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Quiz

Students
will acquire number sense and perform operations with whole numbers,
simple fractions, and decimals.





Demonstrate
multiple
ways to represent whole numbers and decimals, from hundredths
to one million, and fractions.


Mystery Picture Rags to Riches




a.

Read and write numbers in
standard and expanded form. 

Matching Game Concentration




b.

Demonstrate multiple ways to
represent whole numbers and decimals by
using models and symbolic representations (e.g., 36 is the same as the
square of six, three dozen, or 9 x 4). 
Base 10 Blocks Tens & Ones

Base Ten Tens & Ones Game




c.

Identify the place and the value
of a given digit in a sixdigit
numeral, including decimals to hundredths, and round to the nearest
tenth. 

Place Value Game Shoot the Target Seashell Rounding




d.

Divide regions, lengths, and
sets of objects into equal parts using a variety of models and
illustrations. 

Naming Fractions




e.

Name and write a fraction to
represent a portion of a unit whole,
length, or set for halves, thirds, fourths, fifths, sixths, eighths,
and tenths. 

Parts of a Whole
Visualizing Fractions




f.

Identify and represent square
numbers using models and symbols. 











Analyze
relationships among whole numbers, commonly used fractions, and
decimals to hundredths.






a.

Compare the relative size of
numbers (e.g., 475 is comparable to 500; 475 is small compared to
10,000 but large compared to 98).






b.

Order whole numbers up to six
digits, simple fractions, and decimals
using a variety of methods (e.g., number line, fraction pieces) and the
symbols <, >, and = to record the relationships. 

One False Move




c.

Identify a number that is
between two given numbers (e.g., 3.2 is between 3 and 4; find a number
between 0.1 and 0.2). 





d.

Identify equivalences between
fractions and decimals by connecting models to symbols. 

Number Line Bars  Fractions Fraction Models 



e.

Generate equivalent fractions
and simplify fractions using models, pictures, and symbols. 

Number Line Bars  Fractions Equivalent Fractions










Model
and illustrate meanings of multiplication and division of whole numbers
and the addition and subtraction of fractions.


Electronic Abacus




a.

Model multiplication (e.g.,
equalsized groups, rectangular arrays, area models, equal intervals on
the number line), place value, and properties of operations to
represent multiplication of a one or twodigit factor by a twodigit
factor and connect the representation to an algorithm.

Number Line Arithmetic 
Rectangle
Multiplication Factorize




b.

Use rectangular arrays to
interpret factoring (e.g., find all
rectangular arrays of 36 tiles and relate the dimensions of the arrays
to factors of 36). 
Rectangle Multiplication of Integers

Factorize




c.

Demonstrate the mathematical
relationship between multiplication and
division (e.g. 3 x =12 is the same as 12 ÷ 3 = and = 4) and use
that
relationship to explain that division by zero is not possible. 





d.

Represent division of a
threedigit dividend by a onedigit divisor,
including whole number remainders, using a variety of methods (e.g.,
rectangular arrays, manipulatives, pictures), and connect the
representation to an algorithm. 
Rectangle Division

Rectangle Division 



e.

Use models to add and subtract
simple fractions where one singledigit
denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4; 3/4  1/8).


Fraction Game










Solve
problems involving multiplication and division of whole numbers and
addition and subtraction of simple fractions and decimals. 





a.

Use estimation, mental math,
paper and pencil, and calculators to perform mathematical calculations
and identify when to use each one appropriately.


Diffy




b.

Select appropriate methods to
solve a single operation problem and
estimate computational results or calculate them directly, depending on
the context and numbers involved in a problem. 





c.

Write a story problem that
relates to a given multiplication or
division equation, and select and write a number sentence to solve a
problem related to the environment. 





d.

Solve problems involving simple
fractions and interpret the meaning of
the solution (e.g., A pie has been divided into six pieces and one
piece is already gone. How much of the whole pie is there when Mary
comes in? If Mary takes two pieces, how much of the whole pie has she
taken? How much of the pie is left?) 
Fraction Bars











Compute
problems involving multiplication and division of whole numbers and
addition and subtraction of simple fractions and decimals. 





a.

Demonstrate quick recall of
basic multiplication and division facts.


Product Game Times Table Times Square*




b.

Multiply up to a three digit
factor by a twodigit factor with fluency, using efficient procedures. 





c.

Divide up to a threedigit
dividend by a onedigit divisor with fluency, using efficient
procedures. 





d.

Add and subtract decimals and
simple fractions where one singledigit
denominator is 1, 2, or 3 times the other (e.g., 2/4 + 1/4 = 3/4; 1/3 
1/6 = 1/6). 











Mathematical Language and Symbols Students
Should Use
sum, difference, expanded form, standard form, square number, dividend,
divisor, quotient, factor, product, array, multiple, numerator,
denominator, sixths, eighths, tenths, equivalent, estimate, <, >,
=, ≠





Exploratory Concepts and Skills
 Use concrete objects and visual models to add and subtract
common decimals.
 Explore numbers less than zero by extending the number line
and by using familiar applications such as temperature.
 Investigate the concept of ratio (e.g., the number of
students to the number of teachers).











Students
will use patterns and relations to represent mathematical problems and
number relationships.





Identify,
analyze,
and determine rules for describing numerical patterns
involving operations and nonnumerical growing patterns. 





a.

Analyze growing patterns using
objects, pictures, numbers, and tables to determine a rule for the
pattern.

Color Patterns

Chairs




b.

Recognize, represent, and extend
simple patterns involving multiples
and other number patterns (e.g., square numbers) using objects,
pictures, numbers, and tables. 

Number Patterns
Sieve
of Eratosthenes Chairs




c.

Identify simple relationships in
reallife contexts and use
mathematical operations to describe the pattern (e.g., the number of
legs on a given number of chairs may be determined by counting by fours
or by multiplying the number of chairs by 4). 

Chairs










Use
algebraic expressions, symbols, and properties of the operations to
represent, simplify, and solve mathematical equations and inequalities.






a.

Use the order of operations to
evaluate, simplify, and compare mathematical expressions involving the
four operations, parentheses, and the symbols <, >, and = (e.g.,
2x (4  1) + 3; of the two quantities 7  (3  2) or (7  3)  2, which
is greater?).






b.

Express singleoperation problem
situations as equations and solve the equation. 





c.

Recognize that a symbol
represents the same number throughout an equation or expression (e.g.,
+ = 8; thus, = 4). 





d.

Describe and use the
commutative, associative, distributive, and
identity properties of addition and multiplication, and the zero
property of multiplication. 




Mathematical Language and Symbols Students
Should Use
growing pattern, order of operations, parentheses, inequality,
expression, equation, associative property, commutative property,
distributive property, zero property of multiplication, >, <, =





Exploratory Concepts and Skills
 Use concrete materials to build an understanding of
equality and inequality.
 Explore properties of equality in number sentences (e.g.,
when equals are added to equals, then the sums are equal; when equals
are multiplied by equals, then the products are equal).




Students
will understand attributes and properties of plane geometric objects
and spatial relationships.





Identify
and describe attributes of twodimensional geometric shapes. 





a.

Name and describe lines that are
parallel, perpendicular, and intersecting.






b.

Identify and describe right,
acute, obtuse, and straight angles. 
Stretch the angle

Angle Quiz




c.

Identify and describe the radius
and diameter of a circle. 





d.

Identify and describe figures
that have line symmetry and rotational symmetry. 

Cyclic Figures










Specify
locations using grids and maps.






a.

Locate coordinates in the first
quadrant of a coordinate grid.






b.

Give the coordinates in the
first quadrant of a coordinate grid. 





c.

Locate regions on a map of Utah. 





d.

Give the regions on a map of
Utah. 











Visualize
and
identify geometric shapes after applying transformations.






a.

Identify a translation,
rotation, or a reflection of a geometric shape.


Shape Cutter Shape Tool




b.

Recognize that 90°,
180°, 270°, and 360° are associated, respectively, with
1/4, 1/2, 3/4, and full turns. 











Mathematical Language and Symbols Students
Should Use
parallel, perpendicular, intersecting lines, right angle, acute angle,
obtuse angle, straight angle, circle, radius, diameter, line symmetry,
rotational symmetry, coordinate, first quadrant, degree, translate,
rotate, reflect, transformation





Exploratory Concepts and Skills
 Analyze results of transformations (e.g., translations,
rotations, reflections) on twodimensional shapes.
 Investigate twodimensional representations of
threedimensional objects.











Students
will describe relationships among units of measure, use appropriate
measurement tools, and use formulas to find area measurements.





Describe
relationships among units of measure for length, capacity, and weight,
and determine measurements of angles using appropriate tools.






a.

Describe the relative size among
metric units of length (i.e., millimeter, centimeter, meter), between
metric units of capacity (i.e., milliliter, liter), and between metric
units of weight (i.e., gram, kilogram).






b.

Describe the relative size among
customary units of capacity (i.e., cup, pint, quart, gallon). 





c.

Estimate and measure capacity
using milliliters, liters, cups, pints,
quarts, and gallons, and measure weight using grams and kilograms. 





d.

Recognize that angles are
measured in degrees and develop benchmark
angles (e.g., 45°, 60°, 120°) using 90° angles to
estimate angle
measurement. 





e.

Measure angles using a
protractor or angle ruler. 
Interactive protractor Protractor How to use a protractor











Recognize
and
describe area as a measurable attribute of twodimensional shapes
and calculate area measurements.






a.

Quantify area by finding the
total number of samesized units of area needed to fill the region
without gaps of overlaps.






b.

Recognize that a square that is
1 unit on a side is the standard unit for measuring area. 





c.

Develop the area formula for a
rectangle as the number of unit squares
that fit in the rectangle, and identify the unit of measure as square
units. 





d.

Develop and use the area formula
for a right triangle by comparing with
the formula for a rectangle (e.g., two of the same right triangles
makes a rectangle). 





e.

Develop the formulas and justify
the relationships among area formulas
of triangles and parallelograms by decomposing and comparing with areas
of right triangles and rectangles. 





f.

Determine possible perimeters,
in whole units, for a rectangle with a
fixed area, and determine possible areas when given a rectangle with a
fixed perimeter. 











Mathematical Language and Symbols Students
Should Use
millimeter, centimeter, meter, milliliter, liter, gram, kilogram, cup,
pint, quart, gallon, area, perimeter





Exploratory Concepts and Skills
 Investigate perimeter of rectangles and squares.
 Investigate area of trapezoids.p











Students
will interpret and organize collected data to make predictions, answer
questions, and describe basic concepts of probability.





Collect,
organize, and display data to answer questions.






a.

Identify a question that can be
answered by collecting data.


Circle Grapher




b.

Collect, read, and interpret
data from tables, graphs, charts, surveys, and observations. 
Create A Graph

Spinners Box Plotter




c.

Represent data using frequency
tables, bar graphs, line plots, and stem and leaf plots. 
Bar Chart

Bar Chart Bar Grapher Box Plotter Histogram Tool Stem & Leaf Plotter 



d.

Identify and distinguish between
clusters and outliers of a data set. 











Describe
and predict simple random outcomes.






a.

Describe the results of
investigations involving random outcomes as simple ratios (e.g., 4 out
of 9, 4/9).


Spinners 



b.

Conduct simple probability
experiments, with and without replacement,
record possible outcomes systematically, and display results is an
organized way. 

Spinners Box Plotter Random Drawing Tool 



c.

Use the results of simple
probability experiments, with and without
replacement, to describe the likelihood of a specific outcome in the
future. 

Spinners 









Mathematical Language and Symbols Students
Should Use
data, line plot, line graph, bar graph, stem and leaf plot, cluster,
outlier, frequency table, probability

Create a Graph

Create a Graph Stem & Leaf Plotter



Exploratory Concepts and Skills
 Explore minimum and maximum values for a set of data
 Explore mean, median, mode, and range.


Box Plotter

