Download 5th Grade: Unit 1

5th Grade Unit 1
September 9th – October 25th
5th Grade: Unit 1
Curriculum Map: September 9th – October 25th
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September 9th – October 25th
5th Grade Unit 1
Common Core Standards
REVIEW OF GRADE 4 FLUENCY
4.NBT.4
Fluently add and subtract multi digit whole numbers using the standard algorithm.
EXPECTED 5TH GRADE FLUENCY
5.NBT.5
Fluently multiply multi-digit whole numbers using standard algorithm.
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September 9th – October 25th
5th Grade Unit 1
GRADE 3 MEASUREMENT AND DATA
5,OA.2
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating
them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 +
921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Students use their understanding of operations and grouping symbols to write expressions and
interpret the meaning of a numerical expression.
Examples:
• Students write an expression for calculations given in words such as “divide 144 by 12, and
then subtract 7/8.” They write (144 ÷ 12) – 7/8.
Students recognize that 0.5 x (300 ÷ 15) is ½ of (300 ÷ 15) without calculating the quotient.
GRADE 3 NUMBERS AND OPERATIONS IN BASE TEN
5.NBT.2
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.
Students might write:
• 36 x 10 = 36 x 101 = 360
• 36 x 10 x 10 = 36 x 102 = 3600
• 36 x 10 x 10 x 10 = 36 x 103 = 36,000
• 36 x 10 x 10 x 10 x 10 = 36 x 104 = 360,000
Students might think and/or say:


I noticed that every time, I multiplied by 10 I added a zero to the end of the number. That makes
sense because each digit’s value became 10 times larger. To make a digit 10 times larger, I
have to move it one place value to the left.
When I multiplied 36 by 10, the 30 became 300. The 6 became 60 or the 36 became 360. So I
had to add a zero at the end to have the 3 represent 3 one-hundreds (instead of 3 tens) and the
6 represents 6 tens (instead of 6 ones).
Students should be able to use the same type of reasoning as above to explain why the following
multiplication and division problem by powers of 10 make sense.
• 523 x 103= 523,000 The place value of 523 is increased by 3 places.
• 5.223 x 102 = 522.3 The place value of 5.223 is increased by 2 places.
• 52.3 x 10 = 5.23 The place value of 52.3 is decreased by one place.
Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and
5.NBT.3
expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ×
(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.
Students build on the understanding they developed in fourth grade to read, write, and compare decimals to
thousandths. They connect their prior experiences with using decimal notation for fractions and addition of
fractions with denominators of 10 and 100. They use concrete models and number lines to extend this
understanding to decimals to the thousandths. Models may include base ten blocks, place value charts, grids,
pictures, drawings, manipulatives, technology-based, etc. They read decimals using fractional language and write
decimals in fractional form, as well as in expanded notation as show in the standard 3a. This investigation leads
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5th Grade Unit 1
September 9th – October 25th
them to understanding equivalence of decimals (0.8 = 0.80 = 0.800).
Use place value understanding to round decimals to any place.
5.NBT.4
When rounding a decimal to a given place, students may identify the two possible answers, and use their
understanding of place value to compare the given number to the possible answers.
Example:
Round 14.235 to the nearest tenth.

Students recognize that the possible answer must be in tenths thus, it is either 14.2 or 14.3. They then
identify that 14.235 is closer to 14.2 (14.20) than to 14.3 (14.30).

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.
This standard requires students to extend the models and strategies they developed for whole numbers in grades
1-4 to decimal values. Before students are asked to give exact answers, they should estimate answers based on
their understanding of operations and the value of the numbers.
5.NBT.7
Examples:
• 3.6 + 1.7
 A student might estimate the sum to be larger than 5 because 3.6 is more than 3 ½ and 1.7 is more than
1 ½.
• 5.4 – 0.8
 A student might estimate the answer to be a little more than 4.4 because a number less than 1 is being
subtracted.
• 6 x 2.4
 A student might estimate an answer between 12 and 18 since 6 x 2 is 12 and 6 x 3 is 18. Another student
might give an estimate of a little less than 15 because s/he figures the answer to be very close, but
smaller than 6 x 2 ½ and think of 2 ½ groups of 6 as 12 (2 groups of 6) + 3 (½ of a group of 6).
Students should be able to express that when they add decimals they add tenths to tenths and hundredths to
hundredths. So, when they are adding in a vertical format (numbers beneath each other), it is important that they
write numbers with the same place value beneath each other. This understanding can be reinforced by
connecting addition of decimals to their understanding of addition of fractions. Adding fractions with denominators
of 10 and 100 is a standard in fourth grade.
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September 9th – October 25th
5th Grade Unit 1
Model Curriculum Student Learning Objectives
SLO/CCSS
1
2
3
4
5
Description
Write numerical expressions when given a
word problem or a scenario in words and use
words to interpret numerical expressions.
Recognize and explain patterns of the number
of zeros and the placement of the decimal point
in a product or quotient when a number is
multiplied or divided by powers of 10.
Compare decimals to thousandths based on
the value of the digits in each place using the
symbols >, =, < when presented as base ten
numerals, number names, or expanded form.
Round a decimal to any place.
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, subtraction, multiplication, and division.
CCSS
5.OA.2
5.NBT.2
5.NBT.3
5.NBT.4
5.NBT.7
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5th Grade Unit 1
Vocabulary
Term
Definition
Rectangular Array
An arrangement of objects in rows, and columns that form a rectangle.
Commutative
Property of
Multiplication
Product
A property of multiplication that two numbers can be multiplied in either oder, without
changing the product.
Factor
Each of the two or more numbers in a product.
Turn-Around -Rule
Factor pair
A rule for solving addition and multiplication problems based on the Commutative property of
Multiplication.
Two factors of a counting number n whose product is n
Remainder
An amount left over when one number is divided by another number.
Even Number
A counting number that is divisible by two.
Odd Number
A counting number that is not divisible by two.
Divisible by
Factor rainbow
If the larger of the two counting numbers can be divided by the smaller with no remainder ,
then the larger is divisible by the smaller.
A way to show factor pairs in a list of all the factors of a number.
Quotient
The result of dividing one number by another number.
Divisibility Rule
Composite number
A shortcut for determining whether a counting number is divisible by another counting
number without actually doing the division.
A counting number greater than 1 that has more than two factors.
Prime number
A counting number greater than 1 that has exactly two whole number factors, 1 and itself.
The result of multiplying two numbers, called factors.
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Potential Student Misconceptions
Number and operations in Base Ten
Students may believe that decimals with more places must be greater than decimals with fewer
places.
While students may believe that 0.289 is greater than 0.9 because it has more places, but in reality it is
not. An example is that 0.9 has fewer digits than
0.289, but 0.9 is greater.
Students may compute the sums or differences of decimals using the traditional algorithm but
disregard the decimal point.
For example, to compute the sum of 15.34 + 12.9, students may write the problem in this manner:
15.34
+ 12.9
16.63
Have students estimate the sum before computing, and use their estimate to check whether their
answer is reasonable. In this instance, an estimate might be 27, simply by combining the whole
numbers. So an answer of 16.63 does not make sense. Additionally, have students represent the
numbers using manipulatives or visual models to emphasize the meaning of the digits.
Operations and Algebraic Thinking
Students reverse the points while plotting them on a coordinate plane. For example, students might
count up first on the y-axis and then count over on the x-axis. Have students investigate what happens
when the plotting sequence is reversed, for example (4, 5) and (5, 4). Discuss real world examples
where inconsistencies in plotting points would be a problem.
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September 9th – October 25th
5th Grade Unit 1
Pacing Guide
Activity
Common Core
Standards/SLO
Estimated Time
1-1
Introduction to the Student
Reference Book
1-2
5.NBT.2
Rectangular Arrays
1-3
5.OA.2
Factors
1-4
5.OA.2, 5.NF.5
The Factor Captor Game
1-5
5.NBT.2
Divisibility
1-6 and Sieve of Eratosthenes
Project 1 p. 440
5.NBT.2
Prime and Composite Numbers
1-7
5.OA.2
Square Numbers
1-8
Part 2 only
5.NBT.2
Multiplication Facts (Extended
Facts Version)
1-9
5.OA.1, 5.NBT.2
Factor Strings and Prime
Factorizations
1-10
Progress Check
2-1
Estimation Challenge
Supplemental Activity (U6
2.1)
Fill Two
2-2
Addition of Whole Numbers
and Decimals
Illuminations DEEP SEA
DUEL
Supplemental Activity (U6
2.2)
Jeweler’s Gold
CC U6 2.5A
Decimal Subtraction Problems
2-3
Subtraction of Whole
Numbers and Decimals
2-4
Addition and Subtractions
Number Stories
2-7
Estimating Products
Number and Numeration,
Goal 3
5.NBT.2 5.MD.1
5.NBT.3a, 5.NBT.3b, 5.NBT.7
5.NBT.1, 5.NBt.3a, 5.NBT.3b,
5.NBT.7
5.OA.2
5.NBT.3a, 5.NBT.3b, 5.NBT.7
5.NBT.1, 5.NBT.7
5.NBT.1, 5.NBT.3a, 5.NBT.4,
5.NBT.7
5.OA.2, 5.NBT.3a, 5.NBT. 7
5.NBT.4, 5.NBT.7
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September 9th – October 25th
5th Grade Unit 1
2-8
Multiplication of Whole
Numbers and Decimals
Illustrative Mathematics:
Marta’s Multiplication Error
CC U6 3A.1
Multiplying Powers of Ten
CC U6 3A.2
Multiplying by “Small”
Numbers
CC U6 3A.3
Multiplying Decimals
CC U6 3A.4
Multiplying Decimals
(Continued)
2-9
The Lattice Method of
Multiplication
2-10
Comparing Millions, Billions
and Trillions
2-11
Progress Check
3-3
Exploring Angle Measures
3-6
Congruent Triangles
3-7
Properties of Polygons
3-8
Regular Tessellations
3-11
Progress Check (skip
problems from the chapter
that were not covered)
5.NBT.3a, 5.NBT.4, 5.NBT.7
5.NBT.2
5.NBT.2
5.NBT.2
5.NBT.2
5. NBT.2, 5.NBT.7
5.NBT.1, 5.MD.1
SMP3
SMP5,
5.NBT.4
SMP6, SMP8
5.G.3, 5.G.4
SMP1, SMP8
5.NBT.2, 5.G.3, 5.G. 4
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5th Grade Unit 1
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Assessment Checks
5.OA.2
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5.NBT.2
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5.NBT.3
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5.NBT.4
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5.NBT.7
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5th Grade Unit 1
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Extensions
Online Resources
5.OA.2
Algebra: Write variable expressions (Fifth grade - Q.2)
Assessment Resources:
K-5 math Resources:
Make the Largest product: See attached
Comparing Digits: See attached
Hunt for the Decimals: See attached.
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