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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 six-digit 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., equal-sized groups, rectangular arrays, area models, equal intervals on the number line), place value, and properties of operations to represent multiplication of a one- or two-digit factor by a two-digit 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 three-digit dividend by a one-digit 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 single-digit 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 two-digit factor with fluency, using efficient procedures.

c.
Divide up to a three-digit dividend by a one-digit divisor with fluency, using efficient procedures.

d.
Add and subtract decimals and simple fractions where one single-digit 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 real-life 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 single-operation 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 two-dimensional 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 two-dimensional shapes.
• Investigate two-dimensional representations of three-dimensional 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 two-dimensional shapes and calculate area measurements.

a.
Quantify area by finding the total number of same-sized 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.
Area Tool

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
* Activities labeled with an '*' require registration and then logging in at Calculation Nation. More about Calculation Nation here.