Download Number in Base 10

Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
4.NBT. 1 (Unit 2, Unit 4)
Recognize that in a multidigit whole number, a digit
in one place represents ten
times what it represents in
the place to its right. For
example, recognize that 700
÷ 70=10 by applying
concepts of place value
and division.
4.NBT.2 (Unit 2) Read and
write multi-digit whole
numbers using base-ten
numerals, number names,
and expanded form.
Compare two multi-digit
numbers based on meaning
of the digits in each place,
using >, =, and < symbols to
record the results of
comparisons.
4.NBT.3 (Unit 2, Unit 5) Use
place value understanding
to round multi-digit whole
numbers to any place.
5th Grade CCSS
5.NBT.1(Unit5)
Recognize that in a multi-digit
number, a digit in one place
represents 10 times as much as it
represents in the place to its right
and 1/10 of what it represents in
the place to its left.
5.NBT.2(Unit 5)
Explain patterns in the number of
zeros of the product when
multiplying a number by powers of
10, and explain patterns in the
placement of the decimal point
when a decimal is multiplied or
divided by a power of 10. Use
whole-number exponents to
denote powers of 10.
Progressions
Foundational Knowledge of Decimals:
Students should have a strong understanding
of the connection between fractions and
decimals. They should also be able to
understand and explain that decimals are
an extension of the base-ten system.
Students should understand that the value of
each place is ten times the value of the
place to the right (moving to the left the
numbers are increasing 10 times). When
moving to the right, the value of each place
is divided by 10.
Students should understand and be able to
explain the following:

When one factor in a multiplication
sentence is a multiple of 10 you can use
your understanding of place value
patterns and basic facts to find the
product.

Why can you “add zeros” when
multiplying by powers or multiples of 10?
6th Grade CCSS
6.NS.5 Understand that positive
and negative numbers are used
together to describe quantities
having opposite directions or
values (e.g., temperature
above/below zero, elevation
above/below sea level,
credits/debits, positive/negative
electric charge); use positive
and negative numbers to
represent quantities in realworld contexts, explaining the
meaning of 0 in each situation.
6.NS.2 Fluently divide multi-digit
numbers using the standard
algorithm.
6.NS.3 Fluently add, subtract,
multiply, and divide multi-digit
decimals using the standard
algorithm for each operation.
Proof/Reasoning that students should know:
Example: 30x600=(3x10) x (6x100)
=(3x6) x (10x100)
= 18x1,000
=18,000
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.
Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
4.NBT.2 (Unit 2) Read and
write multi-digit whole
numbers using base-ten
numerals, number names,
and expanded form.
Compare two multi-digit
numbers based on meaning
of the digits in each place,
using >, =, and < symbols to
record the results of
comparisons.
5th Grade CCSS
5.NBT.3(Unit 5)
Read, write and compare
decimals to thousandths.
a. Read and write decimals to the
thousandths using base-ten
numerals, number names, and
expanded form, e.g. 347.392 = 3 x
100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x
(1/100) + 2 x (1/1000).
b. Compare two decimals to
thousandths based on meanings of
the digits in each place, using >, =,
and < symbols to record the results
of comparisons.
Progressions
Comparing decimals:
Students should know that when
comparing decimals they should
compare like places, beginning in the
place with the highest value. This will
always work because of the structure of
the base-ten system. Example: A tenth
is greater than any number made of only
hundredths because once you have ten
hundredths it has to be recorded as 0.1
or one tenth.
For example:
0.12 > 0.099 because 12 hundredth has
one tenth while ninety nine thousandths
has zero tenths.
6th Grade CCSS
Understand ordering and absolute
value of rational numbers.
6.NS.C.7a Interpret statements of
inequality as statements about the
relative position of two numbers on a
number line diagram. For example,
interpret –3 > –7 as a statement that –
3 is located to the right of –7 on a
number line oriented from left to right.
6.NS.C.7b Write, interpret, and explain
statements of order for rational
numbers in real-world contexts. For
example, write –3 oC > –7 oC to
express the fact that –3 oC is warmer
than –7 oC.
6.NS.C.7c Understand the absolute
value of a rational number as its
distance from 0 on the number line;
interpret absolute value as
magnitude for a positive or negative
quantity in a real-world situation. For
example, for an account balance of
–30 dollars, write |–30| = 30 to
describe the size of the debt in
dollars.
6.NS.C.7d Distinguish comparisons of
absolute value from statements
about order. For example, recognize
that an account balance less than –
30 dollars represents a debt greater
than 30 dollars.
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.
Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
5th Grade CCSS
4.NBT.3 (Unit 2, Unit 5) Use
place value understanding
to round multi-digit whole
numbers to any place.
5.NBT.4 (Unit 5)
Use place value understanding to
round decimals to any place.
4.NBT.5 (Unit 1) Multiply a
whole number of up to four
digits by a one-digit whole
number, and multiply two
two digits numbers, using
strategies based on place
value and the properties of
operations. Illustrate and
explain the calculation by
using equations, rectangular
arrays, and/or area models.
5.NBT.5(Units 2 and 9)
Fluently multiply multi-digit whole
numbers using the standard
algorithm.
Progressions
6th Grade CCSS
Make sure that students are fluent with rounding
to the nearest whole. This will help students make
sense of adding, subtracting, multiplying, and
dividing decimals because estimates will help
them to determine if their answers are
reasonable.
Work toward fluency: Connect to area models,
open arrays, and the standard algorithm.
Example: 15x14= 210
Open Array
Area Model:
10
+ 5
100
50
40
20
6.NS.2 Fluently divide multi-digit
numbers using the standard
algorithm.
6.NS.3 Fluently add, subtract,
multiply, and divide multi-digit
decimals using the standard
algorithm for each operation.

10
+


4


Both the area model and open array show
100+50+40+20=210 so 15x14=210
The standard algorithm also connects because the
bottom of the area model and open array show
40+20=60 just like the first row in the standard algorithm.
The top of the area model and open array show
100+50=150 just like the second row of the standard
algorithm. Both result in adding the products of
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
2
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.
15
X14
60
+150
Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
5th Grade CCSS
Progressions
6th Grade CCSS
decomposed facts to find the actual product of the
original equation 15x14.
Standard Algorithm
4.NBT.5 (Unit 1) Multiply a whole
number of up to four digits by a
one-digit whole number, and
multiply two two digits numbers,
using strategies based on place
value and the properties of
operations. Illustrate and
explain the calculation by using
equations, rectangular arrays,
and/or area models.
4.NBT.6 (Unit 1) Find whole
number quotients and
remainders with up to four-digit
dividends and one-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
5.NBT.6 (Units 3 and 9)
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.
Students should understand how to decompose division
problems into related division problems. Example:
48÷4=(40÷4) + (8÷4) so 48÷4=10+2 or 12
Students should completely understand simple division
patterns using multiples of 10 and 100 in order to solve
larger division problems.
Students should understand how to use open arrays to
decompose larger dividends based on place value.
Example: 120÷4=30
6.NS.2 Fluently divide multi-digit
numbers using the standard
algorithm.
6.NS.3 Fluently add, subtract,
multiply, and divide multi-digit
decimals using the standard
algorithm for each operation.
10 + 10 + 10 = 30
4
40+
40+
40
=120
Students can also decompose numbers in multiple ways
to divide:
Example 1: 434÷7=62
Using the distributive proerty and partial quotients:
Decomposed Example1
434=420+14=(60x7)+(2x7)=(60+2)x7=62x7
Example 2: 434÷7=62
0r using multiples of 10 (sometimes referred to as
chimney division or partial products)
Decomposed Example 2
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.
Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
5th Grade CCSS
models.
Progressions
434=10x7+20x7+20x7+10x7+2x7=(10+20+20+10+2)x7=62x7
***This is an introductory approach to long division.
Students need to learn to generate close factors for
each place value to work towards using an efficient
strategy and the standard algorithm(6.NS.2).
7
Pictures to support array drawings::51÷3=17
10
3
+
30
4.NBT.4 (Unit 2, Unit 6, Unit 9) Fluently
add and subtract multi-digit whole
numbers using the standard
algorithm.
4.NBT.5 (Unit 1) Multiply a whole
number of up to four digits by a
one-digit whole number, and
multiply two two digits numbers,
using strategies based on place
value and the properties of
operations. Illustrate and explain
the calculation by using equations,
rectangular arrays, and/or area
models.
4.NBT.6 (Unit 1) Find whole number
quotients and remainders with up
to four-digit dividends and one-digit
divisors, using strategies based on
5.NBT.7 (Unit5)
Add, subtract, multiply, and divide
decimals to hundredths, using
concrete models or drawings and
strategies based on place value,
properties of operations, and/or
the relationship between addition
and subtraction; relate the strategy
to a written method and explain
the reasoning used.
7
21
51
4.NF.6 (Unit 8) Use decimal notation
for fractions with denominators 10
or 100. For example, rewrite 0.62 as
62/100; describe a length as 0.62
meters; locate 0.62 on a number
line diagram.
6th Grade CCSS
= 17
Examples
of partial
quotients
using
close
factors
10
3




Adding and Subtracting Decimals:
Make sure students can make whole number
estimates of the decimal equations.
Refer back to the ideas and methods used by
students to add and subtract whole numbers,
including base-ten models, digi-blocks, and the
standard algorithm. Make sure students have the
conceptual understanding that only digits in like
places can be added or subtracted because
they have the same unit value.
Encourage students to explain their strategies
using place value language. Work towards
procedural fluency.
Multiplication and Division:
Students should understand that multiplying two
numbers, when one number is less than 1 can
result in a product smaller than one of the factors.
Students need opportunities to explain that
3x0.7 means three groups with 0.7 in each or
2.1(multiplication as grouping) or 0.7+0.7+0.7=2.1
(multiplication as repeated addition).
Students should understand that when dividing
two decimals the quotient is greater than the
6.NS.2 Fluently divide multi-digit
numbers using the standard
algorithm.
6.NS.3 Fluently add, subtract,
multiply, and divide multi-digit
decimals using the standard
algorithm for each operation.
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.
Fifth Grade CCSS Progressions
5.NBT (Numbers in Base Ten)
4th grade Progression
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.
5th Grade CCSS
Progressions
6th Grade CCSS
dividend and the divisor. Example: 0.5÷0.1 can
be thought of as 0.5-0.1 repeatedly. Five groups
of one tenth can be subtracted so 0.5÷0.1=5
Students can also build area models using baseten models to show multiplication.
The number(s) in parenthesis behind each CCSS indicates the CCPS unit(s) in which the standard is located. See the instructional strategies and expectations in the Instructional
Guide for each indicated unit prior to moving on to the next grade level standard. Resources: Focus in Grade 5: Teaching with Curriculum Focal Points NCTM and Math Matters
Second Edition: Grades K-8 Understanding the Math You Teach Suzanne H. Chapin and Art Johnson.