The data shows the wolf population is decreasing by about 8 wolves every 2 years. If the rate remains constant, the wolf population will drop below 15 in the year 2006.
The document provides instructions for preparing for a programming contest, including:
1) Creating folders to store practice problems and wrong solutions.
2) Learning common programming languages, data structures, algorithms and discrete math topics.
3) Solving sample problems involving permutations, combinations, and dividing objects into groups.
4) Finding the number of solutions to equations with constraints on the variables.
The goal is to practice a variety of algorithmic problem solving techniques in preparation for programming contests.
This document provides strategies for solving addition and subtraction problems mentally in stages 5 through 7. It presents sample word problems and shows how students can use strategies like making ten, doubles, compatible numbers, place value, compensation, reversibility, and multiplication to solve them. Students are asked to work with a neighbor to practice explaining and applying the strategies to additional problems.
The document presents the results of a survey about gaming habits and their potential impact on schoolwork. Graphs show that all 10 respondents have a games console, most spend 1-6 hours a day playing various game types. The majority play games rated for their age group. Graphs also show respondents' grades ranging from levels 4-7, with most spending less than 30 minutes on homework each day. Finally, most respondents go to sleep between 8-10pm.
This document provides an overview, standards, and tasks for a third grade mathematics unit on number and operations in base ten. The unit focuses on place value, rounding, addition, subtraction, and multiplication of whole numbers within 1,000 using strategies based on place value. Students will also draw scaled picture graphs and bar graphs to represent data sets and solve problems using the graphs. The unit includes 16 tasks for students involving word problems, mental math strategies, place value, properties of operations, measurement, and data representation.
This document provides information to help parents support their child's maths learning at home. It includes:
1) The key instant recall facts (KIRFs) the child is working on memorizing this half term, such as multiplication and division facts.
2) Tips for parents on how to practice KIRFs in a fun, engaging way using examples, games, songs and timed activities.
3) Suggested vocabulary for parents to use to help explain maths concepts.
The goal is for the child to instantly recall important number facts so they can solve problems quickly and confidently. Regular short practice sessions are encouraged along with praise to build the child's confidence in maths.
The document provides instructions for preparing for a programming contest, including:
1) Creating folders to store practice problems and wrong solutions.
2) Learning common programming languages, data structures, algorithms and discrete math topics.
3) Solving sample problems involving permutations, combinations, and dividing objects into groups.
4) Finding the number of solutions to equations with constraints on the variables.
The goal is to practice a variety of algorithmic problem solving techniques in preparation for programming contests.
This document provides strategies for solving addition and subtraction problems mentally in stages 5 through 7. It presents sample word problems and shows how students can use strategies like making ten, doubles, compatible numbers, place value, compensation, reversibility, and multiplication to solve them. Students are asked to work with a neighbor to practice explaining and applying the strategies to additional problems.
The document presents the results of a survey about gaming habits and their potential impact on schoolwork. Graphs show that all 10 respondents have a games console, most spend 1-6 hours a day playing various game types. The majority play games rated for their age group. Graphs also show respondents' grades ranging from levels 4-7, with most spending less than 30 minutes on homework each day. Finally, most respondents go to sleep between 8-10pm.
This document provides an overview, standards, and tasks for a third grade mathematics unit on number and operations in base ten. The unit focuses on place value, rounding, addition, subtraction, and multiplication of whole numbers within 1,000 using strategies based on place value. Students will also draw scaled picture graphs and bar graphs to represent data sets and solve problems using the graphs. The unit includes 16 tasks for students involving word problems, mental math strategies, place value, properties of operations, measurement, and data representation.
This document provides information to help parents support their child's maths learning at home. It includes:
1) The key instant recall facts (KIRFs) the child is working on memorizing this half term, such as multiplication and division facts.
2) Tips for parents on how to practice KIRFs in a fun, engaging way using examples, games, songs and timed activities.
3) Suggested vocabulary for parents to use to help explain maths concepts.
The goal is for the child to instantly recall important number facts so they can solve problems quickly and confidently. Regular short practice sessions are encouraged along with praise to build the child's confidence in maths.
This document outlines an agenda and goals for a new teacher institute on teaching K-5 math and science. It introduces the presenters and their contact information. The agenda includes discussing favorite numbers, instructional blocks and minutes, Singapore Math and Math in Focus curricula, lesson structure, assessment, and meeting student needs. It also covers pedagogical approaches like concrete-pictorial-abstract, relational understanding, and multiple representations. Curriculum topics like anchoring to 10, number bonds, place value, and lesson structure are examined.
The document provides information about Singapore Math training and implementation over three years. It includes the following:
- Details of professional development sessions for teachers including the hours spent on topics like pedagogy, assessments, and lesson studies.
- Plans for instructional blocks and homework for grades K-1 and 2-5 focused on developing number sense and fact fluency.
- Examples of part-whole relationship activities using pictures, counting, and number bonds to teach foundational math skills.
- Illustrations of how bar models can be used to represent word problems involving addition, subtraction, multiplication, division, and fractions.
The document is a table of contents for a mathematics textbook for third grade students in the Philippines. It lists 46 lessons on topics like multiplication, division, properties of operations, and solving word problems involving these operations. The document also provides information about copyright and permissions for using materials in the book. It was developed by the Department of Education of the Republic of the Philippines.
The document provides rhymes and stories to help remember multiplication facts. It includes examples like 3 x 8 = 24 which is related to the number of hours in a day, and 4 x 8 = 32 which represents freezing temperature. Other examples include 8 x 8 = 64 which refers to a fallen plate, and 6 x 7 = 42 which is about a trip to Peru. The goal is to make the multiplication facts easier to learn by finding patterns and relating them to existing knowledge.
The document provides rhymes and stories to help remember multiplication facts. It includes clues and rhymes for multiplying numbers like 3 x 4, 7 x 8, 3 x 3, 3 x 7, 7 x 7, 3 x 6, 3 x 8, 4 x 8, 8 x 8, 4 x 4, 4 x 7, and 6 x 7. The answers are provided after students are prompted to recall the clues and state the answers. Rhymes include references to dates, freezing temperatures, dropping plates, driving jeeps, and visiting heaven to match multiplication number sentences.
This document contains a math exam with 40 multiple choice questions testing concepts like number writing, place value, operations, rounding, and word problems. The exam is assessing a 4th grade math class on topics related to numbers, operations, and problem solving.
The previous lesson taught me how to use the Fundamental Counting Principle to count the number of possible outcomes of compound events. Today's lesson built on that by teaching me how to use permutations to calculate probabilities by taking the number of favorable outcomes and dividing by the total number of possible outcomes. Understanding how to count outcomes using the Fundamental Counting Principle was necessary to understand how to calculate probabilities using permutations, as the total number of possible outcomes is needed for the denominator of a probability fraction. So the previous lesson provided the foundation for understanding the key concepts and calculations in today's probability lesson.
Kid Cudi is no longer pursuing a career in rap and is focusing on rock music instead. He formed a rock duo called WZRD with Dot da Genius. Their debut album explores Cudi's personal struggles with drug addiction and relationships through a rock-influenced sound. While some of the album's ideas were not fully realized, the musical experimentation provides an interesting artistic journey. Cudi has also contributed rock tracks to movie soundtracks and performed with WZRD on television to further pursue his new musical direction in rock.
The document describes various types of data storage devices including Zip disks, Mini CDs, CD-RWs, floppy disks, tape drives, CD-Rs, Mini DVDs, DVD-RWs, memory pens, secure digital cards, TransFlash cards, multimedia cards, compact flash cards, SmartMedia cards, and XD cards. Key details are provided about the introduction date, size, storage capacity, and usage of each type of storage medium.
Kid Cudi is no longer interested in pursuing a rap career and is focusing on rock music instead. He has formed a rock duo called WZRD with Dot Da Genius. Their debut self-titled album touches on Cudi's personal struggles with drugs and relationships. While some of the musical ideas did not work well, the album provided an interesting artistic journey as Cudi explored rock. He now seeks to continue his rock career by contributing music to movies.
Dmitri Mendeleev created the periodic table by arranging elements in order of increasing atomic mass, finding that elements' properties repeated periodically. The periodic table groups elements with similar properties into columns and periods. The periodic law states that when elements are arranged by increasing atomic number, their chemical and physical properties repeat periodically, with metals usually on the left and nonmetals on the right.
Dmitri Mendeleev is credited with creating the first periodic table of elements in 1869, arranging the elements in order of increasing atomic mass and grouping them into columns and periods based on repeating properties. The periodic table displays a periodic repetition of chemical and physical properties when elements are arranged by atomic number, with metals generally to the left and non-metals to the right.
The Bethesda Mennonite Church youth room will receive a face-lift. Check out this powerpoint to see inspiration pictures that have created the vision for the renovation project.
This document outlines an agenda and goals for a new teacher institute on teaching K-5 math and science. It introduces the presenters and their contact information. The agenda includes discussing favorite numbers, instructional blocks and minutes, Singapore Math and Math in Focus curricula, lesson structure, assessment, and meeting student needs. It also covers pedagogical approaches like concrete-pictorial-abstract, relational understanding, and multiple representations. Curriculum topics like anchoring to 10, number bonds, place value, and lesson structure are examined.
The document provides information about Singapore Math training and implementation over three years. It includes the following:
- Details of professional development sessions for teachers including the hours spent on topics like pedagogy, assessments, and lesson studies.
- Plans for instructional blocks and homework for grades K-1 and 2-5 focused on developing number sense and fact fluency.
- Examples of part-whole relationship activities using pictures, counting, and number bonds to teach foundational math skills.
- Illustrations of how bar models can be used to represent word problems involving addition, subtraction, multiplication, division, and fractions.
The document is a table of contents for a mathematics textbook for third grade students in the Philippines. It lists 46 lessons on topics like multiplication, division, properties of operations, and solving word problems involving these operations. The document also provides information about copyright and permissions for using materials in the book. It was developed by the Department of Education of the Republic of the Philippines.
The document provides rhymes and stories to help remember multiplication facts. It includes examples like 3 x 8 = 24 which is related to the number of hours in a day, and 4 x 8 = 32 which represents freezing temperature. Other examples include 8 x 8 = 64 which refers to a fallen plate, and 6 x 7 = 42 which is about a trip to Peru. The goal is to make the multiplication facts easier to learn by finding patterns and relating them to existing knowledge.
The document provides rhymes and stories to help remember multiplication facts. It includes clues and rhymes for multiplying numbers like 3 x 4, 7 x 8, 3 x 3, 3 x 7, 7 x 7, 3 x 6, 3 x 8, 4 x 8, 8 x 8, 4 x 4, 4 x 7, and 6 x 7. The answers are provided after students are prompted to recall the clues and state the answers. Rhymes include references to dates, freezing temperatures, dropping plates, driving jeeps, and visiting heaven to match multiplication number sentences.
This document contains a math exam with 40 multiple choice questions testing concepts like number writing, place value, operations, rounding, and word problems. The exam is assessing a 4th grade math class on topics related to numbers, operations, and problem solving.
The previous lesson taught me how to use the Fundamental Counting Principle to count the number of possible outcomes of compound events. Today's lesson built on that by teaching me how to use permutations to calculate probabilities by taking the number of favorable outcomes and dividing by the total number of possible outcomes. Understanding how to count outcomes using the Fundamental Counting Principle was necessary to understand how to calculate probabilities using permutations, as the total number of possible outcomes is needed for the denominator of a probability fraction. So the previous lesson provided the foundation for understanding the key concepts and calculations in today's probability lesson.
Kid Cudi is no longer pursuing a career in rap and is focusing on rock music instead. He formed a rock duo called WZRD with Dot da Genius. Their debut album explores Cudi's personal struggles with drug addiction and relationships through a rock-influenced sound. While some of the album's ideas were not fully realized, the musical experimentation provides an interesting artistic journey. Cudi has also contributed rock tracks to movie soundtracks and performed with WZRD on television to further pursue his new musical direction in rock.
The document describes various types of data storage devices including Zip disks, Mini CDs, CD-RWs, floppy disks, tape drives, CD-Rs, Mini DVDs, DVD-RWs, memory pens, secure digital cards, TransFlash cards, multimedia cards, compact flash cards, SmartMedia cards, and XD cards. Key details are provided about the introduction date, size, storage capacity, and usage of each type of storage medium.
Kid Cudi is no longer interested in pursuing a rap career and is focusing on rock music instead. He has formed a rock duo called WZRD with Dot Da Genius. Their debut self-titled album touches on Cudi's personal struggles with drugs and relationships. While some of the musical ideas did not work well, the album provided an interesting artistic journey as Cudi explored rock. He now seeks to continue his rock career by contributing music to movies.
Dmitri Mendeleev created the periodic table by arranging elements in order of increasing atomic mass, finding that elements' properties repeated periodically. The periodic table groups elements with similar properties into columns and periods. The periodic law states that when elements are arranged by increasing atomic number, their chemical and physical properties repeat periodically, with metals usually on the left and nonmetals on the right.
Dmitri Mendeleev is credited with creating the first periodic table of elements in 1869, arranging the elements in order of increasing atomic mass and grouping them into columns and periods based on repeating properties. The periodic table displays a periodic repetition of chemical and physical properties when elements are arranged by atomic number, with metals generally to the left and non-metals to the right.
The Bethesda Mennonite Church youth room will receive a face-lift. Check out this powerpoint to see inspiration pictures that have created the vision for the renovation project.
The document is a prayer asking God for guidance, strength, and blessings in one's learning and ability to serve others. It thanks God for life, another day, and the opportunity to learn and help others, asking God to enlighten one's mind and give strength for the lessons while remembering God's glory. The prayer is offered to God Almighty and concludes with "Amen".
A histogram is a graph that displays the frequency of data using bars of different heights. It uses intervals on the x-axis to bin the data and the height of each bar represents how many scores fall into that interval. The document provides examples of histograms showing data on student sleep habits, dice rolls, movie ticket prices, coin flips, math test scores, travel times to school, and pet ownership. It includes problems asking readers to interpret data from the histograms and draw their own histograms for additional data sets.
This document provides an overview of 5 lessons on patterns involving different types of fictional insects called Pedes. The lessons involve continuing numerical and shape patterns, generalizing the patterns, and answering questions to demonstrate understanding of the patterns. Students are asked to create PowerPoint slides to represent patterns involving Humped-Back Pedes, Spotted Pedes, and Big-Headed Pedes. They are to record their observations and generalizations about the patterns. The goal is for students to learn to continue simple patterns, generalize patterns, and show they have understood the patterns through their responses.
This document describes the rules and structure of a mental math competition consisting of 5 rounds. It provides sample questions and answers for each round, with the rounds getting more difficult. The competition involves teams answering math problems within time limits, with points awarded for correct answers and deducted for incorrect ones. Teams can optionally pass questions to other teams in some rounds. The final round involves answering multiple questions at once within a time limit.
1. The document discusses permutation, which is the arrangement of objects in a definite order without repetition. It provides examples of calculating permutations using factorials for arrangements of objects, letters in words, and seating arrangements.
2. The fundamental counting principle and different types of permutations are explained, including permutation of n objects, distinguishable permutation, permutation of n objects taken r at a time, and circular permutation.
3. Examples are provided to demonstrate calculating permutations for a variety of scenarios involving arrangements of objects, letters, people, and keys to illustrate the different permutation concepts.
1. The standard bowling lane setup has pins arranged in four rows, with the number of pins in each row increasing by one from front to back.
2. If a fifth row is added, the total number of pins can be calculated using the formula for the sum of the first n positive integers, which is n(n+1)/2.
3. For 100 rows of pins, this same formula can be used to calculate that there would be 100*101/2 = 5,050 total pins.
The document discusses a classroom activity where students are divided into groups of 9. Each group sends a representative to the front where the teacher shows them a fruit without naming it. The representative then has 30 seconds to describe the fruit to their group using adjectives. If the group guesses the fruit correctly, they earn 1 point. Each group takes a turn sending a representative to participate in the activity. The purpose is to practice using adjectives to describe objects without directly stating the name. The activity is meant to be done in rounds with all student groups participating.
Teacher Sarah arranges the seating of her three tutees - Ana, Beauty, and Carl - differently each Saturday to see if their learning is affected by the seating arrangement. There are 6 possible seating arrangements that can be found using systematic listing, a tree diagram, or a table. The document then provides examples of determining the number of permutations in different situations using the fundamental counting principle and factorial notation.
MTAP Program of Excellence in Mathematics
Grade 5 Session 2
Contents:
-Multiplication and Division of Whole Numbers
-PRIME FACTORIZATION
is breaking a number down into the set of prime numbers which multiply together to result in the original number. This is also known as prime decomposition. We cover two methods of prime factorization: find primes by trial division, and use primes to create a prime factors tree.
-Greatest Common Factor
-Least Common Multiple
-Problem Solving
This document contains examples and solutions for permutations and combinations problems from pre-calculus. It includes 12 problems covering topics like counting the total outcomes of removing coins from bags, determining the number of possible Braille patterns, and finding coefficients in binomial expansions using Pascal's triangle. The document uses formulas, diagrams, and step-by-step workings to explain the solutions.
The document discusses adjectives and their order in sentences. It explains that adjectives describe or modify nouns, and lists the typical order of adjectives as opinion, size, age, shape, color, origin, and material. An activity is described where students are grouped and take turns describing a fruit to their group without naming it, using adjectives within a time limit to see if their group can correctly identify the fruit.
This document discusses a proportional reasoning word problem and its step-by-step solution. It begins by presenting the original problem: if 5 cats can catch 5 mice in 5 days, how many days does it take 3 cats to catch 3 mice? It then explains that the obvious answer of 3 days is incorrect, as the relationship is one of direct proportion. The document walks through setting up a proportional relationship between cats and mice caught per day, and determines that it takes 1 cat 5 days to catch 1 mouse. Therefore, it takes 3 cats 5 days to catch 3 mice.
The document discusses methods for helping students memorize multiplication facts. It suggests starting with knowing basic facts like 4 x 4 and using those to derive other facts. Students are quizzed on facts to make the process more engaging. The document then explores patterns in multiplication, like the rule that a number times itself is always one more than the product of that number minus one times itself plus one. These patterns provide shortcuts to derive new facts and build understanding of multiplication relationships.
The document discusses methods for helping students memorize multiplication facts. It suggests starting with knowing basic facts like 4 x 4 and using those to derive other facts. Students are quizzed on facts to make the process more engaging. The document then explores patterns in multiplication, like the rule that a number times itself is always one more than the product of that number minus one and that number plus one. These patterns provide shortcuts to derive new facts and build understanding of multiplication relationships.
1. A Number Day event was held at a school where 55 students participated in math questions using Q6 handsets in teams of 5.
2. The students answered multiple choice, numerical, and paper questions on the handsets about topics like geometry, time, distance, history, sequences, and more.
3. The teacher's notes discuss arranging the students into teams, assigning handsets, asking questions to the handsets, reviewing answers, and concluding with a Tarsia activity.
1) Students will collect data on favorite fast foods in their class and grade to create bar graphs. They will write a report sharing their findings.
2) Fraction concepts are explored through examples of parts of wholes, such as one-third and two-sixths being equivalent.
3) A problem solving activity involves arranging digits 1-9 in groups so the sum is the same in each group, with discussion of multiple solutions.
The document discusses sample questions from TCS recruitment tests. It provides details about the new test pattern introduced in 2010, including that it is computer-based, has 35 questions to be answered in 60 minutes, and excludes English questions. The questions are divided into four categories: quantitative ability, logical reasoning, analytical reasoning, and reading comprehension. Several sample quantitative questions are then presented covering topics like trigonometry, probability, linear equations, and more. Step-by-step solutions are provided for each sample question.
This is a keynote for teaching 3rd graders how to process multiplication using repeated addition. There is a video, from Discovery Education, included in the presentation.
FINAL-SOLVING QUADRATIC EQUATION USING QUADRATIC FORMULA.pptxJODALYNODICTA
The document describes Phineas and Ferb helping their friends find Isabella by solving quadratic equations along the way. They encounter obstacles like a rollercoaster, forest traps, and a giant wave that can only be passed by correctly solving quadratic equations using the quadratic formula. With the formula, they are able to determine lengths, widths, and solutions to area equations in order to clear obstacles and ultimately find Isabella.
2. 1. Understand the problem
Step 1: Read the problem. Ask yourself
A. What information am I given?
B. What is missing?
C. What am I being asked to find or do?
3. 2. Make a Plan to Solve the Problem
A. Choose a Strategy.
B. The more you try using different strategies, the
better you will pick a good strategy to solve a problem.
PRACTICE!
4. 3. Carry Out the Plan
A. Solve the problem using your plan.
B. Show all your work.
C. Give yourself enough space to organize your work!
5. 4. Check your answer to be sure it is REASONABLE!!!
A. Look back at your work and compare your answer
to what information and/or questions in the problem.
B. Ask yourself “Is there a way I can check my answer?
TRY SUBSTITUTION!
C. Did you check your work for errors?
6. 1. Draw a Picture
2. Look for a Pattern
3. Systematic Guess and Check
4. Act it out
5. Make a Table
6. Work A Simpler Problem
7. Work Backwards
8. Write an Equation
7. A worm is trying to escape from a well 10 feet deep.
The worm climbs up 2 feet per day, but each night it
slides back 1 foot. How many days will it take for the
worm to climb out of the well?
Use THE FOUR STEP PLAN.
1. Understand
2. Plan
3. Carry Out
4. Check
8. 1. UNDERSTAND
READ!!
What am I given?
10 foot deep well
2 feet per day up
1 foot down per night
What do you need to solve for?
I need to know the number of days needed to get out of
the well
9. Strategy 1: Draw a picture given the information!
10 foot well
2 feet up per day
1 foot down per night
Show me your picture!
What is your answer!!!
Does your picture show that the worm progresses 1 foot per
day, except the last day when it can crawl 2 feet and get out
of the well, not have to spend another night in the well?
The answer is 9 days!!!
10. 9
8
7
Number of 6
Feet
5
Climbed
4
3
2
1
1 2 3 4 5 6 7 8 9
Days
12. Suppose the worm in the
example climbs up 3 feet per
day and slides back 2 feet per
night. How many days will it
take for the worm to climb out
of the 10 feet well?
13. Suppose the worm in the example climbs up 3 feet per
day and slides back 2 feet per night. How many days
will it take for the worm to climb out of the 10 feet
well? HERE IS MY TABLE: 9 DAYS AGAIN!
Day Night Progress Total
1 3 -2 1
2 3 -2 1 2
3 3 -2 1 3
4 3 -2 1 4
5 3 -2 1 5
6 3 -2 1 6
7 3 -2 1 7
8 3 -2 1 8
9 3 3 11
14. How about if the worm needed to climb out of a 12 foot
well and went up 3 feet during the day and slid back 2
foot per night? How long would it take for the worm
to get out of the well? DRAW THE PICTURE ANY
WAY YOU WANT!
15. How about if the worm needed to climb out
of a 12 foot well and went up 3 feet during
the day and slid back 2 foot per night? How
long would it take for the worm to get out of
the well? ANSWER 8 DAYS!
17. A Pizza party is having pizzas with pepperoni,
pineapple chunks, and green pepper slices. How many
different pizzas can you make with these toppings?
What are the questions you ask?
Read
What Am I Given?
What Am I Solving For?
18. A Pizza party is having pizzas with pepperoni, pineapple
chunks, and green pepper slices. How many different
pizzas can you make with these toppings? 7 Pizza
Combinations
p P,GP P,PC
P,GP,P
C
GP GP,P
C
PC
19. You can look for a pattern by looking at similar cases.
For Example: What is the sum of the measures of the
angles of a 12 sided polygon?
Well—you don’t have this memorized so can you look
at a easier shape and figure out the pattern?
20. 3 sides 4 sides 5 sides 6 sides
The number of triangles formed is TWO LESS than
the number of sides of a polygon. This means the sum
of the measures of the angles of each polygon is the
number of triangles TIMES 1800. For a 12 sided
polygon, the number of triangles is 12-2=10. The sum
of the measures of the angles is 10 x 1800=1,8000.
21. Step 1: Understand
The goal is to find the sum of the measures of the
angles. So can we start from a triangle and work up?
Step 2: Plan
Draw a 3 sides polygon, 4 sided polygon, etc. to
look for a pattern.
Step 3: Carry out
We know a triangle has three angles that total 1800.
22. Step 4 Check Your Answer
Draw a 12 sides polygon and CHECK that there are
exactly 10 triangles formed when you draw diagonals
from one vertex of a 12 sides polygon.
23. Can you draw a pattern and calculate the number of
black tiles needed to have nine rows of tiles. See Page
35
24. Page 35, Practice problem 2: A triangle has four rows
of small triangles. How many small triangles will you
need for eight rows?
26. In a 3 x 3 grid, there are 14 squares of different sizes.
There are 9 1 x 1 squares, four 2 x 2 squares, and one 3
x 3 square. How many squares of different sizes are in
a 5 x 5 grid?
28. This strategy works when you can make a reasonable
estimate of the answer.
A group of students is building a sailboat. The
students have 48 ft2 of material to make a sail. They
design the sail in the shape of a right angle. Find the
length of the base and height.
1.5 x
x
29. Understand
The height is 1 and ½ times more than the base.
Plan
Test possible dimensions where the height is 1 and ½ times more
than the base.
Carry Out
The formula for area of triangle is : ½ bh
So guess a few height/base
6 base 9 height
10 base 15 height
What else could you try?
30. Did you try 8 base and 12 height?
½( 8) (12) = 48
31. The width of a rectangle is 4 cm less than its length.
The area of the rectangle is 96 cm2. Find the length
and width of the rectangle.
x
x-4
Area = 96 cm2
32. Answer: 12 cm and 8 cm
12 cm
8 cm
Area = l w
= 12(8)
= 96 cm2
33. Exit Ticket: A dance floor is a square with an area of
1,444 square feet. What are the dimensions of the
dance floor? Try systematic guess. Answer: 38 x 38
34. You have $10 saved and plan to save an additional $2
each week. How much will you have after 7 weeks?
Make a table Answer: $24
When you simplify 10347, what is the digit in the ones
place? Answer: 0 (use work a simpler problem)
35. You can use this strategy to simulate a problem. Use a
coin, spinner, or number cube.
We use this in probability quite often!
A cat is expecting a litter of four kittens. The probability of
male and female kittens are equal. What is the probability
that the litter contains three females and one male?
We can use a head and tail simulation since that is close to
simulating male and female (only two options available).
36. Understand
Your goal is to find the EXPERIMENTAL PROBABILITY that a litter
of four kittens contains 3 females and 1 male.
Plan
Act out the problem (if you act it out, it is experimental)
Carry Out
When you flipped the coin 100 times, each T was a female and a H
was a male kitten. So of 25 “litters” (4 x 100) the trials showed that 6
of 25 trials had 3 female and 1 male . 6/25=24%
Check
The THEORETICAL PROABILITY IS :
(TTTH), (TTHT), (THTT) and (TTHT) OR 4/16 =25%
37. A sports jersey number has two digits. Even and odd
digits are equally likely. Use a simulation to find the
probability that both digits are even.
38. Answer
What are the possible digits in the first number? 0-9
What are the possible digits in the second number? 0-9
39. If you are given a set of data and asked to draw a
conclusion.
Example: A wildlife preserve surveyed its wolf
population in 1996 and counted 56 wolves. In 2000
there were 40 wolves. In 2002 there were 32 wolves. If
the wolf population changes at a constant rate, in what
year will there be fewer than 15 wolves?
40. Understand
Given the data, predict when the wolves will number less
than 15.
Plan
Find a rate of change. Make a table to check for the rate of
change.
Carry Out
Make a Table
41. Year Wolves
2000 40
2002 40-8=32
2004 32-8=24
2006 24-8=16
At the beginning 0f 2006 there are 16 wolves so we can assume there will be less
than 15 by the end of the year.
42. Check
Set up an equation.
56 wolves-15 wolves=41 wolves
The population of wolves decreases 4 wolves/yr. Let X
represent the number of years until there is 15 wolves.
Solve 4x=41
X is about 10 years. From 1996 -2006 is 10 years. So the
correct answer is 2o06.
43. You are starting a business selling lemonade. You
know that it cost $6 to make 20 cups of lemonade and
$7 to make 30 cups of lemonade. Who much will it
cost to make 50 cups of lemonade?
Set up a table.
48. Some problems seem to have a lot of steps, or a lot of
numbers and mysterious operations.
Try using smaller numbers. This strategy works
finding numerical or geometrical patterns.