Dear Parents,
Welcome to week 28, the final week of third quarter! This
week we have our long-awaited trip the MIM on Tuesday. If you have not handed
in a permission slip and $10 bus fee for your student, you have one last chance
to do so tomorrow. Otherwise, you student will become an honorary third grader
for the day!
A few students have asked me about the results of their
recent math and science tests, and I have been happy to discuss the test with
them. If parents would like to know the results of the tests, they can always
contact me. In order to improve communication with parents regarding tests and
help parents gain clarity about the tests, I did send one math test and one
science test home this quarter. However, in order to meet administrative
requirements, I need to keep some tests on file for students' records. From
here on out, I will attempt to send approximately every other test home,
starting with the first math and science tests in fourth quarter. When tests
are taken on a Friday, as they usually are in my classes, you can expect to see
them in the students' Friday folders on the following Friday. For tests that
are not being sent home, please wait one week before inquiring about tests
results, and I will be sure to have your students' tests graded and ready to
discuss at that time.
In science class this week we will briefly cover some topics
that may appear on the state test but are not ordinarily covered by our
curriculum. These include natural disasters, erosion, and environmental concerns.
In math we will continue to work with fractions, converting mixed fractions and
improper fractions and finding equivalent fractions.
We also have our final meth test of the quarter this week. For
those that are interested, here is the study guide:
1. Fractions are equal
parts of a whole. The denominator of the fraction is the bottom number. It
tells us how many parts make up one whole. The numerator is the top number. It
tells us how many parts are being considered.
2. There are also two other main, important ways to think
about fractions. One of them is as division. The numerator then becomes the
dividend of the division problem and the denominator becomes the divisor. For
example, 3/4 = 3÷4. 5÷7 = 5/7. 255/100 = 255 ÷ 100. 35/17 = 35÷17. Students
should be able to change fractions to division problems and division problems
to fractions.
3. The last main concept of fractions is typically
unfamiliar to Americans. It is as follows: We can think of a fraction x/y as
the amount each person gets if you divided x items among y people. (I would NOT
expect students to understand the algebraic language, but it is usually easier to generalize ideas for adults
in algebraic language.) For example, if there are 4 pizzas and 7 people, divide
each pizza into 7 slices and each person gets four slices, one from each pizza.
Each of the 4 slices is 1/7 of a pizza, so each person gets 4/7. (It may help
to write names of seven people, draw four circles, divide them into seven
parts, and draw lines from each person's slices to their name to see that this
actually works. It took me awhile to understand this concept when I was first
introduced to it.) Similarly, 9/4 could mean 9 pizzas divided among 4 people.
If you divide each pizza into 4ths and give each person one slice per pizza,
each person gets 9/4. Students should be able to model this concept by drawing
a number of shapes equal to the numerator, dividing those shapes into parts
equal to the denominator, and shading one part from each.
4. Proper fractions are fractions where the numerator is
less than the denominator. Improper fractions are fractions where the numerator
is greater than or equal to the denominator. Because proper fractions have a
numerator less than the denominator, they are always less than 1. (Take 7/8: if
you have one pie divided into 8 slices and your family eats 7 slices, they have
not yet eaten the whole pie.) Improper
fractions with numerators and denominators equal are equal to 1. (Take 8/8: if
you divide a cake into 8 slices and eat all 8 slices, you've eaten the whole
cake. Also, any number divided by itself equals 1.) Improper fractions with
numerators greater than the denominators are greater than 1. (Take 9/8: if you
have two cakes divided into 8 slices and you eat 8 slices of one cake and 1
slice of another cake, you've eaten one whole cake and an extra slice.)
5. Students should know and be able to give examples of
proper fractions and of both kinds of improper fractions. They should be able
to accurately compare fractions to 1 using <, >, and = signs.
6. When using the greater than/ less than sign the rule is
that the larger end always goes toward the larger number. 56 < 57; 56 >
55. 3/4 < 1; 5/4 > 1.
7. Mixed numbers are numbers expressed with two parts, a
whole part and a fractional part. 4 1/2 is a mixed number with a whole part of
4 and a fractional part of 1/2. The fractional part of a mixed number must
always be a proper fraction. Students should be able to identify and give
examples of mixed numbers and their whole and fractional parts.
8. We can convert improper fractions to whole numbers or mixed
numbers by dividing. Improper fractions that divide evenly become whole
numbers. 10/5 = 10÷5 = 2. Improper fractions that divide and have remainders
become mixed numbers. The whole number answer to the division problem becomes
the whole part of the mixed number, and we write the original denominator of
the improper fractions as the denominator of the remainder, and this fraction
becomes the fractional part of the mixed number. 13/5 = 13÷5 = 5 R3 = 5 3/5.
9. We can convert mixed numbers to improper fractions by
multiplying the denominator of the fractional part by the whole part and adding
the fractional part to the resulting fraction. 3 1/4 3x4 =12 12/4 +1/4 = 13/4, so 3 1/4 = 13/4. Intuitively, this should make sense.
Division and multiplication are inverse operations; the one undoes the other.
If we convert improper fractions to mixed numbers by dividing, it makes sense
that we would convert mixed numbers back to improper fractions by multiplying.
Also, think about it this way: if you have 3 1/4 pizzas and you divide the
three whole pizzas into 4 parts each, 3 pizzas x 4 fourths per pizza = 12/4 of
pizza Now add the extra 1/4 from the
fractional part of the mixed number 12/4 + 1/4 = 13/4.
10. Students should be able to convert improper fractions to
mixed numbers and vice-versa.
These are all the notes I have for you this week! If you
have any questions, comments, or concerns, please email me at
rwycklendt@archwaytriviumeast.org.
Sincerely,
Rebecca Wycklendt
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