Fraction Skill-Building

After our Introduction to Fractions in March, we will work during April and May on skill-building. Children will continue to add concepts to their MLBs.

The Introduction to Fractions needs to be done very slowly and carefully to ensure there aren't enduring misunderstandings that show up later on!

I wanted to share the rest of my fractions planning for the year now since it is ready. If I make any changes to this as we go along, I will update it.

You will see that even though we went very slowly at the start, they will end up doing standard fifth grade fraction problems by the end of the ten weeks!

Themes Covered in Week 1

Mon - K/W/L Chart

Tue - 1/2, 1/4, 1/8

Wed - Making Thirds & Halving Thirds

Thu - Fractions of a Group, Equivalent Fractions (Houses on a Street)

Themes Covered in Week 2

Mon - Fractions of a Number

Tue - Puddle Question

Wed - Reading a Ruler, Fractions in Lowest Terms

Thu - Build-an-Animal

Themes Covered in Week 3

Mon - Restaurant Simulation

Tue - Coins as Fractions & Decimals

Wed - Basic Operations with Fractions

Thu - Converting Improper Fractions to Mixed Numbers

Themes Covered in Week 4

Mon - Converting Mixed Numbers to Improper Fractions

Tue - Elapsed Time

Wed - Making Arrays

Thu - Using Arrays to Simplify Fractions

week of April 6

Mon - Comparing Fractions

recall Thursday's work with arrays

look back at Fraction of a Group and find the equivalent fractions (2/4, 4/6) visually but also "prove it mathematically" on the board

look back at Colorful Fraction Circles and see if you can find the equivalent fractions (4/8, 2/4, 5/10, 2/10)

have children come up to the board to demonstrate the steps in how to convert each of these fractions to their simplest form

what happens if you reduce 4/8 by dividing both numbers by 2? nothing, you'll just have to simplify it again by repeating the process

so if there are multiple things you can divide the top and bottom number by, you should choose the largest one because that'll save you the most time

notice that a unit fraction (with a 1 on top) is always in simplest form because its only factors are 1, and 1 isn't allowed in factor trees (YCCOM)

have children work independently on Comparing Fractions worksheet
https://www.superteacherworksheets.com/fractions/comparing-fractions-tape-diagrams_QWERT.pdf

for the two equivalent fractions on that worksheet, we then used the chalkboard to "prove it mathematically"

notice that for 6/8 = 3/4, we divide the top and bottom by 2

but for 4/5 = 8/10, we multiply the top and bottom by 2

we can make them larger by multiplying the top and bottom by the same number, and there are times in math when we want to do that!

it's like Alice in Wonderland; you can make her bigger and smaller by nibbling and sipping, but she's still Alice while her size is changing

why does it work? remember that the top number is how many and the bottom number is what kind. if you have a plan to eat 5 pieces of cake, but your mom cuts them in half to make twice as many (so now there are 10 and they are smaller) but you just adapt by eating twice as many, you have still had the same amount of cake!

Arnold Schwarzenegger and the 2 ply toilet tissue fiasco!

he switched to 1 ply at the government offices in California to save money during the budget crisis, and everyone promptly switched to using twice as much toilet tissue

"if you're going to give half as much, I'm going to take twice as much"




Carlyn Beccia book - which 6 of these 9 cures for Wounds worked? that's 2/3!

Tue - Add to MLB

add the steps in making equivalent fractions to the MLB

add new observations and new questions about fractions

Wed - Alice in Wonderland

practice making equivalent fractions by either multiplying the top and bottom number by the same thing or dividing them

go bigger and smaller just like Alice in Wonderland

assignment: write three fractions that are equivalent to one another

Thu - Fact Families

as I watched children working on yesterday's assignment, I realized that the class needed a review of Fact Families

I had each child just choose a few multiplication facts that they were having trouble with and write out the fact families for them

week of Apr 13

Mon - +/- Fractions with Common Denominators

have students practice addition and subtraction of fractions with common denominators by creating problems for classmates to solve (an answer key must be provided)

a fun spin on this is "Secret Code," where the children come up with a fraction to represent each letter of the alphabet and then write a series of math problems for a friend to solve

the answers to the problems spell out a secret message!

note: a very good way to see if children understand a skill is to have them create their own problems; if children understand that the denominator of a fraction is its name and does not represent an amount, they will resist the temptation to add or subtract them

Tue - Rounding Fractions

practice Rounding Fractions to 0, 1/2, or 1

observe, can children visualize the fractions in order to round them?
or do some kids still need to see them, draw them, or build them?

Wed - Simplifying Fractions Mandala

solve and color the Simplifying Fractions Mandala

Thu - "Of" Means "Times"

explain that, in math, the word "of" means "times"

sing the song,

"Multiplying fractions
Is no big problem
Top times top over
Bottom times bottom"

do Fractions of a Group (a whole number has a denominator of 1)

do Multiplying Fractions (notice that the answers are very tiny! 1/3 of 1/4 is 1/12! cut up the Comparing Fractions worksheet to prove this)

week of Apr 20

Mon - First to 50

play First to 50: Fractions of a Group Game with red counters

Tue - Dividing IS Multiplying by the Reciprocal

recall Fractions of a Group worksheet and yesterday's game

is it true that 1/3 of 12 can be written as 1/3 x 12 OR as 12 ÷ 3?

do Dividing Fractions

Wed - Reciprocals of Mixed Numbers

explain the process for finding the reciprocals of mixed numbers

do Finding the Reciprocal

Thu - Add to MLB

add adding and subtracting fractions (with common denominators) and multiplying and dividing a fraction by a fraction to the MLB

add new observations and new questions about fractions

week of Apr 27

Mon - Factor Trees

read the introduction to YCCOM

have fun by drawing factor trees and creating the artwork for them!

Tue - Finding the GCF

do Simplifying Fractions

how have you been solving these? have you ever found an equivalent fraction but it was still the wrong answer because it wasn't in lowest terms? how can you be absolutely sure you're dividing by the biggest possible number that goes into both, and there are no more steps?

explain how to write factors in parentheses to find the GCF

Wed - Add to MLB

practice Simplifying Fractions with the GCF

add factor trees and finding the greatest common factor to the MLB

add new observations and new questions about fractions

Thu - Factors for Numbers 1 to 100

write out the factors for the numbers from 1 to 100 (in parentheses)

week of May 4

Mon - Finding the LCM

this is it! our final fractions skill! and then you will be able to do anything you ever need to with fractions

what would happen if we wanted to add fractions from different sections of the box together?

what if I ate half of my birthday cake during the daytime and then I got really hungry in the middle of the night and went back and ate 1/5 more?



yes, you could do it... but how would you express the answer?

if you say well, 1/2 + 1/5 = 1/2 and 1/5 more, then you have basically just repeated the question

the answer has to have only one denominator; therefore,
you need those two fractions to share a name before you add them

is this possible mathematically?

absolutely! we know how to make fractions smaller by dividing both parts by the same number but we can also make them bigger by multiplying, and the fractions will still be equivalent

here we need to figure out not what factors but what multiples two numbers have in common

as we will still have to simplify our answer at the end of the process, it saves time to go with the smallest common multiple (if I turn 1/2 into 50/100 and 1/5 into 20/100, I will get 70/100 and then reduce... if I turn 1/2 into 5/10 and 1/5 into 2/10, I will get 7/10 right away)

practice with Least Common Denominator task cards

Tue - Task Cards

practice with Adding and Subtracting Fractions With Unlike Denominators Task Cards

Wed - +/- Mixed Numbers with Unlike Denominators

do Adding & Subtracting Mixed Numbers with Unlike Denominators

Thu - Add to MLB

write in adding and subtracting fractions with different denominators to the MLB

add new observations and new questions about fractions

week of May 11

Mon - Brain Drawings

do Addition of Fractions with Visual Representation

post them up on the wall!

Tue - Multiples for Numbers 1 to 100

using another paper that goes from 1 to 100, write out as many skip counts as you want for each number

Wed - Word Problems

do Fraction Task Cards (Addition, Subtraction, Multiplication, Division)

Thu - Quiz

assess the class by giving Fractions Operations Review as a quiz (meaning students had to work independently and without help)

week of May 18

Error Analysis

To wrap up 10 busy weeks of this topic, I'll give the children Fraction Operations Error Analysis. This is a really fun way for them to assess themselves, and see if they have achieved total mastery of the skills!

I love Error Analysis and have written an entire blog post about it!

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