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Success Story
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Success Story
It’s not too hard to form the number 9 using three 3’s and any of the four standard
mathematical operations +, –, × and ÷. But can you come up with four different
solutions, each of which uses only one of the four operations? (Other standard
mathematical symbols can be used as needed.)
9
= 3 + 3 + 3
Problems
Grades: 3rd to 5th
Algebraic Thinking
Write and interpret numerical expressions.
Multiply and divide within 100.
3.OA.C.7, 5.OA.A.1
Assign each letter a value
equal to its position in the alphabet (A = 1, B = 2, C = 3, …). Then find the
product value of a word by multiplying the values together. For example, CAT
has a product value of 60, because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.
How many other words can you
find with a product value of 60?
Problems
Grades: 3rd to 5th
Num & Ops Base Ten
Algebraic Thinking
Use place value understanding and properties of operations to perform multidigit arithmetic.
Multiply and divide within 100.
3.OA.C.7, 4.NBT.B.5
The factorial of n is the
product of all positive integers less than or equal to n. It is represented as n!.
An example with n = 8 is
shown below. With that in mind, can you find three sets of numbers (a, b,
c) such that a! × b! = c! and a < b < c < 25?
Problems
Grades: 3rd to 5th
Algebraic Thinking
Multiply and divide within 100.
3.OA.C.7
A
rectangular wooden block (not necessarily a cube) is painted on the outside and
then divided into oneunit cubes. As it happens, the total number of painted
faces equals the total number of unpainted faces. What were the dimensions of
the block before it was painted?
Problems
Grades: 3rd to 5th, 6th to 8th
Measurement & Data
Geometry
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Solve realworld and mathematical problems involving area, surface area, and volume.
5.MD.C.3a, 5.MD.C.3b, 6.G.A.2, 6.G.A.4, 5.MD.C.4, 5.MD.C.5a
The number groups below are the last five digits of the fifth powers
of the numbers 31 through 39. However, the groups aren't in the right
order to represent the fifth powers of 31 through 39 sequentially. Using
only these digits, and without using a calculator, can you place the
groups in the correct order?
35393 

35424 

29151 
24199 

21875 

35168 
54432 

43957 

66176 
Problems
Grades: 6th to 8th, 3rd to 5th
Expression/Equation
Num & Ops Fractions
Apply and extend previous understandings of arithmetic to algebraic expressions.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B.5a, 6.EE.A.1
In the chart, color each square according to the clues below.
 Two positive odd numbers that have a sum of 40 and the largest possible product.
 The smallest square number that is the sum of two non‑zero square numbers.
 The next five numbers in the arithmetic sequence 8, 19, 30, __, __, __, __, __.
 The maximum possible number of givens in a standard 9 × 9 Sudoku grid that does not render a unique solution.
 Two different odd numbers, one of whose digits are the reverse of the other, whose sum is 154.
 The two prime numbers whose product is 4 less than 5
^{2}
.
 In a normal distribution, the percent of values within one standard deviation of the mean.
 The 43
^{rd}
positive even number.
 The first four positive multiples of 4.
 The integer lengths of three sides of a right triangle whose area is 600 square units.
 The value of the sum 2
^{0}
+ 2
^{1}
+ 2
^{2}
+ 2
^{3}
.
 The value of the sum 2
^{0}
+ 2
^{1}
+ 2
^{2}
+ 2
^{3}
+ 2
^{4}
.
Problems
Grades: 6th to 8th, 9th to 12th, 3rd to 5th
Expression/Equation
Functions
Stats & Probability
Num & Ops Base Ten
Algebraic Thinking
Apply and extend previous understandings of arithmetic to algebraic expressions.
Interpreting Functions
Summarize and describe distributions.
Use place value understanding and properties of operations to perform multidigit arithmetic.
Generate and analyze patterns.
Gain familiarity with factors and multiples.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Multiply and divide within 100.
3.OA.C.7, 3.OA.D.9, 3.NBT.A.2, 4.OA.B.4, 4.OA.C.5, 4.NBT.B.4, 4.NBT.B.5, 6.SP.B.5c, HSFIF.A.3, 6.EE.A.1
Tom was born on Thanksgiving Day.
On his seventh birthday, he noticed that Thanksgiving had never fallen on
his birthday. How old will he be when he finally has a Thanksgiving birthday?
Problems
If
x^{2} + y^{2} = 36, xy = 32,
what is the positive value of x + y?
Problems
Grades: 9th to 12th
Functions
Algebra
Interpreting Functions
Reasoning with Equations and Inequalities
HSAREI.B.4b, HSFIF.C.8a
In the diagram at left, three different line segments each divide a quartercircle
into two regions of equal area. Rank those three segments from shortest to
longest.
Problems
The numbers 1 through 9 are
placed along the sides of the following triangle so that each side has the same
sum. However, three of the nine numbers are covered. What number is in the
circle with the question mark?
Problems
How can a cabinetmaker, using straightline cuts, saw the two oval
frames into parts that will form a circular tabletop from the parts with no
waste?
Problems
Grades: 3rd to 5th
Geometry
Classify twodimensional figures into categories based on their properties.
5.G.B.4
Every day in a non‑leap year, John took a different path from home to his favorite
store. He walked on the grid of streets shown at left, and he only walked north
or east along each street. His home is in the lower left corner of the diagram.
He started on January 1, and on December 31 he took the last possible path. At
what intersection is his favorite store located?
Problems
Make a square with 9 dots as shown. Cross all the dots with 4
straight lines without taking your pencil off the paper.
Problems
Grades: 3rd to 5th
Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
4.G.A.1
What
is the smallest positive number with exactly ten positive integer divisors?
And what is the next one after that?
Problems
Grades: 3rd to 5th
Algebraic Thinking
Gain familiarity with factors and multiples.
4.OA.B.4
Two
chess players compete in a bestoffive match. If Chekmatova has a 60% chance
of winning any particular game, what is the likelihood that she will win the
match?
Problems
Grades: 9th to 12th, 6th to 8th
Stats & Probability
Conditional Probability and the Rules of Probability
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.C.5, 7.SP.C.7a, 7.SP.C.8a, 7.SP.C.8b, HSSCP.B.8, HSSCP.B.9
When the ends of the rope at left are pulled in opposite directions, how many knots will be formed along the rope's length?
Problems
IlluminAir
is a small international airline that provides service between Toronto,
Ontario; Reston, Virginia; and Doha, Qatar. There are 17 different routes from Doha to Reston, including those that go
through Toronto. There are 11 different routes from Reston to Toronto,
including those that go through Doha. How many routes are there from Doha to
Toronto?
Problems
A rectangular wooden block (not necessarily a cube) is painted on the
outside and then divided into oneunit cubes. It turns out that exactly
half of the cubes have paint on them. What were the dimensions of the
block before it was painted?
Problems
Grades: 3rd to 5th, 6th to 8th
Measurement & Data
Geometry
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
Solve realworld and mathematical problems involving area, surface area, and volume.
5.MD.C.3a, 5.MD.C.3b, 6.G.A.2, 6.G.A.4, 5.MD.C.4, 5.MD.C.5a