Operations
and Algebraic Thinking (5.OA) |
Write
and interpret numerical expressions.
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Use
parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols. |
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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. |
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Analyze
patterns and relationships. |
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Generate
two numerical patterns using two given rules. Identify
apparent relationships between corresponding terms. Form ordered pairs
consisting of corresponding terms from the two patterns, and graph
the ordered pairs on a coordinate plane. For example, given the
rule “Add 3” and the starting number 0, and given the
rule “Add 6” and the starting number 0, generate terms
in the resulting sequences, and observe that the terms in one sequence
are twice the corresponding terms in the other sequence. Explain informally
why this is so. |
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Number
and Operations in Base Ten (5.NBT) |
Understand
the place value system. |
| 5.NBT.1
|
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.
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| 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.
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Read,
write, and compare decimals to thousandths. |
Tenths
Models (Sheppard)
Hundredths
Models (Sheppard) |
| 5.NBT.3a
|
Read
and write decimals to thousandths using base-ten numerals, number
names, and expanded form, e.g., 347.392 = 3 × 100 + 4 ×
10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 ×
(1/1000).
|
Decimal
Summation |
| 5.NBT.3b
|
Compare
two decimals to thousandths based on meanings of the digits in
each place, using >, =, and < symbols to record the results
of comparisons.
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Compare
Decimals (thatquiz.com)
Fruit
Shoot (Sheppard) |
| 5.NBT.4
|
Use
place value understanding to round decimals to any place.
|
Rounding
Decimals (thatquiz.com)
Scooter
Quest (Sheppard)
Half
Court Rounding (3 pointers) |
Perform
operations with multidigit whole numbers and with decimals to hundredths.
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Fluently
multiply multi-digit whole numbers using the standard algorithm. |
Drag
& Drop Multiplication
Batter's
Up Baseball (pencils) |
|
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. |
Drag
& Drop Division
Create
an Assessment
Online
Division Practice (use
paper and pencil)
Scored
Practice (use paper and pencil) |
| |
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. |
Play
Decimal Speedway
(x)
Sheppard
(+) Matching
Sheppard
(-) Matching |
Numbers
and Operations - Fractions (5.NF) |
Use
equivalent fractions as a strategy to add and subtract fractions. |
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Add
and subtract fractions with unlike denominators (including mixed numbers)
by replacing given fractions with equivalent fractions in such a way
as to produce an equivalent sum or difference of fractions with like
denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general,
a/b + c/d = (ad + bc)/bd.) |
EZ
Fractions (mrnussbaum.com)
(+)
Fruit Shoot Pick
Level 3
(-)
Fruit Shoot Pick Level 3
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Solve
word problems involving addition and subtraction of fractions referring
to the same whole, including cases of unlike denominators, e.g.,
by using visual fraction models or equations to represent the problem.
Use benchmark fractions and number sense of fractions to estimate
mentally and assess the reasonableness of answers. For example,
recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that
3/7 < 1/2. |
Adding
Fractions Game |
Apply
and extend previous understandings of multiplication and division
to multiply and divide fractions. |
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Interpret
a fraction as division of the numerator by the denominator (a/b =
a ÷ b). Solve word problems involving division of whole numbers
leading to answers in the form of fractions or mixed numbers, e.g.,
by using visual fraction models or equations to represent the problem.
For example, interpret 3/4 as the result of dividing 3 by 4, noting
that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared
equally among 4 people each person has a share of size 3/4. If 9 people
want to share a 50-pound sack of rice equally by weight, how many
pounds of rice should each person get? Between what two whole numbers
does your answer lie? |
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Apply
and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction. |
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Interpret
the product (a/b) × q as a parts of a partition of q into b
equal parts; equivalently, as the result of a sequence of operations
a × q ÷ b. For example, use a visual fraction model
to show (2/3) × 4 = 8/3, and create a story context for this
equation. Do the same with (2/3) × (4/5) = 8/15. (In general,
(a/b) × (c/d) = ac/bd.) |
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Find
the area of a rectangle with fractional side lengths by tiling it
with unit squares of the appropriate unit fraction side lengths, and
show that the area is the same as would be found by multiplying the
side lengths. Multiply fractional side lengths to find areas of rectangles,
and represent fraction products as rectangular areas. |
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Interpret
multiplication as scaling (resizing), by: |
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Comparing
the size of a product to the size of one factor on the basis of the
size of the other factor, without performing the indicated multiplication. |
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Explaining
why multiplying a given number by a fraction greater than 1 results
in a product greater than the given number (recognizing multiplication
by whole numbers greater than 1 as a familiar case); explaining why
multiplying a given number by a fraction less than 1 results in a
product smaller than the given number; and relating the principle
of fraction equivalence a/b = (n×a)/(n×b) to the effect
of multiplying a/b by 1. |
Play
Fraction Frenzy |
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Solve
real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent
the problem. |
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Apply
and extend previous understandings of division to divide unit fractions
by whole numbers and whole numbers by unit fractions. |
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5.NF.7a
|
Interpret
division of a unit fraction by a non-zero whole number, and compute
such quotients. For example, create a story context for (1/3)
÷ 4, and use a visual fraction model to show the quotient.
Use the relationship between multiplication and division to explain
that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
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Divide
Fractions by Integers |
| 5.NF.7b
|
Interpret
division of a whole number by a unit fraction, and compute such
quotients. For example, create a story context for 4 ÷
(1/5), and use a visual fraction model to show the quotient. Use
the relationship between multiplication and division to explain
that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
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| 5.NF.7c
|
Solve
real world problems involving division of unit fractions by non-zero
whole numbers and division of whole numbers by unit fractions, e.g.,
by using visual fraction models and equations to represent the problem.
For example, how much chocolate will each person get if 3 people
share 1/2 lb of chocolate equally? How many 1/3-cup servings are
in 2 cups of raisins? |
|
Measurement
and Data (5.MD) |
Convert
like measurement units within a given measurement system.
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Convert
among different-sized standard measurement units within a given
measurement system (e.g., convert 5 cm to 0.05 m), and use these
conversions in solving multi-step, real world problems. |
Metric
Length
Metric
Volume
Metric
Weight |
Represent
and interpret data. |
5.MD.2
|
Make
a line plot to display a data set of measurements in fractions of
a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade
to solve problems involving information presented in line plots. For
example, given different measurements of liquid in identical beakers,
find the amount of liquid each beaker would contain if the total amount
in all the beakers were redistributed equally. |
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Geometric
measurement: understand concepts of volume and relate volume to
multiplication and to addition. |
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Recognize
volume as an attribute of solid figures and understand concepts of
volume measurement. |
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A
cube with side length 1 unit, called a “unit cube,” is
said to have “one cubic unit” of volume, and can be used
to measure volume. |
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A
solid figure which can be packed without gaps or overlaps using n
unit cubes is said to have a volume of n cubic units. |
Build
3-Dimensional Solids
Build
with Unit Cubes |
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Measure
volumes by counting unit cubes, using cubic cm, cubic in, cubic ft,
and improvised units. |
Count
Cubes in 3-D Solids |
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Relate
volume to the operations of multiplication and addition and solve
real world and mathematical problems involving volume. |
Calculate
Volume
Find
Missing Values
Compare
Volume |
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Find
the volume of a right rectangular prism with whole-number side lengths
by packing it with unit cubes, and show that the volume is the same
as would be found by multiplying the edge lengths, equivalently by
multiplying the height by the area of the base. Represent threefold
whole-number products as volumes,
e.g., to represent the associative property of multiplication. |
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Apply
the formulas V = l × w × h and V = b × h for rectangular
prisms to find volumes of right rectangular prisms with whole number
edge lengths in the context of solving real world and mathematical
problems. |
Play
Find That Volume |
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Recognize
volume as additive. Find volumes of solid figures composed of two
non-overlapping right rectangular prisms by adding the volumes of
the non-overlapping parts, applying this technique to solve real world
problems. |
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Graph
points on the coordinate plane to solve real-world and mathematical
problems. |
5.G.1
|
Use
a pair of perpendicular number lines, called axes, to define a coordinate
system, with the intersection of the lines (the origin) arranged to
coincide with the 0 on each line and a given point in the plane located
by using an ordered pair of numbers, called its coordinates. Understand
that the first number indicates how far to travel from the origin
in the direction of one axis, and the second number indicates how
far to travel in the direction of the second axis, with the convention
that the names of the two axes and the coordinates correspond (e.g.,
x-axis and x-coordinate, y-axis and y-coordinate). |
Locate
Points
Identify
Points
BBC
Grids
Stock
the Shelves |
5.G.2
|
Represent
real world and mathematical problems by graphing points in the first
quadrant of the coordinate plane, and interpret coordinate values
of points in the context of the situation. |
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Classify
two-dimensional figures into categories based on their properties. |
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Understand
that attributes belonging to a category of two-dimensional figures
also belong to all subcategories of that category. For example, all
rectangles have four right angles and squares are rectangles, so all
squares have four right angles. |
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Classify
two-dimensional figures in a hierarchy based on properties. |
Shape
Conveyor |
