LESPA
For each day, write or draw a short response to one of the following:
-- What did we do in class today?
-- How did this connect to something I learned before?
-- What was one thing I learned today?
-- Where might this be useful outside of math class?
-- What was one thing that was confusing today?
-- What is something I’d like my math teachers to know?
-- How would I explain what we did today to someone
who was absent?
-- What was a mistake I made that I will try to correct?
-- What was the best part of school today?
-- Write a haiku that talks about today’s math class.
1.
7.
2.
8.
3.
9.
4.
10.
5.
6.
Name: ____________________________________________________________ Period: ________ Date: ______________
LESPA 1: Translating To/From Math and English
1a. Write three words that are clues to do these operations.
Addition: _____________________________
Subtraction: _______________________________________
1b. Write two words that are clues to these operations.
Multiplication: ________________________
Division: ________________________________________
2. What are the two words that are clues to switch? __________________________________________________
3. Translate, using x as “the number.”
a) the number increased by 5
d) 5 times the sum of x and 2
b) four times a number
e) 3 subtracted from three times the difference of 2 and
a number
c) 8 less than twice a quantity
f) 9 times the number decreased by 15
4. Translate, using x as “the number.” You do not need to solve!
a) Four times a number decreased by 10 yields 30.
d) Sixteen decreased by twice a number yields four more
than twice the number.
b) Seven less than three times a number is equivalent to
25.
e) Three times the sum of a number and 8 is equivalent
to 15 less than four times the number.
c) Eight times a number decreased by 14 is the same as 5
less than four times the number.
f) The total of seven times a number and 8 is equal to 16
decreased by four times a number.
5. Use the variables given to translate. You do not need to solve!
a) The number is x.
c) The first number is n.
Seven times a number decreased by 19 yields 40.
The second number is 2n + 3.
Twice the first number increased by three times the
second yields 49.
b) The number is n.
Four times the number increased by 10 is equivalent to 5
less than the number.
d) The first number is p. The second number is two more
than three times the first. The sum of these numbers is
16.
Name: ___________________________________________________________ Period: __________ Date: ______________
LESPA 2: Proving / Disproving Possible Answers
There are 2 consecutive integers (numbers in a row). Triple the first increased by 5 times the second yields 45. What
are the numbers?
Claim: 1st number is 10 and the second is 11.
Prove or disprove the following answers.
1. Four times a number increased by 3 yields 1 less than
five times the number. What’s the number?
Claim: The number is 4.
2. Two times the difference of a number and 4 yields 8.
What is the number?
Claim: The number is 6.
3. There are two consecutive integers (numbers in a
row). Five times the first increased by twice the second
equals 44. What are the numbers?
Claim: The first is 6 and the second is 7.
4. There are three consecutive integers in a row. Five
times the first decreased by twice the second is 3 less
than twice the third. What are the numbers?
Claim: The first is 8. The second is 9. The third is 10.
5. The Vipers flag football team* won by 11. Both teams
together scored 45 points together. How many did they
score?
Claim: The Vipers won 28 to 17.
6. Stephen Curry scores 2-point layups and 3-point
jumpers. He makes 1 more layup than jumpers. If he
scores 27 points, how many of each did he get?
Claim: He scored 7 three-pointers and 3 two-pointers.
7. Aliza has 240 cents in dimes and quarters. She has
twice as many quarters and dimes. How many of each
does she have?
Claim: She has 5 dimes and 10 quarters.
For each of the claims that were wrong, use trial and
error to figure out the right answer.
Name: __________________________________________________________ Period: __________ Date: ______________A
LESPA 3: Trial and Error Contest!
Try to determine the answers to the following questions.
1. Ten times a number decreased by 3 is equivalent to 13
more than twice the number. What is the number?
2. Four times a number decreased by twice the sum of
the number and 1 yields 4. What’s the number?
3. There are two consecutive integers (numbers in a row).
Triple the first increased by five times the second yields
45. What are the numbers?
4. Briana and Jennifer have books. Briana has four more
books than Jennifer. If they have 38 altogether, how
many do they each have?
5. Henry has 310 cents in total. The number of dimes he
has is 5 less than twice the number of quarters. How
many of each does he have?
6. Vanessa buys 5 cookies and 3 brownies. A brownie is
one dollar more than a cookie. If she spends $15, how
much are each?
7. There are three consecutive odd integers (odd
numbers in a row). Two more than twice the first yields
three times the second decreased by the third. What are
the numbers?
8. There are three consecutive integers (numbers in a
row). Six times the first decreased by 4 times the second
is equivalent to 3 more than twice the third. What are the
numbers?
Name: __________________________________________________________ Period: __________ Date: ______________B
LESPA 3: Trial and Error Contest!
Try to determine the answers to the following questions.
1. Ten times a number decreased by 3 is equivalent to 21
more than twice the number. What is the number?
2. Four times a number decreased by twice the sum of
the number and 1 yields 2. What’s the number?
3. There are two consecutive integers (numbers in a row).
Triple the first increased by five times the second yields
37. What are the numbers?
4. Briana and Jennifer have books. Briana has four more
books than Jennifer. If they have 42 altogether, how
many do they each have?
5. Henry has 345 cents in total. The number of dimes he
has is 2 more than twice the number of quarters. How
many of each does he have?
6. Vanessa buys 4 cookies and 2 brownies. A cookie is one
dollar more than a brownie. If she spends $19, how much
are each?
7. There are three consecutive integers (numbers in a
row). Six times the first decreased by 4 times the second
is equivalent to 3 more than twice the third. What are the
numbers?
8. There are three consecutive odd integers (odd
numbers in a row). Two more than twice the first yields
three times the second decreased by the third. What are
the numbers?
Name: ___________________________________________________________ Period: __________ Date: ______________
LESPA 4: What is LESPA?
Three decreased by four times a number yields 9 more than twice the number. What is the number?
Legend:
Proof:
Equation:
Answer:
Solution:
1. A good l_________ tells everyone what ________________________________. A good e___________ models the
situation correctly. A good s____________ finds the correct number(s). A good p______________ convinces
_____________________. A good a_____________ is correct and uses the words of the question.
2. For the following, write ONLY the L and the E. You do not need to SPA!
a) Five times a number decreased by b) Six times a number increased by 4
10 yields 3 less than three times the
is equivalent to 4 times the sum of
number.
the number and 5.
c) There are two numbers, where the
larger number is 1 more than the
smaller. Three times the smaller plus
two times the larger yields 28.
3. Use LESPA to answer the question and show a reader your answer is correct.
a) Ten times a number increased by 4 yields 84. What is the number?
Legend:
Proof:
anEquation:
Answer:
Solution:
b) Five less than four times a number is the same as twice the number increased by 7. What is the number?
Legend:
Proof:
Equation:
Answer:
Solution:
c) Nine times a number increased by twice the sum of the number and 4 yields 52. What is the number?
d) There are two numbers, where the larger number is 2 more than the smaller. Four times the smaller increased by
twice the larger is 34. What is the LARGER number?
Name: ___________________________________________________________ Period: __________ Date: ______________
LESPA 5: Consecutive Integer Problems
There are 2 CIs. Twice the first increased by four times the second is 34. What are the numbers?
Legend:
Proof:
Equation:
Answer:
Solution:
1. Fill in the blanks with the next consecutive integers.
12, ____, _____, ______
-6, _____, _____, ______
n, _______, _______, _______
2. Prove or disprove the claims:
a) There are two consecutive integers. Twice the first
increased by the second yields 16. What are the
numbers?
Claim: The numbers are 5 and 6.
x + 6, ______, ______, _______, ______
y – 2, _____, _______, _______, ______
b) There are three consecutive integers. If the first is
increased by four times the second, the result is 10 times
the third. What is the smallest number?
Claim: The numbers are -3, -2, and -1.
3. Write a legend and an equation. Do not attempt to solve!
a) There are two consecutive integers. Three times the
b) There are three consecutive integers. Five times the
first increased by 10 yields twice the second.
middle number decreased by twice the smallest number
is equivalent to four times the largest.
4. Use LESPA to answer the question and prove that it works.
a) The sum of two consecutive integers is 21. Find the numbers.
b) There are two consecutive integers. Three times the first increased by four times the second yields 39. Find the first
number.
c) Of three consecutive integers, twice the smallest increased by double the middle is 5 more than three times the
largest. What is the middle number?
Name: _________________________________________________________ Period: ___________ Date: _______________
LESPA 6: Consecutive Odd/Even Integers
There are two consecutive even integers. One more than 7 times the first yields one less than 5 times the second. What
is the second number?
1. Fill in the blanks with the next largest desired integers.
Consecutive odd:
5, ____, ____, _____
-11, ____, ____, ____
x, _____, ______, ______, _____
y – 10, _____, _____, _____, _____
b + 3, _____, _____, _____, _____
2. Prove or disprove Timmy’s answers.
a) There are two consecutive even
integers. Four times the first
decreased by three times the second
yields 0. What are the numbers?
Claim: The numbers are 6 and 8.
Consecutive even:
24, ____, ____, _____
-4, ____, ____, ____
x, _____, ______, ______, _____
y – 10, _____, _____, _____, _____
b + 3, _____, _____, _____, _____
b) There are three consecutive odd
integers. Their sum is 21. What is the
largest number?
Claim: The largest number is 9.
c) Abby, Betty, and Caroline have
ages that are three consecutive even
integers. The sum of Abby’s and
Betty’s ages is 5 more than
Caroline’s age. How old are the girls?
Claim: Abby is 6, Betty is 7, and
Caroline is 8.
3. Write a legend and an equation. You don’t need to solve!
a) There are two consecutive even integers. Their sum is b) There are three consecutive odd integers. Twice the
26. What are the numbers?
first increased by five times the second yields 4 less than
3 times the third. What are the numbers?
4. Use LESPA to solve these problems.
a) There are three consecutive even integers. Their sum is 18. What is the middle number?
b) There are two consecutive even integers. Eight times the second yields 40 more than five times the first. What is the
second number?
c) There are three consecutive odd integers. Four times the smallest increased by triple the largest is equal to 12 less
than five times the middle. What is the largest number?
Name: ______________________________________________________________ Period: _________ Date: ____________
LESPA 7: Problems with “Combined” Objects
1a. The words “combined” and “altogether” are keywords for the _______ operation.
1b. Pema has n baseball cards. Chelsea has 3n – 1 cards. How many cards do they have altogether?
2. Prove or disprove Timmy’s answers.
a) Mary and Bob have marbles. Bob has twice the number
of marbles Mary has. If they have 30 marbles altogether,
how many does Mary have?
Claim: Mary has 10 and Bob has 20.
b) Emely’s age is one more than twice Logan’s age. If
their ages together are 16, how old is Logan?
Claim: Logan is 6 years old.
3. Write a legend and an equation for each of these situations.
a) Genesis has big stamps and little stamps. The number
b) Raymond and Michael are eating muffins. The number
of big stamps is 4 more than the number of little stamps. of muffins Michael eats is one less than nine times the
If she has 22 stamps altogether, how many little ones
number of muffins Raymond eats. If they’ve eaten 29
does she have?
muffins combined, how many muffins did they each eat?
4. Solve using LESPA.
a) Beyonce and Destiny have marbles. Beyonce has three more marbles than Destiny. If they have 27 marbles
combined, how many do they each have?
b) Odette’s age is 3 less than three times Shahid’s age. If their ages together are 21, how old is Shahid?
c) Briana, Yoli, and Juanita have candy. Briana has five more than Yoli. Juanita has three times as much as Yoli. If they
have 45 candies combined, how many do they each have?
d) Ahmed, Bryan, and Crystal are eating marshmallows. Bryan ate four more marshmallows than Ahmed. Crystal ate
twice as many marshmallows as Bryan. If they ate 40 marshmallows combined, how many marshmallows did Bryan eat?
Name: ________________________________________________________ Period: __________ Date: _______________
LESPA 8: Coin Problems
1. When we want to find how much money we have in coins, we use the formula ______________________.
2. How many cents are each of the following worth? Write out your calculation.
5 dimes
7 nickels
12 pennies
6 quarters
5 dimes and 7 nickels
3 nickels and 6 dimes
2 quarters and 4 nickels
4 nickels, 3 quarters, and 4 dimes
10 pennies, 4 dimes, 2 nickels
3. How much are each of the following worth? In terms of the variable?
n nickels
d dimes
q quarters
p pennies
n nickels and 3 dimes
d dimes and 2 quarters
n nickels and 2n dimes
d dimes and d + 3 quarters
q quarters and 2q + 1 dimes
p pennies and 4p – 3 nickels
n nickels, n + 3 dimes, and 2n – 4 quarters
q quarters, 2n – 3 dimes, and 3n + 1
nickels
Bianca has dimes and quarters. She has twice as many dimes as quarters. If she has 180 cents, how many dimes does
she have?
Legend:
Proof:
Equation:
Answer:
Solution:
2. Prove or disprove these claims.
a) Kevaughn has two more nickels than dimes. If he has
100 cents, how many of each does he have?
Claim: Kevaughn has 6 dimes and 8 nickels.
3. Write a legend and an equation.
a) Caroline has dimes and nickels. If she has 5 more
dimes than nickels and has 80 cents total, how many of
each does she have?
b) Sherley has nickels and quarters. She has 3 fewer
quarters than nickels. If she has 105 cents total, how
many quarters does she have?
Claim: Sherley has 6 quarters and 3 nickels.
b) Cheyanne has 155 cents in pennies, nickels, and
dimes. The number of nickels she has is one more than
the number of pennies. She has twice as many dimes as
pennies. How many nickels does she have?
4. Solve using LESPA.
a) Maria has dimes and nickels. If she has 3 more dimes than nickels and has 105 cents total, how many of each does
she have?
Legend:
Proof:
Equation:
Answer:
Solution:
b) Mamadou has three times the number of pennies as quarters. If he has 168 cents in total, how many pennies does he
have?
c) Luis has 150 cents nickels and quarters. If the number of nickels he has is 5 less than the twice the number of
quarters, how many nickels does he have?
d) Jasi has 305 cents in nickels, dimes, and quarters. The number of nickels he has is 7 more than the number of dimes.
The number of quarters he has is one less than the number of nickels. How many dimes does he have?
Name: ___________________________________________________________ Period: __________ Date: _____________
LESPA 9: Value Problems
How much are 5 two-point questions and 3 five-point
questions worth?
How much are 4 stamps each costing x stamps worth?
How much are 3 seven-cent stamps and 5 four-cent
stamps worth?
How much are 5 shirts that cost x dollars and 7 shirts
that cost x + 5 dollars worth?
How much are x 7-cent stamps worth?
How much are 2 pairs of Nikes worth n dollars and 4 pairs
of Adidas worth n – 30 dollars worth?
2. Write a legend and an equation. You do not need to solve!
a) Binta has 3 small stamps and 7 large stamps. The large b) Mariana has cards worth $5 and $8. The number of
ones are worth one cent more than the small ones. If
expensive cards is two more than three times the
they are worth 47 cents together, how much is a large
number of cheaper cards she has. If the cards are worth
stamp?
$74, how many of each does she have?
3. Solve using LESPA.
a) Wei Bin has some cards worth $3 and some cards worth $4. The number of $4 cards is one more than the number of
$3 cards. If all the cards together are worth $39, how many $4 cards are there?
b) Brian spent $37 four small chocolate bars and five large ones. If the cost of a large is one less than twice the
smaller, how much is a large chocolate bar?
c) Tiffany is buying pizza for her friends. She is buying four plain slices and six sausage slices. A sausage slice is one
dollar more than a plain. If she spends $31 on all of them, how much is a plain slice?