April 2010 • DynaMath • T1 TeAcher’s ediTion April 2010 Vol. 28, No. 7 ISSN 0732-7773 A SupplemeNt to Dynamath scholastic DynaMath 555 Broadway, room 474 new York, nY 10012 (212) 343-6458 dynaMath@scholastic.com sUBscriPTion/deLiVerY inQUiries: 1-800-schoLAsTic (1-800-724-6527) www.scholastic.com/custsupport Are some DynaMath activities too difficult for your students? Or perhaps too easy? Go to www.scholastic.com /dynamath for differentiated repros! This month, you get 4 leveled activities to use with pages 6–7 and 10–11, plus a PowerPoint slideshow of the math instructions from pages 6–7 for use on interactive whiteboards. Let us know what you think of these and other features by filling out the survey at www.scholastic.com /dynamathspring10survey. Thanks! Digitally yours, Matt Friedman, Editor Differentiated repros Content and SkillS Guide difficulty Level: H = Easy HH = On-Level HHH = Challenging PAGe ArTicLe TiTLe, diFFicULTY LeVeL PriMArY MATh sKiLL sUPPLeMenTArY sKiLLs/APPLicATions ncTM sTAndArds (see below for details) cover Spring Into Spring! HH Working backward Computation +, 5 1, 2, 6, 8 2–3 Numbers in the News HH LcM, elapsed time Equivalent measures 1, 2, 4, 8, 9 4–5 Tigers in Trouble! HH reading a circle graph Percent of a number 1, 2, 5, 6, 8, 9 6–7 The Power of Area HH Area of a rectangle Computation 5, ÷ 1, 3, 8, 9 8–9 Wild Angles HH estimating angle measures Reading a protractor 3, 7, 8 10–11 Fantastic Fraction Foods HHH Adding frax w/unlike denoms LCD, LCM 1, 8 12–13 Count on the Census HH Analyzing data Problem solving 1, 5, 6, 7, 8, 9 14–15 What’s ART Up To? HH issue skills review Test-taking practice 1, 3, 4, 5, 6, 8 16 Derek’s the Greatest H comparing fractions LCD, LCM 1, 8 T4 Earth Angles HHH Measuring angles pp. 8–9 extension 1, 3, 4, 8 T5 Problem Solved Prep Page HH Analyzing data pp. 12–13 extension 1, 4, 7, 10 T6 Funny Franklin Fractions HH comparing fractions visually p. 16 extension 5, 7, 8 issue dates: 9/09 10/09 11–12/09 1/10 2/10 3/10 4/10 5-6/10 need Funding for DynaMath? Go to www.scholastic.com/classmags and click on Looking for Funding to learn how DynaMath qualifies for funding such as NCLB grants. ncTM standards 1. Number and Operations 2. Algebra 3. Geometry 4. Measurement 5. Data Analysis & Probability 6. Problem Solving 7. Reasoning and Proof 8. Communication 9. Connections 10. Representation Standards listed above in a bold box (such as 1) indicate that the article also connects with a new NCTM Curriculum Focal Point. Your stuDents can win a DYnaMath t-shirt! Ask your students to be on the lookout for interesting events or places that they’d like DynaMath to feature in “numbers in the news.” have them send a copy of, or a Web link to, their news idea. if we use it in the magazine, they’ll win a DynaMath T-shirt. see page 2 of this issue’s student edition for details.
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need Funding for DynaMath?Go to www.scholastic.com/classmags and click on Looking for Funding to learn how DynaMath qualifies for funding such as NCLB grants.
ncTM standards 1. Number and Operations 2. Algebra 3. Geometry 4. Measurement 5. Data Analysis & Probability
6. Problem Solving 7. Reasoning and Proof 8. Communication 9. Connections 10. Representation
Standards listed above in a bold box (such as 1) indicate that the article also connects with a new NCTM Curriculum Focal Point.
Your stuDents can win a DYnaMath t-shirt!Ask your students to be on the lookout for interesting events or places that they’d like DynaMath to feature in “numbers in the news.” have them send a copy of, or a Web link to, their news idea. if we use it in the magazine, they’ll win a DynaMath T-shirt. see page 2 of this issue’s student edition for details.
COVER: SPRING INTO SPRING!
STRATEGY: GRID PAPER
Have students draw three bars on
grid paper to represent the three
leaps. Let each square on the grid
represent five feet.
2–3: NUMBERS IN THE NEWS
EXTENSION: GIRAFFES . . .
Giraffe facts: There are three main
types of giraffes: the Maasai, reticu-
lated, and Rothschild giraffes. Maasai
giraffes have irregular star- shaped
markings that cover most of their
bodies. The Rothschild giraffes have
a coat that is pale and thickset when
compared with Maasai giraffes, and
the coat has less jagged patches.
Also, the area below the knee is usu-
ally unmarked.
EXTENSION: SUNNY & SPEEDY
Bonus question: About how long
would it take (in hours) to travel
1,800 miles in a car that is traveling
55 mph? (Answer: about 33 hours)
EXTENSION: BIG BASKET
Bonus question: A rectangular
basket is 10 inches long, 8 inches
wide, and 4 inches deep. How many
2-inch cubes could it hold? (Answer:
40 2-inch cubes)
4–5: TIGERS IN TROUBLE!
STRATEGY: GRAPH’S PURPOSE
Discuss the purpose of a circle
graph. Ask students why a graph is
sometimes more useful than a chart
of data. Be sure to point out that
the information about tigers on the
graph is based on estimated counts.
6–7: THE POWER OF AREA
STRATEGY: USE GRID PAPER
Have students draw each given rect-
angle on grid paper to “prove” their
calculated answer. Be certain that
students label all answers with the
correct square unit of measure.
8–9: WILD ANGLES
STRATEGY: ESTIMATION TOOL
Give each student a piece of square
note paper. Have them fold the
square diagonally. This creates a
“tool” that has a 45-degree and a
90-degree angle. Students can com-
pare the corners of this tool to each
given angle to find a reasonable esti-
mate of the measure of each angle in
the activity.
10–11: FANTASTIC . . .
STRATEGY: LCD SHORTCUTS
If two denominators are prime
numbers, multiply the two denomi-
nators. If one of the denominators
is a prime number and it is not a
factor of the other denominator,
multiply the two denominators. If
one of the denominators is a prime
number and it is a factor of the other
denominator, the greater denomi-
nator is the LCD.
14–15: WHAT’S ART UP TO?
STRATEGY: TEST TIP
Try to eliminate any answers that
you are sure are wrong, and then
make a reasonable choice from the
remaining answers.
16: DEREK’S THE GREATEST!
STRATEGY: ALTERNATE WAY
To compare the values of two frac-
tions, cross-multiply. Multiply the
numerator of the first fraction by the
denominator of the second fraction.
That is the “product” for the first
fraction. Then multiply the second
numerator by the first denominator.
That is the “product” for the second
fraction. The fraction with the great-
er “product” has the greater value.
Example: Compare 1 _ 2 with 3 _ 4 . Mul-
tiply 1 5 4. The product is 4. Then
multiply 2 5 3. The product is 6.
Therefore, 3 _ 4 is greater than 1 _ 2 . (Why
this works: In cross-multiplication,
you are actually taking a shortcut
to finding fractions with a common
denominator by simply multiply-
ing both denominators together. In
the example 1 _ 2 compared with 3 _ 4 , we
could find a common denominator
by multiplying 2 and 4. The com-
mon denominator would be 8. Then
to find the numerator for 3 _ 4 , we also
must multiply 3 by 2 as we did with
its denominator. To find the numer-
ator for 1 _ 2 , we must multiply the 1 by
4, as we did with its denominator. )
—Dale Beltzner
Mr. Beltzner is the Math Subject Area
Leader for the Southern Lehigh School
District in Bethlehem, Pennsylvania.
Lesson plans
T2 • DynaMath • April 2010
TEACHERS: Make one copy per student, or assign one problem each day to start your math lesson!
Using a Protractor to MeasUre angles4 Place the center mark at the bottom of the protractor on the vertex (point) of the angle. 4 Line up the 0-degree (º) line of the protractor with one ray of the angle. 4 Look at the number on the protractor that aligns with the other ray of the angle. (You may need to extend the ray.)4 Be sure to read the correct number. Acute angles are less than 90°. Right angles are exactly 90°. Obtuse angles are greater than 90°.
1Save water by taking fewer baths and more showers. A full bathtub requires ______ gallons
of water. A 5-minute shower uses about 50 gallons less than that!
4 Measure the angle that appears after the sentence. 3 Write the angle measure without the degrees symbol in the box provided. 4 That number completes the Earth-friendly fact.
What to Do
What can you do to help the planet? Measure angles to find out!
4 If 1 _ 4 of the food Americans throw away is saved instead, ______ million hungry people
could be fed each day.
5Use both sides of a piece of paper! Every year, each American uses the amount of
paper that comes from one ______-foot-tall Douglas fir tree.
For question 1: Find the box in the chart where the “Population 5 to 14 years old” row meets the “Steepest Hills” column.
FOR QUESTION 2: Think: What row of the chart do you need to look at to compare the three towns’ total populations?
FOR QUESTION 3: Think: Which age range listed on the chart includes 16- to 30-year-olds? And which town has the greatest population in that age range?
FOR QUESTION 4: Think: Which row of the chart is most important to look at?
FOR QUESTION 5 and supermath: Try to think through each of these problems on your own!
On pages 12 and 13, we ask you to analyze data to help make sense of the U.S. Census. Below, we give one way you can think about each question from those pages. Remember: There isn’t always just one
way to think about the data. But your answer does need to make sense. That means you need to be able to explain why you chose the answer that you did.
What to DoUse the information below to help you think