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INVENTIONS
- Look at Clue 1. What does the symbol ≥mean? (A is
greater than or equal to 2 x15, or 30.)
- Why did Ima use Clues 1 and 3 to make her list of possi-
ble values for A? (Clue 1 gives the least number possible,
which is 30. Clue 3 gives the greatest number possible, which is
49; 49 + 49, or 98, is less than 100.)
- What are the numbers on Ima’s list? (30, 31, 32,.. .,
and 49)
- Which numbers on Ima’s list match Clue 4? (31, 37, 41,
43, and 47)What are the factors of these numbers? (These
numbers have only 1 and themselves as factors.)
- Which of the numbers that have two factors match Clue 2? (41 because 4 x1 =4, 43
because 4 x3 =12, and 47 because 4 x7 =28.)
- Which of the numbers, 41, 43, and 47 match Clue 5? (43 because 4 – 3 = 1 and 1 < 3.)
- How can you check your answer? (Replace each A in the clues with its value. Be sure that
the statements are true.)
Work together as a class to answer the questions in “Solve the Problem: Inventions.”
Math Chat With the Transparency
Display the “Make the Case: Inventions” transparency on
the overhead. Before students can decide which charac-
ter’s “circuits are connected,” they need to figure out the
answer to the problem. Encourage students to work in
pairs to solve the problem, then bring the class together
for another whole-class discussion. Ask:
- Who has the right answer? (Mighty Mouth)
- Inwhat year was the television invented? (1923)
- How did you figure out the value of B? (From Clues 2 and
3, Bcan be 9 through 30. Clue 4 eliminates all numbers that
have more than two factors leaving numbers 11, 13, 17, 19,
23, and 29. Clue 1 eliminates 11, 13, 17, and 19, leaving 23
and 29. Clue 5 eliminates 29.)
- How do you think CeCe Circuits got 29? (She probably ignored Clue 5.)
- How do you think Boodles got 14? (Boodles probably ignored Clue 4.)
10
Name _____________________________________________ Date __________________Ima ThinkerINVENTIONS11I’ll start with Clues 1 and 3 , and make
a list of values for A. The first three
numbers are 30, 31, and 32.1.What are all of the numbers on Ima’s list?
________________________________
2.What is A? _______
3.How did you figure out the value of A? ________________________
______________________________________________________
4.Check your number with the clues. Show your work here.5.Record Aon the line below to complete the year of the invention.
The Slinky was invented in the U. S. by Richard and
Betty James in 19___.SOLVE
PROBLEMTHE Complete the year of the invention.
The Slinky was invented in the United States by
Richard and Betty James in 19___.
The letter Astands for a 2-digit number.
Use the clues to figure out the value of A.
CLUES:
1 )A≥ 2 x 15
2) The product of its digits is an even number.
3) A+A< 100
4 )Ahas exactly two different factors.
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Of course,
Bis 14.
Obviously
Bis 29.
I believe that
Bis 23.
Complete the year of the invention.
The television was invented in the United States by
Vladimir Zworykin in 19___.
The letter Bstands for a 2-digit number.
Use the clues to figure out the value of B.
CLUES:
1 ) The sum of the digits of Bis not divisible by 2.
2) B≥ 18 ÷ 2
3) B≤ 90 ÷ 3
4 )Bhas no factors except for 1 and itself.
5) The product of the two digits of Bis a single-digit number.
Algebra Readiness Made Easy: Grade 6 © Greenes, Findell & Cavanagh, Scholastic Teaching Resources