Unit 3: Numbers & Operations - Fractions Chapter 8 - Fractions Chapter 9 - Operations with Fractions Chapter 10 - Fractions & Decimals NJ 2016 Student Learning Standards: Mathematics Grade 4 4.OA.4 Find all factor pairs for a whole number in the range of 1 -100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 -100 is a multiple of a given one -digit number. Numbers and Operation s - Fractions A. Extend understanding of fraction equivalence and ordering. 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comp arisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same wh ole. 4.NF.3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between a ddition
4.OA.4 Find all factor pairs for a whole number in the range of 1 -100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 -100 is a multiple of a given one -digit number. Numbers and Operation s - Fractions A. Extend understanding of fraction equivalence and ordering. 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comp arisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 4.NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same wh ole. 4.NF.3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between a ddition
and subtraction. 4 .NF.3d . So lve wo r d p r o b le m s in vo lvin g a d d it io n a n d s u b t ra c t io n o f fr a c t io n s r e fe r r in g to t h e s a m e wh o le a n d h a vin g like d e n o m in a to r s , e .g ., b y u s in g vis u a l fr a c t io n m o d e ls a n d e q u a t io n s t o r e p r e s e n t t h e p r o b le m . 4.NF.4. Apply a nd extend previous understandings of multiplication to multiply a fraction by a whole number. 4.NF.4. .a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the con clusion by the equation 5/4 = 5 × (1/4). 4.NF.4.b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recogni zing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) 4.NF.4.c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each perso n at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? C. Understand decimal notation for fractions, and compare decimal fractions. 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100 .4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e .g., by using a visual model.
Mathematical Practice
MP. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. MP1 - Make sense of problems and persevere in solving them. MP 2 - Reason abstractly and quantitatively. MP 3 - Construct viable arguments and critique the reasoning of others.
MP 4 - Mo d e l with Ma th e m a t ic s . MP 5 - Us e a p p ro p r ia t e t o o ls s t r a t e g ic a lly. MP 6 - At t e n d t o Pre c is io n . MP 7 - Lo o k fo r a n d m a ke u s e o f s t ru c tu re . MP 8 - Lo o k fo r a n d e xp re s s r e g u la r it y in re p e a t e d r e a s o n in g .
21st Century Student Outcomes: K -12
● Be self -directed learners. ● In c o rp o ra t e fe e d b a c k e ffe c t ive ly ● De a l p o s it ive ly with p r a is e , s e tb a c ks a n d c r it ic is m ● Be Self -directed Learners ● Go b e yo n d b a s ic m a s t e ry o f s kills a n d / o r c u r r ic u lu m to e xp lo re a n d
e xp a n d o n e ’s o wn le a rn in g a n d o p p o r tu n it ie s t o g a in e xp e r t is e ● De m o n s t r a t e c o m m itm e n t t o le a rn in g a s a life lo n g p ro c e s s ● Re fle c t c r it ic a lly o n p a s t e xp e r ie n c e s in o rd e r t o in fo rm fu tu re p ro g re s s ● Work Effectively in Diverse Teams ● Re s p o n d o p e n -m in d e d ly t o d iffe r e n t id e a s a n d va lu e s ● Ch a p te r 8 - Wo rk Cre a t ive ly with O th e rs - Sh a d e 5 0 o u t o f 100 s q u a re s o f
h u n d re d th s g r id a n d 5 o u t o f 10 s e c t io n s o f a t e n th s m o d e l. Th e re d o e s n o t n e e d t o b e a s e t wa y o f d o in g t h is . Be c r e a t ive in wh ic h s q u a re s yo u c o lo r . No w t a ke a n o th e r g r a d e p a p e r a n d c r e a t e o th e r e q u iva le n t fr a c t io n s . Pu t t h e m to g e th e r t o m a ke a b o o k o f e q u iva le n t fr a c t io n s
● Ch a p te r 9 - Cr it ic a l Th in kin g - Th e p ro c e s s o f m u lt ip lyin g a fr a c t io n b y a wh o le n u m b e r m a y n o t s e e m to b e lo g ic a l t o s o m e s tu d e n t s . En c o u ra g e t h e m to t h in k a b o u t th e “ru le ” b y r e a lly e m p h a s iz in g t h e p h ys ic a l m o d e lin g o f t h e p ro d u c t a s r e p e a t e d a d d it io n o f t h e fr a c t io n . In t h is wa y, t h e y c a n s e e t h a t t h e d e n o m in a to r d o e s n o t c h a n g e , s o wh e n m u lt ip lyin g t h e y o n ly n e e d t o m u lt ip ly t h e n u m e ra to r b y t h e wh o le n u m b e r .
● Ch a p te r 10 - Cr it ic a l Th in kin g - Divid e t h e c la s s in to g ro u p s o f 3 o r 4 . Th e fir s t s t u d e n t in e a c h g ro u p s h o u ld wr it e a s e n t e n c e t h a t r e p re s e n t s t h e fir s t s e n t e n c e s o f a re a l-wo r ld p ro b le m . Th a t s t u d e n t g ive s t h e ir p a p e r t o t h e s e c o n d s tu d e n t wh o wr it e s a s e c o n d s e n t e n c e , p ro vid in g m o re in fo rm a t io n a b o u t t h a t r e a l-wo r ld p ro b le m . Co n t in u e t h is p a t te rn u n t il t h e p a p e r is h a n d e d t o t h e la s t s t u d e n t . Th e la s t s t u d e n t wr it e s a q u e s t io n a b o u t t h e r e a l-wo r ld in fo rm a t io n t h a t is g ive n . Th e g ro u p t h e n n e e d s t o d e c id e if t h e r e is e xt r a o r m is s in g in fo rm a t io n n e e d e d t o s o lve t h e p ro b le m . If t h e p ro b le m c a n b e s o lve d , h a ve t h e g ro u p s o lve it . If n o t , h a ve t h e m e xp la in wh a t in fo rm a t io n is m is s in g .
En d u r in g Es s e n t ia l Q u e s t io n
Understandings ● H o w to fin d fa c to r p a ir s o f wh o le
n u m b e r s ○ a whole number is a
multiple of each of its factors
How to model equivalent fractions
○ fractions that represent the same part of a number are equivalent
○ the parts of equivalent fractions may be different, but the two fractions themselves are the same s ize
● How to find a fraction that is equivalent to another fraction
○ multiplication and division can be used to find equivalent fractions
○ to create an equivalent fraction, multiply or divide the numerator or denominator of a fraction by the same number
Ho w to compare fractions by using a benchmark fraction
○ two fractions with different numerators and different denominators can be compared using a benchmark fraction
○ a benchmark fraction is a common fraction like 1/2
Chapter 9
● How to use fraction tiles to model the sum of fractions
○ Fractions that have the same denominators are called like fractions
○ Unit fractions can be
Chapter 8 How can different fractions name the same amount? Chapter 9 How can I use operations to model real -world fractions? Chapter 10 How are fractions and decimals related ?
used to model the a d d it io n o f like fr a c t io n s
● H o w to a d d a n d s u b t r a c t like fr a c t io n s
○ Ad d in g fr a c t io n is like jo in in g p a r t s a n d s u b t r a c t in g fr a c t io n s is like s e p a ra t in g p a r t s o f t h e s a m e wh o le
○ To a d d o r s u b t r a c t like fr a c t io n s , a d d o r s u b t r a c t t h e n u m e ra to r s a n d ke e p t h e s a m e d e n o m in a to r
● H o w to a d d a n d s u b t r a c t m ixe d n u m b e r s
○ Re p la c e m ixe d n u m b e r s with e q u iva le n t im p ro p e r fr a c t io n s
○ Ch e c k s u b t r a c t io n o f m ixe d n u m b e r s b y u s in g a d d it io n
● Us e a n e q u a t io n t o wr it e a fr a c t io n a s a m u lt ip le o f a u n it fr a c t io n
○ Us e m o d e ls ○ Us e r e p e a t e d a d d it io n
● H o w to m u lt ip ly a fr a c t io n b y a wh o le n u m b e r
○ Us e r e p e a t e d a d d it io n ○ Us e e q u a t io n s a n d
p ro p e r t ie s
Ch a p t e r 10
● H o w to u s e p la c e va lu e t o wr it e d e c im a ls
○ A d ig it in t h e o n e p la c e r e p re s e n t s 10 t im e s wh a t it r e p re s e n t s in t h e p la c e t o it s r ig h t
● H o w to u s e m o d e ls to r e p re s e n t d e c im a ls
○ A b a s e -t e n m o d e l c a n b e u s e d t o s h o w t e n th s
○ A p la c e -va lu e c h a r t c a n b e u s e d t o s h o w t e n th s a n d h u n d re d th s
● H o w to c o m p a re d e c im a ls ○ Us e p la c e va lu e ○ Us e a n u m b e r lin e
● H o w to u s e d e c im a l n o t a t io n t o r e p re s e n t fr a c t io n s
○ De c im a ls a n d fr a c t io n s c a n s h o w e q u iva le n t a m o u n t s
○ Us e m o d e ls o r n u m b e r lin e s
● H o w to a d d two fr a c t io n s with d e n o m in a to r s o f 10 a n d 100
○ Writ e t h e t e n th s fr a c t io n a s a n e q u iva le n t fr a c t io n with a d e n o m in a to r o f 100
Co n te n t Kn o wle d g e
O ve rvie w
● Use place value understanding and properties of operations to perform multi -digit arithmetic
● Use the four operations with whole numbers to solve problems
● Solve problems involving measurement and conversion of measurements
● Extend understanding of fraction equivalence and ordering.
● Build fractions from unit fractions ● Build fractions from unit fractions ● Represent and interpret data ● Understand decimal notation for
fractions and compare decimal fractions.
● Solve problems involv ing measurement and conversion of measurements
● Use place value understanding and properties of operations to add and subtract
Chapter 8
● I can find factors and multiples of whole numbers
● I can determine if a number is prime or composite
● I can explore equivalent fractions ● I can find equivalent fractions ● I can write a fraction in simplest
form ● I can compare and order fractions ● I can use benchmark fractions to
compare and order numbers
Skills Chapter 8
● Write two fractions that are equivalent to a fraction like 3/8
● Compare two fractions like 2/5 and 5/8 using a benchmark fraction
Chapter 9
● Use models to show sums of like fractions
● Solve subtraction problems of like fractions
● Solve subtraction problems with mixed numbers
● Use an equation to write a fraction like ⅞ as a multiple of a unit fraction
● Find products of a whole number and a fract ion
Chapter 10
● Use place -value charts to write decimals like thirty -seven hundredths
● Use models to represent decimals like five tenths
● Use a number line to compare decimals
● Write a fraction and a decimal
● I c a n u s e lo g ic a l r e a s o n in g to s o lve p ro b le m s
● I c a n r e p re s e n t m ixe d n u m b e r s b y d e c o m p o s in g t h e m in t o a s u m o f wh o le n u m b e r s a n d u n it fr a c t io n s
● I c a n wr it e m ixe d n u m b e r s im p ro p e r fr a c t io n s
Ch a p te r 9
● I c a n u s e m o d e ls t o a d d like fr a c t io n s
● I c a n a d d like fr a c t io n s ● I c a n u s e m o d e ls t o s u b t r a c t like
fr a c t io n s ● I c a n s u b t r a c t like fr a c t io n s ● I c a n wo rk b a c kwa rd to s o lve
p ro b le m s ● I c a n a d d m ixe d n u m b e r s ● I c a n s u b t r a c t m ixe d n u m b e r s ● I c a n u s e m o d e ls t o m u lt ip ly
fr a c t io n s ● I c a n m u lt ip ly fr a c t io n s b y wh o le
n u m b e r s Ch a p te r 10
● I c a n e xp lo r e u s in g p la c e -va lu e c h a r t s a n d g r id s t o m o d e l d e c im a ls
● I c a n m o d e l a n d d e s c r ib e t e n t h s a s p a r t o f a b a s e -t e n s ys t e m
● I c a n m o d e l a n d d e s c r ib e h u n d r e d th s a s p a r t o f a b a s e -t e n s ys t e m
● I c a n e xp lo r e u s in g g r id s a n d n u m b e r lin e s t o fin d t h e r e la t io n s h ip s b e t we e n d e c im a ls
● I c a n id e n t ify, r e a d a n d wr it e t e n th s a n d h u n d re d s a s d e c im a ls a n d fr a c t io n s
● I c a n u s e p la c e va lu e a n d e q u iva le n t fr a c t io n s t o a d d t wo fr a c t io n s with d e n o m in a to r s o f 10 a n d 100
● I c a n c o m p a re a n d o rd e r d e c im a ls to h u n d re d t h s b y r e a s o n in g a b o u t t h e ir s ize
● I c a n fin d e xt r a in fo rm a t io n wh e n s o lvin g p r o b le m s
fo r m o d e ls ● Ad d fr a c t io n s with
d e n o m in a to r s o f 100 a n d 10
Un it Re s o u r c e s
Chapter 8 ● Ch a p te r O p e n e r ● Am I Re a d y?/ Pre -As s e s s m e n t ● Vo c a b u la ry Ca rd s / Fo ld a b le ● 8-1 Fa c to rs a n d Mu lt ip le s ● 8-2 Pr im e a n d Co m p o s it e
Nu m b e r s ● 8-3 H a n d s O n : Mo d e l Eq u iva le n t
Fra c t io n s ● 8-4 Eq u iva le n t Fra c t io n s ● 8-5 Sim p le s t Fo rm ● 8-6 Co m p a re a n d O rd e r
Fra c t io n s ● Ch a p te r 8 Pro je c t : H e a lt h y
Re c ip e s ● 8-7 Us e Be n c h m a rk Fra c t io n s t o
Co m p a re a n d O rd e r ● 8-8 Pro b le m So lvin g
In ve s t ig a t io n : Us e Lo g ic a l Re a s o n in g
● 8-9 Mixe d Nu m b e r s ● 8-10 Mixe d Nu m b e r s a n d
Im p ro p e r Fra c t io n s ● Po s t -As s e s s m e n t ● Pe r fo rm a n c e Ta s k
Ch a p t e r 9
● Ch a p te r O p e n e r ● Am I Re a d y?/ Pre -As s e s s m e n t ● Vo c a b u la ry Ca rd s / Fo ld a b le ● 9-1 H a n d s O n : Us e Mo d e ls t o
Ad d Like Fra c t io n s ● 9-2 Ad d Like Fra c t io n s ● 9-3 H a n d s O n : Us e Mo d e ls t o
Su b t r a c t Like Fra c t io n s ● 9-4 Su b t r a c t Like Fra c t io n s ● 9-5 Pro b le m -So lvin g
In ve s t ig a t io n : Wo rk Ba c kwa rd ● 9-6 Ad d Mixe d Nu m b e r s ● 9-7 Su b t r a c t Mixe d Nu m b e r s ● Ch a p te r 9 Pro je c t - Gro win g Up ● 9-8 H a n d s O n : Mo d e l Fra c t io n s
a n d Mu lt ip lic a t io n ● 9-9 Mu lt ip ly Fra c t io n s b y Wh o le
Nu m b e r s ● Po s t -As s e s s m e n t ● Pe r fo rm a n c e Ta s k
Ch a p t e r 10
● Ch a p te r O p e n e r ● Am I Re a d y?/ Pre -As s e s s m e n t
Vo c a b u la ry Ch a p t e r 8
● fa c to r p a ir s ● p r im e n u m b e r ● c o m p o s it e n u m b e r ● n u m e ra to r ● d e n o m in a to r ● e q u iva le n t fr a c t io n s ● s im p le s t fo rm ● g re a t e s t c o m m o n fa c to r ● le a s t c o m m o n m u lt ip le ● b e n c h m a rk fr a c t io n s ● m ixe d n u m b e r
Ch a p t e r 9
● like fr a c t io n s Ch a p t e r 10
● d e c im a l ● t e n th ● h u n d re d th
● 10-1 H a n d s O n : Pla c e Va lu e Th ro u g h Te n th s a n d H u n d re d th s
● 10-2 Te n th s ● 10-3 H u n d re d th s ● 10-4 H a n d s O n : Mo d e l De c im a ls
a n d Fra c t io n s ● 10-5 De c im a ls a n d Fra c t io n s ● 10-6 Us e Pla c e Va lu e a n d Mo d e ls
t o Ad d ● 10-7 Co m p a re a n d O rd e r
De c im a ls ● Ch a p te r 10 Pro je c t - Ba ke Sa le
Eq u iva le n t s ● 10-8 Pro b le m So lvin g
In ve s t ig a t io n : Ext r a o r Mis s in g In fo rm a t io n
● Po s t -As s e s s m e n t ● Pe r fo rm a n c e Ta s k
Assessments :
● Formative: ○ Exit Slip ○ One -Sentence Summary ○ Quick Draw ○ One -Minute Essay ○ Error Analysis ○ Check My Progress ○ Application Cards ○ Summarize ○ Chapter Review ○ Vocabulary Check ○ Concept Check ○ Problem Solving ○ Test Practice ○ Reflect ○ Example/Non -example ○ Think -Pair -Share ○ Sequence ○ Definitions ○ Number Sort ○ Analogy Prompt ○ Turn to Your Partner ○ Questioning
Summative Assessment ● Pe r fo rm a n c e Ta s k ● Dia g n o s t ic As s e s s m e n t ● Ch a p te r Pre -Te s t
Diffe r e n t ia t e t h e Te s t ● Us e
a lt e rn a t ive le ve le d c h a p te r a s s e s s m e n ts (a p p ro a c h ing le ve l, o n le ve l a n d b e yo n d le ve l) t o d iffe r e n t ia t e a s s e s s m e n t fo r s p e c ific n e e d s o f s tu d e n t s
● Pro vid e o p t io n o f p r in t vs . o n lin e a s s e s s m e n t
● Re d u c e th e n u m b e r o f p ro b le m s g ive n
● Pro vid e m u lt ip lic a t ion c h a r t s / c a lcu la to r s
● Pro vid e h in t s wr it t e n o n t e s t s , s u c h a s m n e m o n ic d e vic e s
● Give e xt r a t im e
● Pro vid e a c h e c klis t o f t h e s t e p s n e e d e d to c o m p le te th e p ro b le m
● Pro vid e p la c e va lu e c h a r t s a n d r e s o u r c e s
● Pro vid e lo t s o f wh it e -s p a c e to m a ke it le s s b u s y
● If s t ill s t r u g g lin g , r e t e a c h & r e t e s t
Differentiation in the Math Classroom
1. Provide multiplication tables (or calculators) to students who struggle with fluency. This allows you to see if they’ve mastered the skill at hand (i.e., adding/subtracting fractions) without the barrier of fact fluency
issues. Click here for a copy of a multiplication chart . 2. Represent numbers in place value charts whenever possible. Give
students their own la minated copies of place value charts so they can organize their thoughts while completing their work.
3. Assign fewer complex problems and have students illustrate or explain the reasoning they use.
4. Emphasize the role of diagramming in interpreting and solvin g problems in mathematics.
5. Provide students with graph paper to help them organize their math in an effort to reduce errors being made due to handwriting.
6. Use tasks that provide multiple entry points and provide scaffolds that support student participation.
7. Have a vocabulary wall. 8. Provide reduced amount of homework for struggling learners. Give them
2 relevant math problems rather than an entire worksheet. 9. Conference with the students often to learn about how they think about
math. 10. Make flashcards for terms and examples, then mix and match. 11. Conference with the students often to learn about how they think about
math. 12. Model decimals using money 13. Use number line for representing decimals
Approaching Level
Chapter 8 ● Us e Am I Re a d y? Wo rks h e e t s t o r e vie w c o n c e p t s s t u d e n t s m is s e d o n
a s s e s s m e n t ● 8-1 Te ll s t u d e n ts t o fin d t h e fa c to r p a ir s o f 12 b y a r r a n g in g 12 u n it c u b e s
o n t h e g r id p a p e r in a s m a n y d iffe r e n t a r ra ys t h a t a r e p o s s ib le . Te ll s t u d e n t s t h a t t h e n u m b e r o f r o ws a n d n u m b e r o f c o lu m n s m a ke t h e fa c to r p a ir . Ad d re s s th e Co m m u ta t ive Pro p e r ty a n d t o n o t r e p e a t a n y p a ir s . Re p e a t t h e a c t ivit y with o th e r n u m b e r s .
● 8-2 Pro vid e s t u d e n ts with c o u n t e rs a n d h a ve t h e m a r r a n g e t h e c o u n t e r s in to two d iffe r e n t a r r a ys u s in g d iffe r e n t fa c to r p a ir s . Po in t o u t th a t if t h e y can make only one array with the count ers (1 × n), the number is prime.
● Check My Progress - Students can use approaching level or on level activities from Lesson 1 to review concepts; use manipulatives
● 8-4 Tell students to color each row a different color, and then show them how to “read” the fraction tiles. To help them track down the rows, show them how to line up a ruler to find equivalent fractions. Write a fraction on the board that can be represented with the tiles and have them find all the equivalent fractions.
● 8-5 Write an unsimplified fraction on the board that can be represented with fraction tiles. Ask students to write, then model the fraction. To simplify the fraction, have students find the one smaller tile that in quantity will match the length of the given fraction. Have them wr ite the
simplified form of the fraction with a symbol of equivalency. You may wa n t t o g ive s o m e fr a c t io n s t h a t a r e s im p lifie d , a ls o .
● 8-6 O n g r id p a p e r , h a ve s t u d e n t s o u t lin e two 2 × 5 r e c t a n g le s . Te ll t h e m to s h a d e in 4 s q u a re s in t h e fir s t r e c t a n g le a n d 6 in t h e s e c o n d o n e . Gu id e s t u d e n t s in la b e lin g e a c h r e c t a n g le with a fr a c t io n t h a t re p re s e n t s t h e a m o u n t o f t h e r e c t a n g le t h a t is s h a d e d . H a ve s t u d e n ts lo o k a t t h e a m o u n t o f e a c h r e c ta n g le t h a t is s h a d e d t o h e lp t h e m c o m p a re t h e fr a c t io n s . Re p e a t t h e p r e vio u s two s t e p s with d iffe r e n t fr a c t io n s .
● 8-7 Gu id e s t u d e n t s t o m a ke t h r e e n u m b e r lin e s . La b e l a s s h o wn o n p . 5 23
o f t h e s t u d e n t b o o k. H a ve s t u d e n t s wr it e e a c h fr a c t io n , , , a n d o n h a lf o f 3 in d e x c a rd s . H e lp t h e m d e c id e wh ic h fr a c t io n s a r e g r e a t e r t h a n
a n d wh ic h a r e le s s th a n b y p la c in g t h e m o n t h e n u m b e r lin e s . Co n t in u e t o g u id e t h e m a s t h e y o rd e r . Re p e a t with m o re fr a c t io n s .
● 8-8 Wo rk with s t u d e n t s o n Exe rc is e 2 fro m Ap p ly t h e St r a t e g y p a g e . Sh o w th e m h o w to m a ke a t a b le t o o rg a n ize t h e g ive n in fo rm a t io n . S in c e a ll t h e fr a c t io n s h a ve d iffe r e n t d e n o m in a to r s , r e vie w m a kin g e q u iva le n t fr a c t io n s a n d o rd e r in g t h e m . Fra c t io n t ile s o r c ir c le s will le n d s u p p o r t . Sh o w h o w to u s e t h e p ro c e s s o f e lim in a t io n t o s o lve .
● 8-9 Wr it e a m ixe d n u m b e r o n t h e b o a rd . Gu id e s t u d e n ts in m o d e lin g t h e m ixe d n u m b e r u s in g fr a c t io n t ile s o r c ir c le s . Th e n a s k s t u d e n t s t o wr it e a n e q u a t io n t o r e p re s e n t t h e m ixe d n u m b e r
● 8-10 H a ve s t u d e n t s p r a c t ic e m o d e lin g wh o le n u m b e r fr a c t io n s , , , a n d s o o n . Aft e r t h e y h a ve m o d e le d e a c h wh o le n u m b e r , a s k t h e m to a d d 1 o r m o re a d d it io n a l e q u a l p a r t s a n d t e ll yo u t h e im p ro p e r fr a c t io n it r e p re s e n t s .
Chapter 9
● Use Am I Rea dy? Worksheets to review concepts students missed on assessment
● 9-2 Hands -On Activity Materials: clear one -cup measuring container with
fractional increments, , , , and measuring cups, uncooked rice, large bowl for each group. In small groups, with a set of measuring cups and a bowl of uncooked rice, read a like -fraction addition problem with a
sum less than or equal to one, such as + .Have students model measuring the fractional amounts and pouring them into the one -cup
container. Students can re a d t h e s u m fro m th e m e a s u re m e n t m a rks o n t h e s id e o f t h e c u p .
● 9-4 Wr it e t h e m in u e n d fro m a fr a c t io n s u b t r a c t io n p ro b le m o n t h e b o a rd . H a ve s t u d e n t s c o lo r t h e t ile s o n t h e ir p a p e r , a n d wr it e t h e m in u e n d in t h e m a rg in . Wr it e t h e s u b t r a h e n d o n t h e b o a rd . S tu d e n ts n o w c ro s s o u t t h a t m a n y t ile s , a n d r e c o rd t h e s u b t r a h e n d , s u b t r a c t io n s ig n , a n d th e d iffe r e n c e in t h e m a rg in . Re p e a t with m o re p ro b le m s .
● Check My Progress - IF students miss 5 or more, THEN choose a resource: Students can use the Approaching Level or On Level RtI activities from Lessons 1 –4 to review the concepts. For reviewing concepts by using manipulatives, turn to the Build Conceptual Understanding section of Lessons 1 –4 or use the Virtu al Manipulatives online.
● 9-5 Work with the students on Exercise 2. Guide them by modeling the problem and talking through your thought process. Allow them to work with a partner mimicking your process while solving Exercise 3.
● 9-6 Use Independent Exercise s 3–11 (odd). Have students model each mixed number addend with fraction circles. Have them combine the fraction pieces first, then the whole circles to add. When necessary, have them trade fraction pieces for whole circles to rename improper fractions. Th en have them count wholes and fraction pieces to find the sum.
● 9-7 Have students draw a fraction bar across the center of a sheet of paper. Place 10 fruit snacks on each student’s paper above the fraction bar. Remind students that the total number of sna cks is the denominator. Have students write 10 under the fraction bar. What fraction is
represented with the snacks? Direct students to eat two pieces of
fruit snacks. What fraction was subtracted? What fraction of the
snack is left? Write the equation . - = . Subtract snacks
until the total is . ● 9-9 Work with the students using Exercises 7 –10. Guide them by modeling
the problems, while talking through your thought process. Allow them to work with a partner mimicking your process for solving the problems.
Chapter 10
● Use Am I Ready? Worksheets to r eview concepts students missed on assessment
● 10-2 Why can we use dimes to model tenths? A dime is one tenth of one dollar. Write one decimal from 0.1 –0.9 on the board. Have students model
the decimal using dimes as they count aloud, one tenth, two tenths, and s o o n . Th e n h a ve t h e m s h a d e t h e g r id a p p ro p r ia t e ly a n d wr it e t h e d e c im a l in t h e p la c e -va lu e c h a r t . Co n t in u e with m o re d e c im a ls .
● 10-3 Wr it e 25¢ o n t h e b o a rd . As k s t u d e n ts to u s e t h e p e n n ie s a n d d im e s t o represent 25¢, using the most possible dimes. How many dimes did you use? 2 How many tenths is 2 dimes? 0.2 Record the 2 in the tenths place of Work Mat 6. How many pennies did you use? 5 How many hundredths is 5 pennies? 0.05 Record the 5 in the hundredths place. The 2 dimes represent tenths, and the 5 pennies represent the hundredths. Repeat with other amounts.
● Check My Progress ● 10-5 Use play money to represent 0.6, 0.2 1, and 0.08 with dimes and
pennies. Then represent each decimal as a fraction. If the number has just dimes, what word is used to name the decimal? Tenths. If the number has dimes and pennies or just pennies that are not multiples of 10, what word is used? hundredths
● 10-6 Give one tenths grid and one hundredths grid to each student. Tell students to find the sum of four tenths and thirty -seven hundredths.
Guide students to shade the correct portion of each grid, write the fraction below each grid, and th en write an addition sentence. Help students solve the addition sentence. Repeat, but this time after the grid is shaded, trade grids with a partner to complete. Watch for students who need more guidance.
● 10-7 Have Student 1 spin two times as Student 2 rec ords each number on the place -value chart. The first spin should be recorded in the tenths place and the second in the hundredths place. Repeat to make four decimals in all. Have students order their four place -value charts from greatest to least and leas t to greatest . Repeat with four more numbers with students trading roles as spinner and writer.
● 10-8 Have the students look at Exercise 7. Have them choral read it together. Using the four -step plan, ask them what they know and what they need to find, unde rlining the information needed to solve the problem and crossing out the extra information. Work together to plan a strategy and solve.
On -Level
Chapter 8 ● Have students correct the items they missed and explain what their
original error was ● Have students complete the chapter pretest to determine what skills in
the chapter they already know ● 8-1 - A s tu d e n t r o lls th e n u m b e r t u b e s a n d m a ke s a two -d ig it n u m b e r . If a
10 is r o lle d , m a ke a t h r e e -d ig it n u m b e r . Writ e t h e n u m b e r a t t h e t o p o f a n in d e x c a rd a n d o n e fa c to r p a ir b e lo w. Pa s s t h e c a rd t o t h e n e xt s t u d e n t wh o wr it e s a n o th e r fa c to r p a ir / . Co n t in u e p a s s in g t h e c a rd u n t il a ll fa c to r p a ir s h a ve b e e n wr it t e n . Se t t h e c a rd a s id e a n d r e p e a t with a n o th e r n u m b e r .
● 8-2 H a ve s t u d e n ts wo rk with c o n n e c t in g c u b e s t o e xp lo re wh y s o m e n u m b e r s a r e p r im e a n d s o m e a r e c o m p o s it e .
● 8-4 In g ro u p s o f fo u r , s t u d e n t s will p la y m e m o ry. Pla c e a ll o f t h e c a rd s fa c e d o wn o n a t a b le . Pla ye r s will t a ke t u rn s flip p in g o ve r two c a rd s a t a t im e t o fin d a p a ir o f e q u iva le n t fr a c t io n s . If a p la ye r fin d s a p a ir , h e o r s h e ke e p s t h e c a rd s a n d c o n t in u e s u n t il h e o r s h e d o e s n o t t u rn o ve r a n e q u iva le n t p a ir . Pla y p a s s e s t o t h e n e xt s tu d e n t .
● Ch e c k My Pro g re s s - H a ve s t u d e n t s c o r r e c t t h e it e m s t h e y m is s e d a n d e xp la in wh a t t h e ir o r ig in a l e r ro r wa s
● 8-5 H a ve s t u d e n t s ro ll a 0-5 n u m b e r s u re o n e t im e t o g e n e ra t e a n u m e ra to r . If a ze ro is r o lle d , h a ve s t u d e n t s ro ll t h e n u m b e r c u b e a g a in . Ne xt , h a ve s t u d e n ts p ic k a d e n o m in a to r o f 6, 8 , 10 o r 12. Te ll s tu d e n t s t o wr it e t h e ir fr a c t io n o n a p ie c e o f p a p e r . Th e n h a ve t h e m wr it e t h e fr a c t io n in s im p le s t fo rm . If it is a lr e a d y in s im p le s t fo rm , t h e y s h o u ld wr it e s im p le s t fo rm . Re p e a t a s t im e a llo ws
● 8-6 In p a ir s , h a ve s t u d e n t s m a ke 20 fr a c t io n c a rd s u s in g d e n o m in a to r s o f 2, 3, 4 , 5 , 6, 8 , 10, 12, a n d 100. O n e s t u d e n t will d e a l o u t t h e c a rd s e ve n ly, fa c e d o wn . Stu d e n t s ke e p t h e ir c a rd s in a p ile fa c e d o wn . Ea c h s t u d e n t will flip o ve r t h e ir t o p c a rd . Th e y c o m p a re t h e fr a c t io n s a n d d e c id e wh o s e fr a c t io n is t h e g r e a t e s t . Th e s t u d e n t with th e g r e a t e s t fr a c t io n win s t h e c a rd s . If t h e fr a c t io n s a r e e q u iva le n t , t h e y flip a n o th e r c a rd . Th e s t u d e n t with t h e m o s t c a rd s a t t h e e n d win s .
● 8-7 Te ll s t u d e n t s t o c h o o s e five fr a c t io n s fro m to d a y’s le s s o n . Th e n t h e y will d r a w a n u m b e r lin e fo r e a c h fr a c t io n , wr it e e a c h fr a c t io n o n t h e n u m b e r lin e , t h e n o rd e r t h e fr a c t io n s greatest to least.
● 8-8 Ask students to write short riddles about fraction s. Begin with, “I am thinking of a fraction that is greater than (insert fraction) and less than (insert fraction).” Students may add other clues to narrow the choices so there is only one correct answer. They will exchange with a partner to solve. Have th em make necessary corrections to the riddle, if needed.
● 8-9 In pairs, Student 1 rolls the 0 –5 number cube and records the whole number. Then Student 1 rolls both number cubes, makes a fraction with the larger number for the denominator, and puts the who le number and fraction together to make a mixed number. Student 2 uses fraction circles to model it. Reverse roles and repeat.
● 8-10 Students will shuffle and place cards facedown. The idea is to create the greatest improper fraction. Each student draws two cards and makes an improper fraction. The student with the largest improper fraction gets
a point. Then each student models their improper fraction as a mixed n u m b e r . A p o in t is g ive n fo r e a c h c o r r e c t m o d e l.
Chapter 9
● H a ve s tu d e n t s c o r r e c t t h e it e m s t h e y m is s e d a n d e xp la in wh a t t h e ir o r ig in a l e r ro r wa s
● H a ve s tu d e n t s c o m p le t e t h e c h a p t e r p r e t e s t t o d e t e rm in e wh a t s kills in t h e c h a p t e r t h e y a lr e a d y kn o w
● 9-2 Give e a c h p a ir o f s t u d e n t s a p a p e r lu n c h b a g with 12 c o u n te r s in it . Ea c h s t u d e n t d r a ws a r a n d o m n u m b e r o f c o u n t e r s fro m th e b a g . H a ve e a c h s t u d e n t c o u n t th e n u m b e r o f c o u n t e r s t h e y d re w fro m th e b a g a n d wr it e t h a t n u m b e r a s a fr a c t io n with a d e n o m in a to r o f 12. H a ve s t u d e n t s r e p e a t t h e p r e vio u s two s t e p s . S tu d e n ts s h o u ld t h e n wr it e t h e ir fr a c t io n s in a n a d d it io n s e n t e n c e t o r e p re s e n t t h e to t a l fr a c t io n o f c o u n te r s d r a wn fro m th e b a g .
● 9-4 Give e a c h p a ir o f s t u d e n t s 10 r e d a n d 10 p u rp le c o u n t e rs . Stu d e n t s a r r a n g e g ro u p s o f r e d c o u n t e r s o ve r p u rp le c o u n t e r s t o s h o w a fr a c t io n e q u iva le n t t o o n e . H a ve s t u d e n t s t a ke t u rn s r e m o vin g a s e c r e t n u m b e r o f r e d c o u n t e r s fro m th e m o d e l. Th e o th e r s tu d e n t m u s t n a m e th e fr a c t io n o f c o u n t e r s r e m o ve d a n d wr it e a n u m b e r s e n t e n c e t o s h o w th e s u b t r a c t io n . Th e r e d c o u n t e r s a r e r e tu rn e d t o t h e g ro u p , a n d s t u d e n t s s witc h ro le s .
● Ch e c k My Pro g re s s - IF s tu d e n t s m is s 3 o r 4 , THEN c h o o s e a re s o u rc e : H a ve s t u d e n t s c o r r e c t t h e it e m s t h e y m is s e d a n d e xp la in wh a t t h e ir o r ig in a l e r ro r wa s . Us e t h e En r ic h wo rks h e e t fro m a p r e vio u s c h a p t e r . Us e a Ma th a t H o m e : Ga m e Tim e wo rks h e e t fro m a p r e vio u s c h a p t e r .
● 9-5 In p a ir s , S tu d e n t 1 ro lls t h e two n u m b e r c u b e s t o m a ke a fr a c t io n with t h e la rg e r n u m b e r a s t h e d e n o m in a to r . Th is fr a c t io n will b e t h e d iffe r e n c e t o a s u b t r a c t io n p ro b le m . Us in g t h e m o d e ls , b o th s t u d e n t s will q u ic kly wo rk b a c kwa rd s t o s e e wh o will b e t h e fir s t t o m o d e l a n y m in u e n d a n d s u b t r a h e n d wh ic h r e s u lt s in t h e ro lle d d iffe r e n c e . Ne xt ro u n d , s t u d e n t s s h o u ld r e ve r s e ro le s .
● 9-6 Th e g o a l o f t h e a c t ivit y is t o m a tc h t h e fir s t h a lf o f a n a d d it io n e q u a t io n t o it s s u m . Gro u p s tu d e n ts a n d h a ve e a c h s t u d e n t wr it e o n e a d d it io n e q u a t io n u s in g m ixe d n u m b e rs . Wr it e t h e fir s t h a lf o f t h e e q u a t io n o n o n e c a rd a n d it s s u m o n a s e c o n d c a rd . S tu d e n t s s e p a ra t e t h e ir c a rd s in to two p ile s . Sh u ffle e a c h p ile . Pla c e e a c h p ile fa c e d o wn in s e p a ra t e a r r a ys . S tu d e n t s t u rn o ve r o n e c a rd fro m th e e q u a t io n g ro u p a n d o n e fro m th e s u m g ro u p in a n a t t e m p t t o m a tc h . If it is a m a tc h t h e y ke e p t h e c a rd s , if n o t , t h e c a rd s a r e t u rn e d fa c e d o wn a n d p la y c o n t in u e s with t h e n e xt s t u d e n t . Co n t in u e u n t il a ll m a t c h e s h a ve b e e n m a d e .
● 9-7 In p a ir s , S tu d e n t 1 c h o o s e s a wh o le n u m b e r c a rd fro m a fa c e d o wn , s h u ffle d p ile . S tu d e n t 2 ro lls e a c h n u m b e r c u b e t o m a ke a fr a c t io n . To g e th e r t h e y h a ve a m ixe d n u m b e r . Ea c h s t u d e n t will t h e n u s e fr a c t io n
models to find two mixed numbers that when subtracted would equal the m ixe d n u m b e r t h e y m a d e .
● 9-9 In p a ir s , S tu d e n t 1 c h o o s e s a wh o le n u m b e r c a rd fro m a fa c e d o wn , s h u ffle d p ile . S tu d e n t 2 ro lls e a c h n u m b e r c u b e t o m a ke a fr a c t io n . Ea c h s t u d e n t will t h e n m o d e l m u lt ip lyin g t h e fra c t io n b y t h e wh o le n u m b e r u s in g a n y fr a c t io n m o d e l.
Chapter 10
● Have students correct the items they missed and explain what their original error was
● Have students complete the chapter pretest to determine what skills in the chapter they already know
● 10-2 Students will make a memory game by cutting apart the small grids so there are 10 tenths grids. Students make a decimal card for each of the decimals from 0.1 to 0.9 and color a tenths grid for each decimal. Once all the cards and grids have been cut apart and made, shuffle each pile and lay the cards in two separate arrays, facedown. Student 1 turns over one card from each array and looks to see if it matches, if it does the student keeps the match, if it does not match Student 1 is done and it is Stu dent 2's turn.
● 10-3 Give each student a hundredths model. Have students write 0.__ __ below their hundredths model. Then tell them to roll a 0 –5 number cube and write the digit rolled in the tenths place. Next, have them roll a 5 –10 number cube and write the digit rolled in the hundredths place. If a 10 is rolled, roll again. Tell students to shade the hundredths model to represent the number they created. Repeat as time allows.
● Check My Progress ● 10-5 Have students label one index card for each: Fourths, Fifths, and
Tenths. Students will write the fractions , , and down the left side of the Fourths card. Next to each fraction, students will write the
equivalent decimal. Repeat with the Fifths index card and the fractions
, , , . Continue with the Tenths card and the fractions through
. ● 10-6 One tenths grid and one hundredths grid is given to each student.
Have students shade in any portion of each grid, and then trade grids with a partner. Tell students to write and solve an addition problem based on the shaded portions of their partner's grid. Solutions should be
written as both a fraction and a decimal. Have partners check each o th e r ’s wo rk.
● 10-7 Ea c h s t u d e n t m a ke s t h r e e d e c im a l c a rd s , s o m e t e n th s a n d s o m e h u n d re d th s . S tu d e n t s p a ir u p , s h u ffle t h e ir c a rd s t o g e th e r , a n d d e a l o u t t h r e e c a rd s fa c e d o wn to e a c h . O n a s ig n a l, s t u d e n ts r a c e t o s e e wh o c a n p la c e t h e ir c a rd s in o rd e r least to greatest first. Repeat the game ordering the decimals greatest to least .
● 10-8 Have studen ts create two problems: one with too much information and one with not enough. Have them exchange problems with a partner, who then decides which has missing and which has extra information. Then the partner solves it.
English Language Learner Instruction al Strategies All WIDA Can Do Descriptors can be found at this link: https://www.wida.us/standards/CAN_DOs/ Grades 4 -5 WIDA Can Do Descriptors:
● Listening ● Speaking ● Reading ● Writing ● Oral Language ● Sentence Frames ● Read -Aloud/Modeled Talk ● Pictures/Photographs ● Pairs or Partners ● Communication Guide ● Turn and Talk ● Anchor Chart ● Utilize Resources ● Turn and Talk ● Activate Prior Knowledge ● Partners Work/Pairs Check ● Tiered Questions ● Mnemonic Device ● Report Back ● Numbered Heads Together ● Cognates
● Mo d ify a c t ivit ie s / a s s ig n m e n t s / p ro je c t s / a s s e s s m e n t s ● Pro vid e a n o p t io n fo r a lt e rn a t ive
a c t ivit ie s / a s s ig n m e n ts / p ro je c t s / a s s e s s m e n t s ● Mo d ify Co n te n t ● Ad ju s t Pa c in g o f Co n te n t ● Sm a ll Gro u p En r ic h m e n t ● In d ivid u a l En r ic h m e n t ● H ig h e r -Le ve l Te xt
Chapter 8 ● H a ve s tu d e n t s c o m p le t e t h e c h a p t e r p r e t e s t t o d e t e rm in e wh a t s kills in
t h e c h a p t e r t h e y a lr e a d y kn o w ● Us e a Ma th a t H o m e : Ga m e Tim e wo rks h e e t fro m p re vio u s c h a p t e r ● 8-1 Dra w a lin e d o wn th e c e n t e r o f a fe w c a rd s . La b e l le ft s id e m u lt ip le
a n d t h e r ig h t s id e fa c to r p a ir s . A s tu d e n t r o lls t h e n u m b e r c u b e , wr it e s t h e n u m b e r a t t h e t o p o f t h e in d e x c a rd a n d o n e m u lt ip le o f t h e n u m b e r . Pla y p a s s e s t o t h e n e xt s t u d e n t wh o wr it e s t h e fa c to r p a ir s fo r th e m u lt ip le g ive n a n d a n e w m u lt ip le o f t h e ro lls n u m b e r . Pla y c o n t in u e s u n t il a ll h a ve a t u rn o r t h e r e a r e n o m u lt ip le s a n d fa c to r p a ir s r e m a in in g . Ro ll a n e w n u m b e r a n d r e p e a t .
● Ch e c k My Pro g re s s - Us e a g a m e o r a c t ivity fro m th e My Le a rn in g St a t io n ; Us e a m a th a t h o m e g a m e t im e wo rks h e e t fro m p re vio u s c h a p te r .
● 8-2 Fo ld a p ie c e o f p a p e r n h a lf lo n g wa ys . La b e l t h e c o lu m n o n t h e le ft s id e Pr im e a n d t h e c o lu m n o n t h e r ig h t s id e c o m p o s it e . In p a ir s , s t u d e n t s will t a ke t u rn s ru lin g t h e n u m b e r c u b e s t o m a ke a two -d ig it n u m b e r , wr it in g it in t h e c o r r e c t c o lu m n . Se e wh o c a n r e a c h 10 p r im e n u m b e r s fir s t .
● 8-4 To g e th e r s t u d e n ts will m a ke 15 p a ir s o f e q u iva le n t fr a c t io n s . Th e n , in g ro u p s o f fo u r . s t u d e n t s will p la y m e m o ry. Pla c e a ll c a rd s fa c e d o wn o n t h e t a b le . Pla ye r s will t a ke t u rn s flip p in g o ve r two c a rd s a t a t im e t o fin d a p a ir o f e q u iva le n t fr a c t io n s . If a p la ye r fin d s a p a ir , h e o r s h e ke e p s t h e c a rd s a n d c o n t in u e s u n t il h e o r s h e d o e s n o t t u rn o ve r a n e q u iva le n t fr a c t io n p a ir . Pla y p a s s e s t o t h e n e xt s t u d e n t .
● 8-5 Te ll s t u d e n ts t h a t t h e r e a r e 365 d a ys , o r 5 2 we e ks , in a ye a r . H a ve t h e m c a lc u la t e t h e n u m b e r o f we e kd a ys a n d we e ke n d d a ys in o n e ye a r . Th e n h a ve s t u d e n t s ro u n d t h e fig u re s t o th e n e a re s t t e n a n d d e t e rm in e a p p ro xim a te ly wh a t fr a c t io n o f a ye a r is m a d e u p o f we e kd a ys a n d wh a t fr a c t io n is m a d e u p o f we e ke n d d a ys . H a ve s t u d e n t s wr it e fr a c t io n
● 8-6 In g ro u p s o f 3 o r 4 , s t u d e n t s m a ke 20 fr a c t io n c a rd s u s in g d e n o m in a to r s o f 2, 3, 4 , 5 , 6, 8 , 10, 12, a n d 100. O n e s t u d e n t will d e a l o u t t h e c a rd s e ve n ly, fa c e d o wn . Stu d e n t s ke e p t h e ir c a rd s in a p ile fa c e d o wn . Ea c h s t u d e n t will flip o ve r t h e ir t o p c a rd . Stu d e n t s will wo rk t o g e th e r t o o rd e r t h e fr a c t io n s least to greatest . Whoever had the greatest fraction
wins all the cards. The student with the most cards wins. ● 8-7 Ea c h s tu d e n t will t a ke a r e c ip e a n d o rd e r t h e fr a c t io n s least to
greatest . Then students will find an equivalent fraction for each of the six fractions. Students will plot the equivalent fractions on a number line.
● 8-8 Have students create their own logical reasoning word problems. They must use fractions f or the quantities and require comparing and ordering of the fractions to solve. They will exchange problems and solve. If time permits, present them to the whole group.
● Check My Progress - Use a game or activity from the My Learning Station; Use a math a t home game time worksheet from previous chapter.
● 8-9 Have students create questions about the value of a quantity of pattern blocks in which the answer will result in a mixed number, i.e. If a hexagon has a value of 1 whole, what is the value of 3 trapez oids? ½ since each trapezoid is half of a hexagon.
● 8-10 Students will each write five mixed numbers and five improper fractions. They combine all the cards, shuffle, and place facedown. In pairs, each student draws a card keeping it facedown. They both count, “1, 2, 3, Go!” and turn over their card. The first s tudent to convert their mixed number or improper fraction correctly, earns a point.
Chapter 9 ● Have students complete the chapter pretest to determine what skills in
the chapter they already know ● Use a Math at Home: Game Time worksheet from previous chapt er ● 9-2 Have students use colored pencils to color the squares of a 10 × 10
grid to create a picture. Students trade pictures with another student and then find the fraction of the picture represented by each color, including the squares that are not color ed. Students should write an addition sentence to find the sum of all the fractions. The sum of the numerators should equal 100 because each piece of the whole is being counted.
● 9-4 On separate cards, each student writes several subtraction problems and their solutions using like fractions. Use only sixths, eighths, tenths, and twelfths as the denominators. Be sure there are at least 24 problems. Collect the cards, and list each solution on the board. Write “free” in any one square and the 24 solutions in the other squares of the grid. Read a problem aloud. Students place only 1 counter on the solution. Follow bingo rules to win.
● Check My Progress - IF students miss 2 or less, THE N choose a resource: Use a game or activity from the My Learning Station. Use a Math at Home: Game Time worksheet from a previous chapter.
● 9-5 Give t h e s t u d e n t s t h e fo llo win g p ro b le m s : a - 50 = b ; b ÷ 10 = c ; c + 5 = 12 a = 120; b = 70; c = 7 In p a ir s , h a ve s t u d e n t s fin d a, b, a n d c u s in g t h e wo rk b a c kwa rd s t r a t e g y a n d in ve r s e o p e ra t io n s . Th e n h a ve t h e m c re a t e a s im ila r p ro b le m , o n a n in d e x c a rd , t h a t r e q u ir e s t h e wo rk b a c kwa rd
strategy to solve. They should trade with a partner to solve. ● 9-6 Th e g o a l o f t h e a c t ivit y is t o m a tc h two m ixe d n u m b e r a d d e n d s t o
t h e ir s u m . Gro u p s tu d e n t s a n d h a ve e a c h s t u d e n t wr it e o n e a d d it io n e q u a t io n u s in g m ixe d n u m b e r s . Writ e e a c h a d d e n d o n s e p a ra te c a rd s a n d t h e s u m o n a t h ird c a rd . Stu d e n t s s e p a ra t e t h e ir c a rd s in to a n a d d e n d p ile a n d a s u m p ile . Sh u ffle e a c h p ile . Pla c e e a c h p ile fa c e d o wn in 2 a r r a ys . Stu d e n t s t u rn o ve r two c a rd s fro m th e a d d e n d g ro u p a n d o n e fro m th e s u m g ro u p in a n a t t e m p t t o m a tc h . If it is a m a tc h t h e y ke e p t h e c a rd s , if n o t , t h e c a rd s a r e t u rn e d fa c e d o wn a n d p la y c o n t in u e s with t h e n e xt s t u d e n t .
● 9-7 In p a ir s , S tu d e n t 1 c h o o s e s a wh o le n u m b e r c a rd fro m a fa c e d o wn , s h u ffle d p ile , a n d t h e n ro lls e a c h n u m b e r c u b e t o m a ke a fr a c t io n . S tu d e n t 2 wr it e s a m ixe d n u m b e r with a like d e n o m in a to r t h a t is le s s t h a n t h e o n e m a d e b y Stu d e n t 1. Th e n e a c h s t u d e n t will wo rk q u ic kly t o s u b t r a c t t h e two m ixe d n u m b e r s t o s e e wh o g e t s t h e c o r r e c t a n s we r fir s t . Ne xt ro u n d , s t u d e n ts s wit c h ro le s .
● 9-9 Stu d e n t 1 s e c r e t ly wr it e s a m u lt ip lic a t io n p ro b le m th a t m u lt ip lie s a fr a c t io n b y a wh o le n u m b e r . Th e n Stu d e n t 1 m o d e ls t h e p ro c e s s t o t h e s o lu t io n , a s we ll a s t h e s o lu t io n . S tu d e n t 2 m u s t fig u re o u t wh a t p ro b le m Stu d e n t 1 wro t e s e c r e t ly b y wa tc h in g t h e m o d e lin g . Ne xt ro u n d , s t u d e n t s s witc h ro le s .
Chapter 10
● Have stud ents complete the chapter pretest to determine what skills in the chapter they already know
● Use a Math at Home: Game Time worksheet from previous chapter ● 10-2 Students cut apart all Work Mats. They count off 1 through 5. Student
1 writes any decimal from 0.1 to 0.9 on a card, and then passes the card. Student 2 models the decimal on a place -value chart, Student 3 models the decimal on a tenths grid, Student 4 models the decimal on a hundredths grid, and Student 5 models the decimal on a number line. Stude nts will check for accuracy and then rotate roles.
● 10-3 Have students use index cards to make two sets of number cards with the digits 0 –9 on them, one digit per card. Tell students to shuffle the cards and place them facedown in a pile. Have students dr aw two cards and place them face -up. Challenge students to write the least and greatest decimals using these digits. Students should check answers with a hundredths grid or a number line.
● Check My Progress ● 10-5 Student pairs will each make a grocery list of five items that are less
than $1. Next to the item the student will write the price as a fraction of a dollar. Students will exchange grocery lists. Next to the fraction, the partners will write the price as a decimal and the change they would
receive from $1. i.e. can of beans. Stu d e n t 1: ; S tu d e n t 2: $0.69; $0.31 ● 10-6 H a ve s t u d e n t s wo rk in p a ir s . O n e p a r tn e r wr it e s a fr a c t io n with 10 a s
a d e n o m in a to r , a n d th e o th e r p a r tn e r wr ite s a fr a c t io n with 100 a s t h e d e n o m in a to r . H a ve p a r tn e r s r e ve a l t h e ir fr a c t io n s t o o n e a n o th e r a t t h e s a m e t im e , t h e n r a c e t o fin d t h e s u m o f t h e two fr a c t io n s . Te ll s t u d e n t s t o wr it e t h e s u m a s b o th a fr a c t io n with a d e n o m in a to r o f 100 a n d a s a d e c im a l. Th e fir s t s t u d e n t t o c o m p le t e t h e a d d it io n p ro b le m win s . S tu d e n t s r e ve r s e ro le s in t h e n e xt r o u n d .
● 10-7 Ea c h s t u d e n t m a ke s fo u r d e c im a l c a rd s , s o m e t e n th s a n d s o m e h u n d re d th s . S tu d e n t s p a ir u p , s h u ffle t h e ir c a rd s t o g e th e r , a n d p la c e t h e m fa c e d o wn .
● Pla c e t h e fir s t c a rd fa c e u p o n t h e t a b le . S tu d e n t 1 p ic ks a c a rd a n d p la c e s it e it h e r b e fo re o r a ft e r t h e fir s t c a rd t o o rd e r t h e two least to greatest . Student 2 repeats, adding it to the two. Students should continue taking turns until all eight cards are ordered.
● 10-8 Student 1 write s the first sentence of a real -world word problem. Student 2 writes a second sentence, providing more information. Continue this pattern until the paper is handed to the last student who writes a question about the information that is given. The group deci des if there is extra or missing information. If the problem cannot be solved,have them decide what is missing.
Resources for Differentiation
XtraMath This program helps students practice their math facts for addition, subtraction, multiplication, and addition. Can individualize the fluency skills for each student. Can run reports to determine progress.
Scholastic Study Jams Fun videos which explain common mathematics concepts. Questions at the end of the video reinforce the concepts.
Number Rock Songs that explain mathematical concepts using visuals, r epetition and examples throughout.
Games and activities that target content and skills to match 4th grade standards reinforcing concepts based on topics. These games can be played as a whole -group, small -group, pairs or individually.
Open Educational Resources 4.NBT.B To regroup or not to regroup 4.NBT.B.6 mental Division Strategy 4.OA.A.3, 4.MD.A.3 Karl's Garden 4.NF.A.1 Explaining Fraction Equivalence with Pictures 4.NF.A.1 Fractions and Rectangles 4.NF.A.2 Comparing Fractions Using Benchmarks Game 4.NF.A.2 Doubling Numerators and Denominators 4.NF.B.3a Comparing Sums of Unit Fractions 4.NF.B.3b making 22 Seventeenths in Different Ways 4.NF.B.3c Cynthia's Perfect Punch
4.NF.B.3c Peaches 4.MD.B.4 Button Diameters 4.NF.B.4 Extending Multiplication From Whole Numbers to Fractions 4.NF.B.4c Sugar in six cans of soda 4.NF.C.5 Adding Tenths and Hundredths 4.NF.C.6 Dimes and Pennies 4.NF.C.6 Expanded Fractions and Decimals 4.NF.C.7 Using Place Value 4.MD.A.2 Margie Buys Apples
Interactive Notebook Math Grade 4 Interactive Notebook for organizing information and applying learning. Students can personalize their learning to fit their needs. Perfect for addressing the needs of individual learners
