CARE
Curriculum Assessment Remediation Enrichment
Grade 5
Mathematics CARE Package Test 2
Domain(s)
Operations and Algebraic Thinking
Cluster(s)
Write and interpret numeric expressions
Number and Operations in Base Ten
Perform operations with multi-digit whole
numbers and with decimals to hundredths
Standard(s) MAFS.5.OA.1.1 - Use parenthesis, brackets, or braces in numerical expressions, and
evaluate expressions with these symbols.
MAFS.5.OA.1.2 - Write simple expressions that record calculations with numbers, and
interpret numerical expressions without evaluating them.
MAFS.5.NBT.2.6 - Find whole number quotients of whole numbers with up to four-digit
dividends and two-digit divisors, using strategies based on place value, the properties of
operations, and/or the relationship between multiplication and division. Illustrate and
explain the calculation by using equations, rectangular arrays, and/or area models.
CURRICULUM
The intended purpose of this performance task is for teachers to engage students in a class discussion
and utilize think aloud strategies. Students should be encouraged to work together in small groups as
the teacher models problem solving strategies through each part of the performance task. (Not intended
to be used as a stand-alone worksheet)
Task:
Ricky’s weekly income from mowing lawns is $84. Khaveta’s weekly income from pulling weeds is
$62. Each of them put half of their weekly income into their savings account at the bank. They want to
find out how many weeks of work it will take them to buy a new lawn shed that costs $365.
A.
Write 2 expressions to show how much money each person has in their savings account at the
end of the first week. Use parentheses.
*Use this as an opportunity to discuss “half” and ways to “take half” of something.
Ricky has: ___($84 – ½ x $84) or [$84 - ($84÷2)] or ($84 - $42)
Khaveta has: ___($62 – ½ x $62) or [$62 - ($62÷2)] or ($62 - $31)
B.
Ricky and Khaveta decide that they want to put their money together to buy a new lawn shed.
Write an expression to show how much money they have each week after contributing to their
savings accounts. Explain.
___($84 - $42) + ($62 - $31); Possible Explanation: Add the amount of money Ricky has left
after putting money in his savings account to the amount of money Khaveta has left after putting
money in her savings account.
C.
The lawn shed Ricky and Khaveta want to buy costs $365. Write an expression to show how
many weeks it will take them to save enough money to buy the lawn shed. Use parentheses and
brackets in your expression. Then evaluate the expression.
$365 ÷ [($84-$42) +($62-$31)]
$365 ÷ [$42 + $31]
$365 ÷ $73
5 Weeks; It will take them 5 weeks to save the money for their new lawn shed.
Teacher notes:
Students need to understand how to use the order of operations to evaluate numerical expressions,
algebraic expressions, and ultimately to solve equations.
Common Error: When using “PEMDAS”, students need to know that this is not always the order in
which operations are performed.
Students need to learn the fundamentals of the order of operations (parenthesis first, then
multiplication OR division from left to right, then addition OR subtraction from left to right).
Parenthesis in an expression or an equation function as grouping symbols. Expressions and equations
may contain multiple grouping symbols (parenthesis ( ), brackets [ ], and braces { }). When working
with multiple grouping symbols, students must work from the innermost set to the outermost set.
Optional Sample Rubric: Can be used for part or all of task
Not yet: Student shows evidence of
misunderstanding, incorrect concept or procedure.
Got It: Student essentially understands the target
concept.
1 Unsatisfactory:
Little Accomplishment
3 Proficient:
Substantial
Accomplishment
The task is attempted
and some mathematical
effort is made. There
may be fragments of
accomplishment but
little or no success.
Further teaching is
required.
2 Marginal:
Partial
Accomplishment
4 Excellent:
Full Accomplishment
Strategy and execution
Student could work to full meet the content, process,
accomplishment with
and qualitative demands of
minimal feedback from
the task or concept. Student
teacher. Errors are minor. can communicate ideas.
Teacher is confident that
May have minor errors that
understanding is adequate do not impact the
to accomplish the
mathematics.
objective with minimal
assistance.
Adapted from Van de Walle, J. (2004) Elementary and Middle School Mathematics: Teaching
Developmentally. Boston: Pearson Education, 65
Part of the task is
accomplished, but there
is lack of evidence of
understanding or
evidence of not
understanding. Further
teaching is required.
ASSESSMENT
The Mini-MAF includes standards MAFS.5.OA.1.1, MAFS.5.OA.1.2, and MAFS.5.NBT.2.6. Use the
following table to assist in remediation efforts.
Questions
1,2,9,10
Standards
MAFS.5.OA.1.1
4,5,7,11
3,6,8,12
MAFS.5.OA.1.2
MAFS.5.NBT.2.6
Go Math Lesson
Lesson(s) 1.11 Evaluate Numerical Expressions; 1.12
Grouping Symbols
Lesson 1.10 Numerical Expressions
Lesson(s) 1.8 Relate Multiplication to Division; 1.9
Multiplication and Division; 2.1 Place the First Digit; 2.2
Divide by 1-Digit Divisors; 2.3 Division with 2-Digit
Divisors; 2.4 Partial Quotients; 2.5 Estimate with 2-Digit
Divisors; 2.6 Divide by 2-Digit Divisors; 2.8 Adjust
Quotients
REMEDIATION / RETEACH
Foundational Vocabulary
Compatible numbers
Dividend
Divisor
Estimate
Factor
Partial Quotients
Product
Quotient
Remainder
Key Vocabulary
Inverse operations
Numerical expression
Evaluate
Order of operations
The words above should be included on your “word wall”. These words should be “student friendly”,
providing visual clues to enhance their meaning. This could be a small group activity, allowing students
to create the word cards to be added to the wall. (ESOL: D5 - word wall / ESE: provide visual aids
/graphics/pre & post organizers, teach through manipulatives, pre-teach vocabulary,
model/demonstrate/simulate concepts)
Activity 1
Present the problem 6 + [3 x (7-6)] to students.
Ask students to identify the grouping symbols from innermost to outermost. parentheses, brackets
Ask students to make a plan to solve the problem by naming each step they will take to simplify the
expression. First, I will find 7-6. Then, I will multiply the difference by 3. Finally, I will add 6 to the
product.
Students will show their work. Have students simplify the expression by executing their plans.
(ESOL: I1- charts/flowcharts / ESE: provide visual aids /graphics/pre & post organizers, teach through
manipulatives, model/demonstrate/simulate concepts)
6 + [3 x (7-6)] =
6 + [3 x ___ ]
6 + ___
___
Simplify within parentheses.
Simplify within brackets; 1
3
9
Present the problem 6 + [(4+3) X (8-5)] to students.
Ask students to identify the grouping symbols from innermost to outermost. parentheses, brackets
Have students simplify the expression by copying the problem and filling in the blanks. Ask students to
identify what they need to do in each step.
6 + [(4+3) x (8-5)]=
6 + [ ___ x ___ ]
6 +___
___
Simplify within parentheses.
Simplify within brackets; 7 x 3
21
27
Activity 2
Teacher Notes:
You may need to review one-digit division using base-ten blocks and/or model drawing prior to the
following activity. (ESOL: G1 - activating and/or building prior knowledge / ESE: provide visual aids
/graphics/pre & post organizers, teach through manipulatives, model/demonstrate/simulate concepts)
Use base-ten blocks to model the division problem 195 ÷ 13. If base-ten blocks are not available,
students can use dry erase boards or pencil and paper to draw quick pictures (model drawing) to
represent the division problem. (ESOL: G5 - ask clarifying questions, G6 - modeling, G8- think aloud)
•
•
•
•
•
How can these blocks be divided into groups of 13? Possible answer: Arrange the blocks to form
13 equal rows.
How many groups of 13 did you make with the hundred block and 3 tens blocks? 10
How many groups did you make with the rest of the blocks? 5
What do the first and second groups you made represent? partial quotients
How can you use the partial quotients to find the quotient? Add 10 and 5 to get the quotient 15.
195 ÷ 13 (base-ten blocks or model drawing)
Additional Resources
www.math-play.com
www.math-aids.com
www.ixl.com/math/grade-5
ENRICHMENT
Extra for Experts 1
Students challenge each other by using the classic Four Fours puzzle. Students use 4 fours, the
basic operation symbols, as well as grouping symbols to form expressions for the numbers 0-10.
Sample expressions:
4 + (4 x ( 4 ÷ 4)) = 8
4 x 4 ÷ (4 + 4) = 2
*Operations can be used more than once.
This could be used as a game where two students follow the steps above to see who can create the
most expressions for the numbers 0-10 (repeated numbers not counted twice) in a given amount of
time.
Extra for Experts 2
On a 10-section spinner (can use a student made spinner, pencil, and paperclip), label each section
with a digit from 0-9.
Each student (2-3 per group) will spin the pointer six times and record the digits spun. They will use
the six digits to write two division examples with 4-digit dividends and 2-digit divisors. Students
need to find two examples that have quotients that are as close as possible.
This could be used as a game where two students follow the steps above to see who can create
examples with the closest quotients. The student with the closest quotients for each round receives
1 point. The game continues until someone scores 5 points.
See below for student pages
Name: __________________________
Performance Task
Ricky’s weekly income from mowing lawns is $84. Khaveta’s weekly income from pulling weeds is $62.
Each of them put half of their weekly income into their savings account at the bank. They want to find
out how many weeks of work it will take them to buy a new lawn shed that costs $365.
A.
Write 2 expressions to show how much money each person has in their savings account at the end
of the first week. Use parentheses.
B.
Ricky has:
_________________________________________________________
Khaveta has:
_________________________________________________________
Ricky and Khaveta decide that they want to put their money together to buy a new lawn shed.
Write an expression to show how much money they have each week after contributing to their
savings accounts. Explain.
______________________________________________________________________________
______________________________________________________________________________
____________________________________________________________________________
C.
The lawn shed Ricky and Khaveta want to buy costs $365. Write an expression to show how
many weeks it will take them to save enough money to buy the lawn shed. Use parentheses and
brackets in your expression. Then evaluate the expression.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Name: ________________________
Extra for Experts 10-Section Spinner
Students write the numbers 0 - 9 in the sections of the spinner.
Students use a large paperclip and a pencil to complete the spinner.