4th Grade - See If An Answer Is Reasonable

 
     
 
     
 
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4th
Problem Solving
See if an Answer is Reasonable
Evaluate the reasonableness of the solution in the context of the original situation.
Use information within the problem to help decide strategies necessary to determine the solution.
 

Sample Problems

(1)

Identify a.m. and p.m. for time.


Jason and Olivia were born on the same date. Jason was born at 3:15 am and Olivia was born at 1:34 pm. Who was born first? What is the difference in time? ________________


(Jason was born first; 8 hours 19 minutes)

(2)

Which equation relates to the words:

Leslie had 15 stickers. She gave 3 stickers each to two of her friends. How many tickers does she have left?


  1. 15 – (3 + 2) = 10

  2. 15 + (3 x 2) = 21

  3. 15 – (3 x 2) = 9


(c)

(3)

Write the rule and equation for the table.


Input

x

3

4

8

10

Output

y

11

14

26

32


________________________________


[Rule: Multiply by 3, add 2; Equation (3x + 2)= y]

(4)

Write the missing prime factor:


160 = 2 x 2 x 2 x 2 x 2 x __


(5)

(5)

Determine the division equation by the explanation of the base-ten blocks.


There are 12 groups with five 1-blocks in each. There are three 1-blocks remaining outside the groups. How would you write the division problem? _______


  1. 65 ÷ 5 = 12 r3

  2. 65 ÷ 3 = 12 r5


(a)

Learning Tips

(1)

AM and PM

Use a line graph to represent morning and night/AM PM

--׀----------------------------------------׀--------------------------------------׀---

12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

Midnight AM noon PM


From 12 midnight to 12 noon = AM

From 12 noon to 12 midnight = PM


Write scenarios on cards that would occur at certain times and have your child determine the reasonable time unit (a.m. or p.m. that the event would occur). For example, I eat dinner at 7:00 __. Your child would give the answer pm.

(2)

Practice word and expressions/equations:

Expression-a part of a number sentence that has numbers and operation signs, but does not have an equal sign (or amount)

Equation- a number sentence which states that two amounts are equal


Write a group of scenarios on an index card and matching expressions or equations to represent the scenario on another index card. Mix the cards and have the child match the expressions/equations with the scenarios


(3)

Pair up cards and have your child figure out the pattern and match the equation.

(4)

Find the missing prime factor tips


Prime number- a number that only has two factors (1 and itself; For example, 3 only has two factors 1 x 3. Therefore, 3 is a prime number).

Composite number- a number that has more than two factors.


Factor Tree- A diagram that helps find prime factors of a product.

Product

/ \

factor x factor

/ \

__x __


12

/ \

6 x 2

/ \

2 x 3


1” is neither prime nor composite


Review how to use factor trees:

Reminder: There can be various ways to begin the factor tree, as long as children get the same result of prime numbers at the end of the tree (highlighted numbers).


12

/ \

6 x 2

/ \

2 x 3


Write the product of prime numbers as: 2 x 2 x 3 = 12


(5)

Base ten blocks –Website you can use to get base ten block cut-outs for ones, tens, and hundreds) http://mason.gmu.edu/~mmankus/Handson/b10blocks.htm


This is the 1-block or unit block the smallest of all the blocks.

This is the 10-block corresponding to 10 units.  It is also referred to as a rod or long.

This is the 100-block and corresponds to 100 units. It is also called a flat.


Use base-ten blocks to model division.

  • Count out the amount of blocks for the dividend (total number)

  • Divide the total by counting the amount for the divisor

  • Count as many blocks as you can for the divisor in even groups

  • How many groups are there (your quotient)

  • If necessary, count how many are left that do not fit evenly into the groups (your remainder)


For example: 89 ÷ 20

Count out base ten blocks that equal to 89

Count out groups of 20

There should be 4 groups of 20 (10-blocks), with 9 1-blocks left over

Answer is 4 r9

Extra Help Problems

(1)

Identify a.m. and p.m. for time.


Tim went to work at 8:30 and was finished at 4:30 am. If he worked for 8 hours, did he begin work at 8:30 am or 8:30 pm? ____________


(pm)

(2)

Identify a.m. and p.m. for time.


The bus will be leaving for the fieldtrip at 20 minutes before 8:00. What time will the bus leave? ______


(7:40 a.m.)

(3)

Identify a.m. and p.m. for time.


Write the time for noon. _______


(12:00 pm)

(4)

Identify a.m. and p.m. for time.


Identify the time that the sun rises?

  1. 6:00 am

  2. 6:00 pm


(a)

(5)

Identify a.m. and p.m. for time.


At what time does a new day begin?


  1. 12:00 pm

  2. 12:00 am

  3. 6:00 am


(b)

(6)

Which expression relates to the words:

Andrea had $15.34. She went to the Farmer’s Market and spent $8.20 and gave her sister and brother $2.00 each. How much money did she have left?


(a) ($15.34 – $8.20) – (2 x $2.00)

(b) ($15.34 - $8.20) + (2 x $2.00)

  1. ($15.00 - $2.00) x 2


(a)

(7)

Which expression relates to the words:

Melanie is organizing her bookshelf. She has 13 rows and will place 8 books on each row, with 6 left over to place on display at the top.


  1. (13 + 8) – 6

  2. (13 x 6) – 8

  3. (13 x 8) + 6


(c)

(8)

Which equation relates to the words:

The baby had five packs of diapers with 40 diapers in each pack. Her mom also had 10 diapers in a diaper bag. How many diapers did they have in all?

  1. (5 + 40) + 10 = 55

  2. (5 x 40) – 10 = 190

  3. (5 x 40) + 10 = 210


(c)

(9)

Which expression relates to the words:

Kris read seven books this summer. Five books had 175 pages and, one book had 200 pages and one book had 125 pages. How many pages did Kris read?

  1. (175 ÷ 5) + (200 + 125)

  2. (175 x 5) + (200 + 125)

  3. (175 + 5) + (200 + 125)


(b)

(10)

Choose the words that relates to the expression:


14 – (2 x 6)


  1. Jordan baked fourteen cookies and gave 6 teammates 2 cookies each

  2. Jordan baked fourteen cookies and gave her teammates 8 cookies

  3. Jordan baked fourteen cookies and gave her teammates 6 cookies


(a)

(11)

Write the rule and equation for the table.


Input

x

4

5

6

7

Output

y

12

16

20

24


________________________________


[Rule: Multiply by 4, subtract 4; Equation (4x - 4)= y]

(12)

Write the rule and equation for the table.


Input

x

4

8

10

12

Output

y

7

9

10

11


________________________________


[Rule: Divide by 2, add 5; Expression (x ÷2) + 5= y]

(13)

Write the rule and equation for the table.


Input

Output

x

y

12

35

11

32

9

26

7

20


_______________________


[Rule: Multiply by 3, subtract 1; Expression (3x - 1)= y]

(14)

Write the rule and equation for the table.


Input

x

35

42

49

56

Output

y

5

6

7

8


________________________________


(Divide by 7; x ÷7)

(15)

Write the rule and equation for the table.


Input

x

1

2

3

4

Output

y

1

10

19

28


________________________________


[Rule: Multiply by 9, subtract 8; Expression (9x -8)= y]

(16)

Write the missing prime factors:


75 = __ x __ x 5


(3 x 3)

(17)

Write the missing prime factor:


84 = 2 x 2 x 3 x __


(7)

(18)

Write the missing prime factor:


16 = 2 x 2 x 2 x ___


(2)

(19)

Write the missing prime factor:


120 = 2 x 2 x 2 x 3 x __ x __


(4 x 5)

(20)

Write the missing prime factor:


115 = 5 x __


(23)

(21)

Determine the division equation by the base-ten blocks.


MAKE MODELS OF BASE-TEN BLOCKS AS DESCRIBED.

4 groups of (1) 10-block with (5) 1-blocks and 7 1-blocks remaining outside the groups.


How would you write the division problem? _______


(67 ÷ 15 = 4 r7)

(22)

Determine the division equation by the base-ten blocks.

MAKE MODELS OF BASE-TEN BLOCKS AS DESCRIBED.

4 groups of (2) 10-blocks with (1) 1-block and one 1-block remaining outside the groups.


How would you write the division problem? _______


(85 ÷ 21 = 4 r1)

(23)

Determine the division equation by the explanation of the base-ten blocks.


There are nine groups of 8 1-blocks. There are two 1-blocks remaining outside the groups. How would you write the division problem? _______


(74 ÷ 8 = 9 r2)

(24)

Determine the division equation by the explanation of the base-ten blocks.


There are 14 groups of one 10-block and four 1-blocks. How would you write the division problem? _______


(84 ÷ 6 = 14)

(25)

Determine the division equation by the explanation of the base-ten blocks.


There are 19 groups of one 10-block and nine 1-blocks. There are four 1-blocks remaining outside the groups. How would you write the division problem? _______


(78 ÷4 = 19 r4)

 

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