Title: Concrete Factions
1Concrete Factions
- How to Using Manipulatives and Not Formulas
- Compare Fractions
- Making Equivalent Fractions
- Simply Fractions
- Improper to Mixed Numbers
2The Old Fashion One Room School
Housestrategies are no longer useful
Because we want to avoid some self invented
strategies!
3Struggles for Students?
- Complete this sentence.
- The one thing that seems to be the most difficult
task for my students with fractions is
___________________. - Turn to a neighbor and share.
44th/5th Grade TEKS
- 4.2 The student describes and compares fractional
parts of whole objects or sets of objects. - (A) Use concrete objects and pictorial models to
generate equivalent fractions. - (B) Model fraction quantities greater than one
using concrete objects and pictorial models. - (C) Compare and order fractions using concrete
objects and pictorial models.
- (5.2) The student uses fractions in
problem-solving situations. - (A) Generate a fraction equivalent to a given
fraction such as ½, and 3/6 or 4/12 and 1/3. - (B) Generate a mixed number equivalent to a given
improper fraction or generate an improper
fraction equivalent to a given mixed number. - (C) Compare two fractional quantities in problem
solving situations using a variety of methods,
including common denominators.
5Understanding Fractions Using Array Models
- Arrays have length and width. It is important
that students be able to identify and name the
different dimensions. - Task Using the color tiles, build an array that
is ½ red.
New Task With color tiles, build an array that
is either ¼ yellow, or 1/8 blue, or 1/3 green.
Which one is correct? Which one do we normally
start with? Can we teach the concept of fractions
with equivalency at the same time?
6What is the whole?
- If this is ½ , what would the whole
be like?
Task If this is ¼, or 2/4, or 3/5
then create the whole?
- If this is 2/3 , what would the
whole be like?
7Comparing Fractions With Models
8Comparing Fractions With Models
- Which is greater ½ or ? So, how do you
help students to see the concrete way to
determine comparison of fractions?
Step 1 Build an array with the dimension of both
denominators. In this case, it would be a 2 x 3.
The array will become the whole.
Step 2 How many pieces of the whole will
represent ½?
Step 3 How many pieces of the whole will
represent ?
Compare New models. ½ is larger.
9Comparing Fractions With Models
Leads to finding common factors
4 8 12 16 20
5 10 15 20
10Making Equivalent Fractions
- Build a fraction
- Talk about numerator/denominator
- Stress that the different colors of cubes does
not determine denominator
Common Denominator helps to create
equivalent fraction by division
11Another look, different fraction
- Build a fraction
- Talk about numerator/denominator
- Stress that the different colors of cubes does
not determine denominator
12- Build a fraction 8/12
- Talk about numerator/denominator
- Stress that the different colors of cubes does
not determine denominator
13Compare Fractions without manipulatives
What is the common denominator? Multiply the
denominators or create factor line Draw an array
with the dimensions One color shade in one
fraction One color shade in on fraction Compare
Area
14Using a Multiplication Chart
15Simplify Fractions
- We dont reduce. Reduce means to make smaller.
The value of fractions doesnt change, just the
way it looks.
3
4
2
2
12 16
2
16Not by 2s?
2 3
1 2
3 6
3
6 9
3
15 30
5
12 18
2
17Now what?
- An Improper Fraction are fractions that have a
larger numerator than denominator. - A Mixed Number is a whole number that also has
a fraction.
18Mixed Up Numbers
- A mixed number is made up of a whole and
fraction. 1 2/3 - What does 1 2/5, 3 ¼, 2 5/6, 1 3/8, and 2 1/3
look like - How do you change 11/8
19Improper Mixed Numbers
- What is the Mixed Number for each model?
20Mixed Numbers Improper
21Other Resources
- Web Pages PISD Math Home Page
- Equivalent Fractions Manipulatives on-line
- Equivalent Fraction Frenzy
- Fresh Baked Equivalent Fractions
- TEXTEAMS
- Games/Centers
22I am committed to ------
- What is one strategy that you are committed to
trying with fractions this coming bundle? - What support do you need to make this work?
- Who can help you?
- When will you ask them?
- Reflect on these questions.
- Complete the evaluation form and drop off at
table. - Pick up a copy of each set of handouts