. The hundred digit increases by 1 every time you add hundred

### Lesson 12.3 Problem Solving: Missing Measurement

**Explore and Grow**

You and your friend each have a piece of yarn. The total length of both pieces is 16 centimeters. Use a ruler to measure your yarn. Then draw your friend’s yarn.

Answer:

Explain how you found the length of your friend’s yarn.

_______________________

_______________________

_______________________

Answer:

Total Length of the yarn = 16 centimeters

Length of my yarn = 7.8 centimeters .

Length of my friend’s yarn = 16 – 7.8 = 8.2 centimeters

**Show and Grow**

Question 1.

A rope is 31 meters long. You cut a piece off. Now the rope is 14 meters long. How much rope did you cut off?

So, ? = ______.

______ inches

Answer:

Length of the rope = 31 meters

Length of the rope after cut off = 14 meters.

Length of the cut off rope = 31 – 14 = 17 meters .

**Apply and Grow: Practice**

Question 2.

A celery stalk is 20 centimeters long. You cut off the leaves. Now it is 13 centimeters long. How much did you cut off?

______ centimeters

Answer:

Length of celery stalk = 20 centimeters

Length of celery stacking after chopping the leaves = 13 centimeters .

Length of the chopped leaves = 20 – 13 = 7 centimeters .

Question 3.

Descartes walked some and then ran 39 yards. He went a total of 75 yards. How far did he walk?

______ yards

Answer:

Total Distance traveled by Descartes = 75 yards

Distance traveled by running = 39 yards

Distance Traveled by walking = 75 – 39 = 36 yards

Question 4.

Your coat zipper is 18 inches long. The zipper gets stuck at 11 inches. How much of the zipper will not zip?

_____ inches

Answer:

Length of coat zipper = 18 inches

Length of zipper got stuck = 11 inches

Length of zipper will not zip = 18 – 11 = 7 inches .

Question 5.

**Number Sense**

The path to school is 181 meters long in all. How long is the missing part of the path?

_______ meters

Answer:

Total path to school = 181 meters

Path from house to first turn = 74 meters

Path from first turn to second turn = 86 meters .

Path from second turn to school is missing = 181 – 74 – 86 = 181 – 160 = 21 meters

**Think and Grow: Modeling Real Life**

You make a paper chain that is 8 feet long. You add 7 feet of chain to the end. Then 6 feet of the chain breaks off. How long is the chain now?

Think: What do you know? What do you need to find?

_____ feet

Answer:

Length of paper chain = 8 feet

Length of chain added in the end = 7 feet .

Length of chain broken = 6 feet

Total length of the chain now = 8 + 7 – 6 = 15 – 6 = 9 feet .

Explanation :

**Show and Grow**

Question 6.

You build a tower that is 48 centimeters tall. You add 34 centimeters to the tower height. Your tower breaks and 29 centimeters fall off. How tall is your tower now?

______ centimeters

Answer:

Height of the tower = 48 centimeters

Height added to the tower = 34 centimeters

Total Height of the tower now = 48 + 34 = 82 centimeters .

Height at which tower broken = 29 centimeters

Height of the tower after broken = 82 – 29 = 53 centimeters

Question 7.

A football team is 78 yards away from scoring. They gain 15 yards on the first play and 21 yards on the second play. How far is the team from scoring now?

_______ yards

Answer:

Distance of foot ball team from scoring = 75 yards

Distance gain in first play = 15 yards

Distance gain in second play = 21 yards.

Distance of foot ball team from scoring now = 75 – 15 – 21 = 39 yards .

### Problem Solving: Missing Measurement Homework & Practice 12.3

Question 1.

A piece of fabric is 36 inches long. Another piece is 18 inches long. What is the total length of both pieces of fabric?

_____ inches

Answer:

Length of first fabric = 36 inches

Length of second fabric = 18 inches

Total length of both fabrics = 36 + 18 = 54 inches.

Question 2.

A rose is 61 centimeters long. You cut off some of the stem. Now it is 48 centimeters long. How much did you cut off?

______ Centimeters

Answer:

Length of rose = 61 centimeters

Length of rose after chopping stem = 48 centimeters .

Length of chopped stem = 61 – 48 = 13 centimeters .

Question 3.

**Number Sense**

Newton’s balloon is 18 inches long. Descartes’s balloon is 23 inches long. Your friend’s balloon is 12 inches long. Which sentences are true?

Newton’s balloon is 6 inches longer than your friend’s.

Your friend’s balloon is 11 inches longer than Descartes’s.

Descartes’s balloon is 5 inches longer than Newton’s.

Answer:

Statement 1 is true and Statement 3 is true

Length of Newton’s balloon =18 inches

Length of Descartes’s balloon = 23 inches .

Length of my Friend’s balloon = 12 inches .

Explanation :

Statement 1 :

Newton balloon and my friends balloon difference in length = 18 – 12 = 6 inches.

It means Newton balloon is 6 inches longer than my friend balloon .

Statement 2 :

Descartes balloon and my friends balloon difference in length= 23 – 12 = 11 inches .

Descartes balloon is 11 inches longer than my friends balloon .

so statement is wrong .

Statement 3 :

Descartes balloon and newtons balloon difference in length = 23 – 18 = 5 inches.

Descartes balloon is 5 inches longer than newton balloon .

Statement is true .

Question 4.

**DIG DEEPER!**

Answer:

Equation 3 is true

Question 5.

**Modeling Real Life**

A piece of wood is 16 feet long. You cut off 6 feet, but it is still too long. You cut off 2 more feet. How long is the piece of wood now?

______ feet

Answer:

Length of wood = 16 feet

Length of wood chopped = 6 feet

Length of wood chopped again = 2 feet

Length of wood after chopping = 16 – 6 – 2 = 16 – 8 = 8 feet .

**Review & Refresh**

Question 6.

Answer:

Question 7.

Answer:

Question 8.

Answer:

### Lesson 12.4 Practice Measurement Problems

**Explore and Grow**

Newton’s piece of string is 24 centimeters long. He gives Descartes 12 centimeters of the string. How long is the string that Newton has left? Draw a picture and write an equation to solve.

______ cm

Answer:

Length of Newton’s peice of string = 24 centimeters

Length of string given to Descartes = 12 centimeters

Length of string left over with Newton = 24 – 12 = 12 centimeters .

24 – 12 = 12 is the equation .

Compare the lengths of string. Is one longer, or are they the same length? Explain.

__________________________

__________________________

Answer:

Both the lengths are same

Newton’s length = Descarte’s length = 12 centimeters .

**Show and Grow**

Question 1.

Your blanket is 66 inches long. Your friend’s blanket is 9 inches longer than yours. How long is your friend’s blanket?

So, ? = ______

_____ inches

Answer:

Length of my blanket = 66 inches

Length of my friend’s blanket = 9 inches longer than yours. = 66 + 9 = 75 inches

My friends blanket is 9 inches longer than my blanket .

**Apply and Grow: Practice**

Question 2.

A blue whale is 31 meters long. A humpback whale is 16 meters long. How much longer is the blue whale than the humpback whale?

_____ meters

Answer:

Length of blue whale = 31 meters

Length of hump back whale = 16 meters

Differences in the length of blue whale and hump back whale = 31 – 16 = 15 meters.

Length of blue whale is 15 meters longer than hump back whale .

Question 3.

Newton runs 450 meters. Descartes runs 25 meters less than Newton. How far do they run in all?

______ meters

Answer:

Distance traveled by Newtons in running= 450 meters

Distance traveled by Descartes in running= 25 meters less than Newton = 450 – 25 = 425 meters .

Total Distance traveled by Newton and Descartes = 450 + 425 = 875 meters .

Question 4.

**Reasoning**

Solve the problem below two different ways.

You want to read 100 books during the school year. You read 25 books in the fall and 54 books in the winter. How many books do you still need to read?

______ books

Answer:

Total Number of books to read = 100 books

Number of books read in fall = 25 books

Number of books read in winter = 54 books

Number of books still needed to read = 100 – 25 – 54 = 100 – 79 = 21 books

**Think and Grow: Modeling Real Life**

A yellow subway train is 18 meters longer than a blue subway train. The yellow subway train is 92 meters long. How long is the blue subway train?

Equation:

______ meters

Answer :

Length of yellow subway tarin = 92 meters .

Length of yellow subway train = 18 meters longer than a blue subway train

Length of blue subway train = 92 – 18 = 74

**Show and Grow**

Question 5.

A brown rabbit hops 24 inches less than a white rabbit. The brown rabbit hops 48 inches. How many inches does the white rabbit hop?

_____ inches

Answer:

Distance traveled by brown rabbit by hopping = 24 inches less than a white rabbit

Distance traveled by brown rabbit = 48 inches .

Distance traveled by white rabbit = 48 + 24 = 72 inches

Question 6.

Your kite string is 47 yards long. You tie 6 yards of string to the end. Now your kite string is 21 yards longer than your friend’s kite string. How long is your friend’s kite string?

_______ yards

Answer:

Length of the kite string = 47 yards

Length attached to kite in the end = 6 yards

Length of my kite string now =47 + 6 = 53 yards

Length of my kite string= 21 yards longer than your friend’s kite string

Length of my friend’s kite string = 53 – 21 = 32 yards .

### Practice Measurement Problems Homework & Practice 12.4

Question 1.

A swimming pool is 28 feet long. The pool cover is 32 feet long. How much longer is the pool cover?

So, ? = ______

_____ feet

Answer:

Length of swimming pool = 28 feet

Length of pool cover = 32 feet

Difference of length in pool and pool cover = 32 – 28 = 4 feet

So, the pool cover is 4 feet longer than pool

Question 2.

**Writing**

Write and solve a word problem about the colored pencils.

Answer:

Which color pencil is longer and how much centimetres it is longer from shorter pencil ?

Explanation :

The length of green pencil = 8 cm

The length of red pencil = 11 cm

The length of blue pencil = 15 cm

green pencil is the shorter pencil

Blue pencil is the longer pencil

Differences in the lengths of blue and green pencils = 15 – 8 = 7 cms

The blue pencil is 7 cms longer than green pencil .

Question 3.

**Modeling Real Life**

You cast out your fishing line 14 yards less than your friend. Your friend casts out her line 33 yards. How many yards do you cast out your fishing line?

______ yards

Answer:

length of my friend’s fishing line = 33 yards

length of my fishing line= 14 yards less than my friend’s

Length of my fishing line= 33 – 14 = 19 yards

Question 4.

**Modeling Real Life**

Your nightstand is 24 inches tall. You put a 20-inch lamp on it. Now your nightstand and lamp are 19 inches taller than your bed. How tall is your bed?

______ inches

Answer:

Height of my nightstand = 24 inches

Height of the lamp = 20 inch

Height of nightstand and lamp = 24 + 20 = 42 inches.

Height of bed = nightstand and lamp are 19 inches taller than your bed.

Height of bed = 42 – 19 = 23 inches .

**Review & Refresh**

Question 5.

Write the number in expanded form and word form.

645

______ + ____ + ______ _________

Answer:

645 = 600 + 40 + 5

Explanation :

Six hundred and forty five represents six hundreds plus four tens and five ones

When numbers are separated into individual place values and decimal places is called expanded form

Question 6.

Write the number in standard form and word form.

800 + 60 + 2

_____ _______________________

Answer:

862

Explanation:

eight hundred and sixty two = 8 hundreds plus 6 tens and 2ones .

When numbers are separated into individual place values and decimal places is called expanded form

### Solve Length Problems Performance Task

Question 1.

A recorder is 1 foot long. A clarinet is 24 inches long. Which instrument is longer? How much longer is the instrument?

Recorder Clarinet

_____ inches

Answer:

Length of the Recorder = 1 foot = 12 inches

Length of the clarinet = 24 inches

Clarinet is longer

Difference in the length of clarinet and Recorder = 24 – 12 = 12 inches .

Clarinet is 12 inches longer than Recorder .

Question 2.

A piano has 27 more keys than a keyboard. There are 52 white keys and 36 black keys on a piano.

a. How many keys are on the keyboard?

_____ keys

Answer :

Number of white keys on piano = 52

Number of black keys on piano = 36

Total Number of keys on piano = 52 + 36 = 88 keys

piano has 27 more keys than a keyboard

Number of keys on key board = 88 – 27 = 61 keys .

b. The number of black keys on the piano is equal to the number of white keys on the keyboard. How many black keys are on the keyboard?

______ black keys

Answer:

Number of black keys on piano = 36 = number of white keys on keyboard

Number of black keys on keyboard = 61 – 36 = 25 keys .

Question 3.

A drum set has drums and cymbals on stands.

a. The cymbals are 77 centimeters from the ground. You raise the stand 18 centimeters. The cymbals are now 23 centimeters higher than one of the drums. What is the height of the drum?

_______ centimeters

Answer :

Length of cymbals from ground = 77 centimeters .

Length of the stand = 18 centimeters .

Length of cymbals now = 77 + 18 = 95 centimeters

cymbals are now 23 centimeters higher than one of the drums.

Height of the drums = 95 – 23 =72 centimeters .

b. Another drum is 60 centimeters from the ground. You raise it 12 centimeters. Are both drums the same height?

Yes No

Answer:

Height of the drum = 60 centimeters

Height of the drum raised = 12 centimeters.

Height of the drum now = 60 + 12 = 72 centimeters .

Both the drums are at equal heights of 72 centimeters

Yes, both drums have the same height .

### Solve Length Problems Activity

**Draw and Cover**

To Play: Players take turns. On your turn, pick a Draw and Cover Card and solve. Then cover the sea turtle that has the answer. Continue playing until all sea turtles are covered.

### Solve Length Problems Chapter Practice

**12.1 Use a Number Line to Add and Subtract Lengths**

Question 1.

You throw a ball 12 yards. Your friend throws it back 8 yards. How far is the ball from you now?

Answer:

Distance traveled by ball when thrown by me= 12 yards

Distance traveled by my friend after throwing = – 8 yards. ( – represents back direction )

Distance of ball far from me = 12 – 8 = 4 yards.

Explanation:

Draw an arrow from 0 to 12 to represent 12. Then draw an arrow 4 units to the left representing subtracting 4.

So, 12 – 8 = 4 yards .

**12.2 Problem Solving: Length**

Question 2.

Your cat’s first collar was 6 inches long. Now your cat has a collar that is 13 inches long. Your puppy’s collar is 11 inches long. How much longer is your cat’s collar now?

Answer:

Length of cat first collar = 6 inches

Length of cat collar now = 13 inches .

Difference in cat collar now and first collar = 13 – 6 = 7 inches

Cat collar is 7 inches longer than first collar

**12.3 Problem Solving: Missing Measurement**

Question 3.

You must be 54 inches tall to ride a roller coaster. At 8 years old, you were 48 inches tall. You grow 3 inches the next year. How much more do you still need to grow to be able to ride the roller coaster?

______ inches

Answer:

Required Height to ride a aroller coaster = 54

My Height at the age of 8 yaers = 48 inches.

Next year my height = 48 + 3 = 51 inches.

Height required more for me to ride a roller coaster = 51 – 48 = 3 inches

Question 4.

**Number Sense**

A car tire is 61 centimeters tall. A truck tire is 84 centimeters tall. A monster truck tire is167 centimeters tall. Which sentences are true?

The car tire is 23 centimeters taller than the truck tire.

The truck tire is 83 centimeters shorter than the monster truck tire.

The monster truck tire is 106 centimeters taller than the car tire.

Answer:

Statements 2 and 3 are true .

Length of car tire = 61 centimeters

Length of truck tire = 84 centimeters

Length of monster truck = 167 centimeters

Explanation:

Statement 1:

Car tire and truck tire difference in lengths = 84 – 61 = 23 centimeters

Truck tire is 23 centimeters longer than car tire

Statement is false

Statement 2 :

Truck tire and monster tire lengths differences = 167 – 84 = 83 centimeters

The truck tire is 83 centimeters shorter than the monster truck tire.

Statement is true .

Statement 3 :

Monster truck and car tire lengths differences = 167 – 61 = 106 centimeters

The monster truck tire is 106 centimeters taller than the car tire.

Statement is true .

**12.4 Practice Measurement Problems**

Question 5.

A kangaroo jumps 24 feet. A frog jumps 19 feet less than the kangaroo. How far does the frog jump?

______ feet

Answer:

Height of kangaroo jump = 24 feet

Height of frog jump = 19 feet less than the kangaroo. = 24 – 19 = 5 feet

Question 6.

A store owner wants to add on to the parking lot to make it 38 meters long. It is currently 21 meters long. How many meters does the store owner want to add?

_____ meters

Answer:

Length of parking after adding parking = 38 meters

Current length = 21 meters

Increase in the length = 38 – 21 = 17 meters .

### Solve Length Problems Cumulative Practice

Question 1.

Which expressions have a sum less than 12?

Answer:

Expressions : 5 + 3 , 1 +0 and 4 +6

Explanation :

5 + 3 = 8

4 + 6 = 10

1 + 0 = 1

7 + 8 = 15

Question 2.

Find each difference.

Answer:

Question 3.

A blue sailboat is 44 feet long. A white sailboat is 36 feet long. A green sailboat is 22 feet long. Which sentences are true?

Answer:

Statement 2 and 3 are true .

Length of blue sail boat = 44 feet

Length of white sail boat = 36 feet

Length of green sail boat = 22 feet

Explanation:

Statement 1 :

Difference of blue and green sail boat = 44 – 22 = 22 feet

The blue sail boat is 22 feet longer than green boat .

Statement 1 is wrong .

Statement 2 :

Difference of white and green sail boat = 36 – 22 = 14 feet.

The green sail boat is 14 feet shorter than white sail boat .

Statement 2 is true .

Statement 3 :

Difference of blue and green sail boat = 44 – 22 = 22 feet

The green sail boat is 22 feet shorter than blue boat .

Statement 3 is true .

Statement 4 :

Difference of blue and white sail boat = 44 – 36 = 8 feet

The blue sail boat is 8 feet longer than white sail boat .

Statement 4 is wrong .

Question 4.

What is the value of the underlined digit?

739

Answer:

3 tens

Question 5.

Use mental math to solve.

403 – 10 = ______

898 – 100 = _____

640 – 10 = ______

204 – 10 = ______

843 – _____ = 833

_______ – 100 = 731

Answer:

403 – 10 = 393

898 – 100 = 798

640 – 10 = 630

204 – 10 = 194

843 – 10 = 833

831- 100 = 731

Question 6.

The cracker is about 2 inches long. What is the best estimate of the length of the cracker box?

Answer:

Length of cracker = 2 inches

The best estimate of the length of the cracker box = 3 inches

Question 7.

You take 14 pictures on Friday. You take 20 more on Saturday. Your friend takes 34 pictures in all on Friday and Saturday. How many pictures did you and your friend take in all?

Answer:

Number of pictures taken on Friday by me= 14 pictures

Number of pictures taken on Saturday by me= 20 more on Saturday = 20 pictures

Number of pictures taken by friend on Friday and Saturday = 34 pictures

Total Number of pictures taken by me and my friend = 14 + 20 + 34 = 68 pictures

Question 8.

Which expressions are equal to 245 + 386?

Answer:

245 + 386 = 631

Expression are 631 and 200 + 300 + 40 + 80+ 5 + 6

Explanation :

631

500 + 130 + 11 = 630 + 11 = 641

200 + 300 + 40 + 80+ 5 + 6 = 500+120+11 = 620 +11 = 631

500 + 120 + 5 = 625

Question 9.

Newton runs 7 yards, takes a break, and runs 3 more yards. Which number line shows how many yards Newton runs?

Answer:

Distance traveled by Newton =7 yards

Distance traveled by newton after break = 3 yards

Total Distance Traveled by Newton = 7 + 3 = 10 yards

Picture 4 represents correct .

Explanation :

in picture 4 the distance traveled by newton will be shown where the arrow ends at 10 .

Question 10

Find the sum.

Answer:

Question 11.

Find each difference.

80 – 53 = ?

79 – 13 = ?

90 – 32 = ?

64 – 40 = ?

Answer:

80 – 53 = 27

79 – 13 = 66

90 – 32 = 58

64 – 40 = 24

Question 12.

Complete the sentences using centimeters or meters.

A teacher’s desk is about 2 ________ long.

A paper clip is about 8 ________ long.

A carrot is about 12 _________ long.

A boat is about 20 _______ long.

Answer:

A teacher’s desk is about 2 meters long.

A paper clip is about 8 centimeters long.

A carrot is about 12 centimeters long.

A boat is about 20 meters long.