Download Problem Card #31A Certain biological cells double each hour. Start

Problem Card #31A
Problem Card #31B
Certain biological cells double each
hour. Start with one cell at 2:00 and find
out how many cells there will be by 5:00.
Create a diagram to represent the cell
growth. Include an equation using
exponential notation.
Certain biological cells quadruple each
half hour. Start with one cell at 2:00
and find out how many cells there will
be by 5:00. Create a diagram to
represent the cell growth. Include an
equation using exponential notation.
6.EE.1 I CAN write and evaluate numerical expressions
involving whole-number exponents.
6.EE.1 I CAN write and evaluate numerical expressions
involving whole-number exponents.
Problem Card #32A
Problem Card #32B
On Tuesday, you invited 2 friends to your
party. On Wednesday, each of these
friends invited 2 other friends. This pattern
continued Thursday and Friday. How many
people were invited on Friday? Write the
answer as a power. How many people
were invited in all? Explain the reasoning.
On Tuesday, you invited 3 friends to your
party. On Wednesday, each of these
friends invited 3 other friends. This pattern
continued Thursday and Friday. How
many people were invited on Friday? Write
the answer as a power. How many people
were invited in all? Explain the reasoning.
6.EE.1 I CAN write and evaluate numerical expressions involving
whole-number exponents.
6.EE.1 I CAN write and evaluate numerical expressions
involving whole-number exponents.
Problem Card #33A
Problem Card #33B
Hannah is 3 years younger than Katie. Joey is twice
as old as Hannah. Let k stand for Katie’s age. Write
an expression to represent Hannah’s age. Using k,
write an expression for Joey’s age.
Jeanne has $17 in her piggy bank. How much money
does she need to buy a game that costs $68? Let x
represent the amount of money Jeanne needs. Write
an equation that can represent this problem and then
solve the equation.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers.
Problem Card #34A
Write each sentence as an algebraic equation:
1. A number increased by nine is fifteen.
2. Twice a number is eighteen.
3. Four less than a number is twenty.
4. A number divided by six is eight.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers. Write expressions that record
operations with numbers and with letters standing for numbers.
For example, express the calculation “subtract y from 5” as 5 – y.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers.
Problem Card #34B
Write each sentence as an algebraic equation:
1. Twice a number, decreased by twenty-nine, is
seven.
2. Thirty-two is twice a number increased by eight.
3. The quotient of fifty and five more than a number
is ten.
4. Twelve is sixteen less than four times a number.
6.EE.2 I CAN write, read, and evaluate expressions in which letters
stand for numbers. Write expressions that record operations with
numbers and with letters standing for numbers. For example, express
the calculation “subtract y from 5” as 5 – y.
Problem Card #35A
Problem Card #35B
Eric had $197 in his savings account before he was Write an algebraic equation that correctly represents
paid his weekly salary. His current savings balance each of the 3 given sentences:
5 - 3t = 46
is $429. How much money does Eric earn each
3t - 5 = 46
week? Using s for Eric’s salary, write an expression
to represent Eric’s money.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers.
Problem Card #36A
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers.
Problem Card #36B
Write each sentence as an algebraic equation:
Write each sentence as an algebraic equation:
1. Eleni is x years old. In thirteen years she will
1. Suzanne made a withdrawal of d dollars
be twenty-four years old.
from her savings account. Her old balance
2. Each piece of candy costs 25 cents. The
was $350, and her new balance is $280.
price of h pieces of candy is $2.00.
2. A large pizza pie with 15 slices is shared
among p students so that each student's
share is 3 slices.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers. Write expressions that record
operations with numbers and with letters standing for numbers.
For example, express the calculation “subtract y from 5” as 5 – y.
6.EE.2 I CAN write, read, and evaluate expressions in which
letters stand for numbers. Write expressions that record
operations with numbers and with letters standing for numbers.
For example, express the calculation “subtract y from 5” as 5 –
y.
Problem Card #37A
Generate an equivalent expression for each of the
following:
4 (x - 2)
15x - 24y
x+x+y+y
5x + 2y
5r + (2s + 2t)
6.EE.3 I CAN apply the properties of operations to generate
equivalent expressions. For example, apply the distributive property
to the expression 3 (2 + x) to produce the equivalent expression 6 +
3x; apply the distributive property to the expression 24x + 18y to
produce the equivalent expression 6 (4x + 3y); apply properties of
operations to y + y + y to produce the equivalent expression 3y.
Problem Card #38A
Problem Card #37B
Generate an equivalent expression for each of the
following:
4 (x+ 5)
24x - 36y
x+x+y+y+z+z=
15x + 12y
5r + (4s + 4t)
6.EE.3 I CAN apply the properties of operations to generate
equivalent expressions. For example, apply the distributive property
to the expression 3 (2 + x) to produce the equivalent expression 6 +
3x; apply the distributive property to the expression 24x + 18y to
produce the equivalent expression 6 (4x + 3y); apply properties of
operations to y + y + y to produce the equivalent expression 3y.
Problem Card #38B
In one packet of nuts, there are two different
types of nuts. There are 5 peanuts (p) and 7
cashews (c) in each container. I have 6 packets of
nuts; write two expressions that show how many
nuts I have all together.
In one packet of nuts, there are two different
types of nuts. There are 8 peanuts (p) and 10
almonds (a) in each container. I have 4 packets of
nuts; write two expressions that show how many
nuts I have all together.
6.EE.3 I CAN apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the expression 3 (2
+ x) to produce the equivalent expression 6 + 3x; apply the distributive property
to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y);
apply properties of operations to y + y + y to produce the equivalent expression
3y.
6.EE.3 I CAN apply the properties of operations to generate equivalent
expressions. For example, apply the distributive property to the expression 3
(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive
property to the expression 24x + 18y to produce the equivalent expression 6
(4x + 3y); apply properties of operations to y + y + y to produce the equivalent
expression 3y.
Problem Card #39A
Problem Card #39B
How many different equivalent expressions for the How many different equivalent expressions for
number 48 can you write? Use at least two
the number 36 can you write? Use at least two
operations and verify that your notation is correct. operations and verify that your notation is
correct.
6.EE.4 I CAN identify when two expressions are equivalent (i.e.,
when the two expressions name the same number regardless of
which value is substituted into them). For example, the expressions y
+ y + y and 3y are equivalent because they name the same number
regardless of which number y stands for.
Problem Card #40A
6.EE.4 I CAN identify when two expressions are equivalent (i.e.,
when the two expressions name the same number regardless of
which value is substituted into them). For example, the expressions y
+ y + y and 3y are equivalent because they name the same number
regardless of which number y stands for.
Problem Card #40B
Jan has $500 in a savings account at the beginning
of the summer. She wants to have at least $200 in
the account by the end of the summer. She
withdraws $25 each week for food and fun.
• Write an inequality that represents Jan’s situation.
Becky has $300 in a savings account at the
beginning of the summer. She wants to have at
least $100 in the account by the end of the summer.
She withdraws $20 each week for food and fun.
• Write an inequality that represents Becky’s situation.
• How many weeks can Jan withdraw money from her
account?
• How many weeks can Becky withdraw money from
her account?
6.EE.5 I CAN understand solving an equation or inequality as a
process of answering a question: which values from a specified set, if
any, make the equation or inequality true? Use substitution to
determine whether a given number in a specified set makes an
equation or inequality true.
6.EE.5 I CAN understand solving an equation or inequality as a
process of answering a question: which values from a specified set,
if any, make the equation or inequality true? Use substitution to
determine whether a given number in a specified set makes an
equation or inequality true.
Problem Card #41A
Problem Card #41B
An appliance repairman charges $50 for coming to a home
for a service call and $40 an hour for the service. Write an
expression to represent her earnings for h hours. Use the
expression to solve how much the total cost is for 1, 2, and
3 hour jobs.
An appliance repairman charges $100 for coming to a
home for a service call and $50 an hour for the service.
Write an expression to represent her earnings for h hours.
Use the expression to solve how much the total cost is for
2, 3, and 4 hour jobs.
6.EE.6 I CAN use variables to represent numbers and write
expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number or,
depending on the purpose at hand, any number in a specified set.
6.EE.6 I CAN use variables to represent numbers and write
expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number
or, depending on the purpose at hand, any number in a specified
set.
Problem Card #42A
Problem Card #42B
Sally delivered 7 newspapers and John delivered x
number of newspapers. Write an expression showing
how many total newspapers were delivered. Write an
expression to represent how many John delivered if
Sally delivered seven more newspapers than John.
6.EE.6 I CAN use variables to represent numbers and write
expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number or,
depending on the purpose at hand, any number in a specified set.
Sally delivered 9 newspapers and John delivered x
number of newspapers. Write an expression showing
how many total newspapers were delivered. Write an
expression to represent how many John delivered if
Sally delivered 2 more newspapers than John.
6.EE.6 I CAN use variables to represent numbers and write
expressions when solving a real-world or mathematical problem;
understand that a variable can represent an unknown number
or, depending on the purpose at hand, any number in a specified
set.
Problem Card #43A
Problem Card #43B
Write an equation to represent these situations and solve.
1. There were some grapes on the table. Logan ate
1/6 of them. He ate 5 grapes. How many grapes
were on the table?
2. Angela bought 5 shirts that each cost the same
amount. She spent $34.65. How much did she
spend on each shirt?
Write an equation to represent these situations and solve.
1. There were some grapes on the table. Logan ate
1/3 of them. He ate 18 grapes. How many grapes
were on the table?
2. Angela bought 3 shirts that each cost the same
amount. She spent $42. How much did she spend
on each shirt?
6.EE.7 I CAN solve real-world and mathematical problems by
writing and solving equations of the form x + p = q and px = q for
cases in which p, q and x are all nonnegative rational numbers.
6.EE.7 I CAN solve real-world and mathematical problems by
writing and solving equations of the form x + p = q and px = q for
cases in which p, q and x are all nonnegative rational numbers.
Problem Card #44A
Problem Card #44B
Water boils at 100ºC. Write an inequality that
represents all the temperatures at which
water does not boil. Represent the solution
on a number line.
Water boils at 32ºF. Write an inequality that
represents all the temperatures at which
water does not boil. Represent the solution
on a number line.
6.EE.8 I CAN write an inequality of the form x > c or x < c to
represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of the form x
> c or x < c have infinitely many solutions; represent solutions of
such inequalities on number line diagrams.
6.EE.8 I CAN write an inequality of the form x > c or x < c to
represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of the form x
> c or x < c have infinitely many solutions; represent solutions of
such inequalities on number line diagrams.
Problem Card #45A
Imagine that you are training for a 13-mile race. On the
first day you run 1.5 miles. Each day you run 0.5 mile
longer than you ran on the previous day. How many
days will it take you to work up to 13 miles? Create a
table, graph, and equation and explain the relationship
between the dependent and independent variables.
6.EE.9 I CAN use variables to represent two quantities in a real-world
problem that change in relationship to one another; write an equation to
express one quantity, thought of as the dependent variable, in terms of
the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using
graphs and tables, and relate these to the equation.
Problem Card #45B
If a jar had 4 pennies inside, and you added 7 pennies
each day, how many pennies will there be after day
one? Day two? Day three? Day ten? Day one hundred?
Create a table and graph the results. Also identify the
equation for this situation (p = 7d + 4).
6.EE.9 I CAN use variables to represent two quantities in a real-world
problem that change in relationship to one another; write an equation to
express one quantity, thought of as the dependent variable, in terms of
the other quantity, thought of as the independent variable. Analyze the
relationship between the dependent and independent variables using
graphs and tables, and relate these to the equation.