Numbers and Operations in Base Ten-multiplication and division of decimals
5.NBT
Essential Questions:
Essential Understanding:
What is the relationship between the base ten number system and
place value?
How does the value of a digit change depending on where it is located
in a number?
Students will demonstrate that they understand the value of digits in
multi-digit numbers that include decimals by modeling the digits in
multiple forms and composing and decomposing the digits in ways
that show their value based on the place value system. Students will
demonstrate an ability to fluently multiply and divide multi-digit
numbers with decimals using several strategies that include the
algorithm and use of models and drawings with explanations.
How does multiplying by a power of 10 impact the product or
quotient of a number?
How do models and strategies used with whole number computation
compare with decimal computation?
How does computing with decimal numbers change estimation
strategies?
How can I represent and solve whole number division problems in
multiple ways?
Vocabulary:
Assessment
Place value, decimal, decimal point, patterns, tenths,
thousands, greater than, less than, equal to, compare,
round, hundredths, >,<,=, multiplication, division, product,
factor, multiple, quotient, dividend, divisor
Summative: Combines application, conceptual, and procedural
problems to allow students to demonstrate that they understand the
place value system, powers of 10 and multiplication and division of
multi-digit numbers to the hundredths place.
Guiding questions:
Why is it important to be flexible in the way you solve a problem?
How do you know if your answer is reasonable?
How can solving a problem in more than one way help you find the best strategy
for you?
How do place-value patterns help you compare and order numbers?
What patterns can you describe in the base-10 number system?
Formative:
We will be using a skills checklist as we progress through the lessons
of this unit.
Lesson
Math
Concept
Standard
Skills
Problems to
Pose
Anticipated
Errors
1
Multiplication of
Whole Numbers
(multi-digit/ not
assess for fluency at
this time)
5.NBT.B5
•
•
Estimation
Models/Strategi
es
Introduce and
relate to
Standard
Algorithm
98 x 34 (basic
problem that all
students can
contribute to)
•
Problems in
context
•
Why does
standard
algorithm make
sense
Standard algorithm
Place holders
Number sense
Reasonableness
Double checking
with other strategies
Multiplication of to
.01
5.NBT.5
5.NBT7
Estimation
Models
Number
lines/multiple
strategies
Relating to
whole number
multiplication
Problems in context
tenths by tenths
Tenths by
hundredths
(not hundredths by
hundredths)
Pg.350 from Van De
Walle text
Number sense with
what to do with
decimal
Estimation
Fact families
Relationships
between
multiplication
and division
4 digit dividends
and 2 digit
divisors
Variety of
strategies
Problems where
there is no
remainder
Not being solid in
multiplication
2
•
•
•
•
•
3
Relating whole
number division to
whole number
multiplication
5.NBT.6
•
•
•
•
•
4
Problems in context
Pre-conceived
notions of what
multiplying means
(doesn’t always
mean getting bigger)
Explanation of what
division means
Large numbers
Double checking
Lesson
Math
Concept
Standard
Skills
Problems to
Pose
Anticipated
Errors
4
Interpreting
Remainders
5.NBT.6
•
•
Variety of Word
Problems with
remainders that are
interpreted in
different ways
(round up, round
down, use the
remainder, turn
remainder into
fraction)
What does the
remainder mean and
why?
•
Divisibility rules
Interpreting
remainders
(turning
remainder into
fractions
Problem Solving
5
Dividing with
decimals up to .01
5.NBT.7
•
•
•
•
•
Estimation
Models
Number lines
Explanations
Strategies (not
needing to be
standard
algorithm)
Word problems in
context
Smaller number with
decimals
What do we do with
the decimal and why
Explaining and using
models
Pre-conceived
notions of division
6
Which operation
to use in context
5.NBT.B5-7
• Interpret
problems
• Problem Solving
Variety of application
word
problems(division,
multiplication, whole
number, decimals)
Difference between
division and
multiplication (whole
numbers and
decimals)
Why they chose their
operations
Computational
errors