Eureka'Math'Mid'Module'Review'4.5' 1. .'' 1'''''...Eureka'Math'Mid'Module'Review'4.5'!...

Eureka'Math'Mid'Module'Review'4.5'

!

Common'Core'Standards:'4.NF.1,'4.NF.2,'4.NF.3,'4.NF.4'

!

Name''''' ' ' ' ' ' ''Date''' ' ' '''''''''''''''''''_____/24'

1. Let'each'small'square'represent'!!.''

'

a. Using'the'same'unit,'draw'and'shade'the'following'fractions.''

Represent'each'as'a'sum'of'unit'fractions.'

23!=" 1

3+" 1

3'''''''''''''''''''''''''''Example:''''''

'

• 1'''''

'

''''''''''''''''''''''''''''

• '!!'''''

'

'''''''''''''''''''''''''''''''''''''''''''''''

• '!!'

''

b. Record'the'decompositions'using'only'2'addends.''

'

• 1''''='

'''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''='

'

c. Rewrite'the'equations'from'Part'(a)'as'the'multiplication'of'a'whole'number'by'a'unit'fraction.'

'

• 1''''=''

'''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''='

''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''='

''


!


!

'

2.''a.' Using'the'fractional'units'shown,'identify'the'fraction'of'the'rectangle'that'is'shaded.''Continue'

this'pattern'by'drawing'the'next'area'model'in'the'sequence'and'identifying'the'fraction'shaded.'

'

'

'

'

'

'

'

'

'

'

b.' Use'multiplication'to'explain'why'the'first'two'fractions'are'equivalent.'

'

'

'

'

'

'

'

3.''Cross'out'the'fraction'that'is'not'equivalent'to'the'other'two.''Show'how'you'know.'

a.''25!!!!!!! 40

10!!!!!!! 4

10!!!' ' ' b.''

68!!!!!!!! 3

4!!!!!!! 12

14!!!' ' ' c.''

14!!!!!!! 4

40!!!!!!!! 3

12!!!'

' !'

'

'

'

1!

1!


!


!

4.' Fill'in'the'circle'with'<,'=,'or'>'to'make'a'true'number'sentence.''Show'how'you'know'with'a'model,'

finding'common'denominators'or'comparing'to'benchmark'fractions.'

'

a.''!!''''''''''''''''

!!''''' ' ' ' ' b.''

!!''''''''''''''

!!'

'

c.''!!''''''''''''''

!!"''''''' ' ' ' ' d.''

!!"''''''''''''''''

!!"'

'

e.!! !!'''''''''''''''!!' ' ' ' ' f.'''

!!''''''''''''''

!!'

'

g.!! !!''''''''''''''''!!' ' ' ' ' h.''

!!'''''''''''''''''

!!'

'

'


!


!

5. Fill'in'the'blanks'to'make'each'number'sentence'true.''Draw'a'number'line,'tape'diagram,'or'area'

model'to'represent'each'problem.'

a.''________'='410!+" 3

10' ' ' ' b.''

49100!–! 29

100!="________'

'

'

'

'

'

c.''48+!_______'='1'' ' ' ' ' d.''

25!+" 4

5!+" 1

5!='_______'

'

'

'

'

'

e.''1 − !! =!________'' ' ' ' f.''

!! −

!! =!________'

'

'

'

'

'

'

'


!


!

6.' Peter,'Mandy,'and'Susan'went'to'the'movies.'

a. They'spent'!!'of'their'money'on'tickets,''

!!'of'their'money'on'snacks,'and'the'rest'on'drinks.''

What'fraction'of'their'money'was'spent'on'drinks?!''Draw'a'model'and'write'an'equation'to'

solve.'

'

'

'

'

'

'

'

b. Susan'noticed'her'popcorn'bucket'was'!!'full'and'Peter’s'was'

!!'full.''Susan'noticed'that'her'

!!'

full'bucket'had'more'popcorn'than'Peter’s'!!'full'bucket.''Explain'how'Susan’s'

!!'bucket'could'

be'more'than'Peter’s'!!!bucket.''

'

'

'

'

'

c. Mandy,'and'Susan'each'had'identical'containers'of'popcorn.''Mandy'ate'!!'of'her'bucket.''

Susan'ate'!!'of'her'bucket.''How'many'total'buckets'of'popcorn'did'they'eat?'

'

'

'

'

'

'

'

'


!


!

d. Express'the'number'of'remaining'buckets'of'popcorn'as'a'product'of'a'whole'number'and'a'unit'

fraction.'

'

'

'

'

'

'

e. Three'out'of'the'five'candy'bars'they'ate'had'nuts.''Write'a'fraction'showing'how'many'

candy'bars'had'nuts'out'of'the'total'candy'bars'they'ate.'What'is'another'fraction'equal'to'3'

fifths?''Write'a'number'sentence'and'draw'a'model'to'show'the'two'fractions'are'equal.'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'

'


!


!

Answer'Key'

1. Let'each'small'square'represent'!!.'''(4pts=all'8'parts'correct,'3pts=6'or'7'parts'correct,'2pts='4'or'5'

parts'correct,'1pt'='less'than'4'parts'correct)(4.NF.3,'4NF.4)'

'

a. Using'the'same'unit,'draw'and'shade'the'following'fractions.''

Represent'each'as'a'sum'of'unit'fractions.'

23!=" 1

3+" 1

3'''''''''''''''''''''''''''Example:''''''

'

• 1''''''''''''''''''''''''''''''''''''''''''1!=" 13+" 1

3'+" 1

3''''''''''''''''''''''''''''''''

'

''''''''''''''''''''''''''''

• '!!''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

!! !="

13+" 1

3'+" 1

3'+" 1

3''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'

'''''''''''''''''''''''''''''''''''''''''''''''

• '!!'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

!! !="

13+" 1

3'+" 1

3'+" 1

3''+" 1

3'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

''

b. Record'the'decompositions'using'only'2'addends.''

'

• 1''''='13''+" 2

3'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''='

33''+" 1

3'''''''''''or'''''''''

23''+" 2

3'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'

c. Rewrite'the'equations'from'Part'(a)'as'the'multiplication'of'a'whole'number'by'a'unit'fraction.'

'

• 1''''='''3''x! 13'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''=''4''x!

13'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''''''''

• '!!''''=''5''x!

13'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''


!


!

''

2.''a.' Using'the'fractional'units'shown,'identify'the'fraction'of'the'rectangle'that'is'shaded.''Continue'

this'pattern'by'drawing'the'next'area'model'in'the'sequence'and'identifying'the'fraction'shaded.'

(4pts=correctly'answers'a'and'b,'3pts=correctly'answers'a'but'not'b,'2pts='correctly'identifies'

fractions'in'a'but'unable'to'create'equivalent'fraction'or'answer'part'b,'1pt'='unable'to'complete'

problem)(4.NF.3,'4NF.4)'

'

'

'

'

'

'

'

'''

'

'

b.' Use'multiplication'to'explain'why'the'first'two'fractions'are'equivalent.'

'

'

3.''Cross'out'the'fraction'that'is'not'equivalent'to'the'other'two.''Show'how'you'know.(4pts=eliminates'

the'incorrect'fraction'and'gives'explanation'for'all'3,'3pts=correctly'identifies'2'of'the'3'incorrect'

fractions'and'gives'reasoning,'2pts='correctly'identifies'1'of'the'3'incorrect'fractions'and'gives'

reasoning,'1pt=attempts'but'incorrect)(4.NF.1)'

a.''25!!!!!!! 40

10!!!!!!! 4

10!!!' ' ' b.''

68!!!!!!!! 3

4!!!!!!! 12

14!!!' ' ' c.''

14!!!!!!! 4

40!!!!!!!! 3

12!!!'

' !'25!!x" 2

2= 4

10!!!''''''''''''''''''''''''''''''''''''''''''''''''''''''''3

4!!x" 2

2= 6

18!!!''''''''''''''''''''''''''''''''''''''''''''''''1

4!!x" 3

3= 3

12!!!'

25!!x" 20

20= 40

100'''''''''''''''''''''''''''''''''''''''''''''''''''''''''68!!x" 2

2= 12

16!!!'''''''''''''''''''''''''''''''''''''''''''''''1

4!!x" 4

4= 4

16!!!'''''''''''''''''''''''''''''''''''''''''''''''''''

25!!does%not%equal 40

10'''''''''''''''''''''''''''''''''''''''

68!!does%not%equal 12

14'''''''''''''''''''''!!!!!!!!!!!!!!1

4!!does%not%equal 4

40'''''''''''''''''''''''''''''''

1!

1!

13!

26!

39!

!!!x!

!!!=!

!!!


!


!

4.' Fill'in'the'circle'with'<,'=,'or'>'to'make'a'true'number'sentence.''Show'how'you'know'with'a'model,'

finding'common'denominators'or'comparing'to'benchmark'fractions.'(4pts='answers'all'8'correct'

with'explanation'or'model,'3pts=correctly'answers'6'or'7'out'of'the'8'with'explanation,'

2pts=correctly'answers'4'or'5'out'of'the'8'with'some'reasoning,'1pt='correctly'answers'3'or'fewer'

with'little'or'no'reasoning.)(4.NF.2)'

'

a.''!!''''''''''''''''

!!''''' ' ' ' ' b.''

!!''''''''''''''

!!'

4'sixths'is'greater'than'2'sixths''''''''''''''''''''''''''''''''''''''''''''''''

c.''!!''''''''''''''

!!"''''''' ' ' ' ' d.''

!!"''''''''''''''''

!!"'

'

e.!! !!'''''''''''''''!!' ' ' ' ' f.'''

!!''''''''''''''

!!'

'

g.!! !!''''''''''''''''!!' ' ' ' ' h.''

!!'''''''''''''''''

!!'

'

=!

=!<!

>!

=! <!

<! <!

Ninths'are'smaller'than'sevenths'so'

5/9'is'smaller'than'5/7!

35!!x"

22= ! 6

10! 5

10!!is#=#to! 1

2"!!"#! 4

12!!is#less#than! 1

2"!!

Thirds'are'bigger'than'fifths'so'7/3'is'

greater'than'7/5!

66!!is#=#to!1!!"#! 2

2!!is#=#to#1#so#they#are#equal!!

36!!="

12!!"#! 4

8= 1

2!

76!!="1 1

6!!"#! 6

5= 1 1

5!

15!!"!!!"#$ℎ!"!!ℎ!"! 1

6!


!


!

5. Fill'in'the'blanks'to'make'each'number'sentence'true.''Draw'a'number'line,'tape'diagram,'or'

area'model'to'represent'each'problem.(4pts='correctly'answers'5'parts'with'reasoning,'3pts='

correctly'answers'4'parts'with'some'reasoning,'2pts='correctly'answers'3'parts'with'some'

reasoning,'1pt=correctly'answers'fewer'than'3'parts'with'little'or'no'reasoning)(4.NF.1,'4.NF.2,'

4.NF.3,'4.NF.4)'

a.''710!'=' 4

10!+" 3

10' ' ' ' b.''

49100!–! 29

100!=" 20

100'

'

'

'

'

'

c.''48+! 4

8!'='1'' ' ' ' ' d.''

25!+" 4

5!+" 1

5!='7

5'

''''1'

'

'

'

'

e.''1 − !! = !

15!'' ' ' ' ' f.''

!! −

!! = !

16'

''''''''''''''1'

'

'

'

'

20100!!!!! 25

100!!!!! 30

100!!!!! 35

100!!!! 40

100!!!!! 45

100!!!!! 50

100!

!

!


!


!

6.' Peter,'Mandy,'and'Susan'went'to'the'movies.(4pts=correctly'answers'5'parts'with'reasoning,'3pts='

correctly'answers'4'of'5'parts'with'some'reasoning'in'a,b'and'c.'2pts='correctly'answers'3'of'5'parts'

with'some'reasoning'in'a,b'and'c.'1pt='correctly'answers'fewer'than'3'parts'with'little'or'no'

reasoining.(4.NF.1,'4.NF.2,'4.NF.3,'4.NF.4)'

a. They'spent'!!'of'their'money'on'tickets,''

!!'of'their'money'on'snacks,'and'the'rest'on'drinks.''

What'fraction'of'their'money'was'spent'on'drinks?!''Draw'a'model'and'write'an'equation'to'

solve.''''''''''''''''''''''''''''1'

'

'

'

'

!! +

!! +

14!= ! 4

4''''''''''''''''They'spent'

14'''of'their'money'on'drinks.'

'

'

b. Susan'noticed'her'popcorn'bucket'was'!!'full'and'Peter’s'was'

!!'full.''Susan'noticed'that'her'

!!'

full'bucket'had'more'popcorn'than'Peter’s'!!'full'bucket.''Explain'how'Susan’s'

!!'bucket'could'

be'more'than'Peter’s'!!!bucket.''

' If'Susan’s'bucket'was'larger'than'Peter’s'than'her'12''bucket'could'be'more'than'Peter’s'

12''bucket.'

'

c. Mandy,'and'Susan'each'had'identical'containers'of'popcorn.''Mandy'ate'!!'of'her'bucket.''

Susan'ate'!!'of'her'bucket.''How'many'total'buckets'of'popcorn'did'they'eat?'

'

'

'''''''''''''''''!! +

!! != !

66''''''''''''''''

!! = 1''bucket'of'popcorn''''

'

'

'

'

'


!


!

'

d. Express'the'number'of'remaining'buckets'of'popcorn'as'a'product'of'a'whole'number'and'a'unit'

fraction.'

'

'''''''''''''''''!! != 6!!! 1

6'''''''''''''''''

'

'

'

e. Three'out'of'the'five'candy'bars'they'ate'had'nuts.''Write'a'fraction'showing'how'many'candy'

bars'had'nuts'out'of'the'total'candy'bars'they'ate.'What'is'another'fraction'equal'to'3'fifths?''

Write'a'number'sentence'and'draw'a'model'to'show'the'two'fractions'are'equal.'

'

!! !!!!

22! = !

!!"!'''''''''''''''''''

!! != !

!!"!''''''''''''''''''''''''''

'

!!!'''''''''

!!"!''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

Eureka'Math'Mid'Module'Review'4.5' 1. .'' 1'''''...Eureka'Math'Mid'Module'Review'4.5'!...

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Transcript of Eureka'Math'Mid'Module'Review'4.5' 1. .'' 1'''''...Eureka'Math'Mid'Module'Review'4.5'!...