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Math SCOPE and SEQUENCE

Whole Number Place Value
- represent the value of each digit in numbers through 1,000,000,000 using expanded notation and numerals
- interpret the value of each digit as 10 times the position to the right and 1/10 of the value of the place to the left
- compare and order whole numbers to 1,000,000,000 (<, >, =)
- round whole numbers through the hundred thousand place

- add and subtract whole numbers using the standard algorithm
- round to the nearest 10, 100, or 1,000 to estimate solutions involving whole numbers
- represent multi-step problems involving the 4 operations using strip diagrams and equations
with a letter standing for the unknown quantity

Multiplication of Whole Numbers
- determine products of a number times 10 and times 100
- represent the product of 2 two-digit numbers using arrays, area models, or equations
(including perfect squares through 15 x 15)
- multiply up to a 4 digit number by a 1 digit number
- multiply a 2 digit number by a 2 digit number
- strategies may include mental math, partial products, and the commutative, associative,
and distributive properties

Division of Whole Numbers
- represent the quotient of up to a 4 digit whole number by a 1 digit whole number using
arrays, area models, or equations

Division of Whole Numbers
- divide up to a 4 digit dividend by a 1 digit divisor
- solve problems involving division, including interpreting remainders

Fractions
- represent a fraction a/b as a sum of fractions 1/b: where a and b are whole
numbers and b > 0 (including when a > b)
- decompose a fraction into a sum of fractions with the same denominator
- determine if two given fractions are equivalent
- compare two fractions with different numerators and different denominators
- add and subtract fractions with equal denominators
- evaluate the reasonableness of sums and differences of fractions using benchmark
fractions 01/41/23/4, and 1, referring to the same whole

Input / Output Tables
- determine products of a number times 10 or times 100 using properties of operations
and place value understanding
- generate a number pattern that follows a given rule representing the relationship of the
values in the resulting sequence and their position in the sequence

Decimal Place Value
- interpret the value of each digit as 10 times the position to the right and 1/10 of the value of the digit
to the left
- represent decimals, including tenths and hundredths, using numerals, expanded notation,
concrete / visual models, and money
- compare and order decimals to the hundredths
- relate decimals to fractions that name tenths and hundredths
- determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line
- Add/subtract whole numbers and decimals to the hundredths place
- represent fractions and decimals to the tenths or hundredths as distances from zero on a number line

Lines, Angles, and 2-D Shapes
- identify points, lines, line segments, rays, angles, and perpendicular/parallel lines
- identify and draw one or more lines of symmetry (if they exist)
- apply knowledge of right angles to identify acute, right, and obtuse triangles
- classify 2D shapes based on the presence or absence of parallel or perpendicular lines
or the presence or absence of angles of a specified size

Angles on a Protractor
- illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle
that is "cut out" by the rays of the angle
- illustrate degrees as the units used to measure an angle, where 1/360 of any circle is 1 degree
and an angle that "cuts" n/360 out of any circle whose center is at the angle's vertex has a measure
of n degrees
- determine the approximate measures of angles in degrees to the nearest whole number using a protractor
- determine an angle with a given measure
- determine the measure of an unknown angle formed by two non-overlapping adjacent angles given one
or both angle measures

Area and Perimeter
- determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w), including the special
form for the perimeter of a square (4s) and the area of a rectangle (l x w)
- solve problems related to perimeter and area of rectangles where dimensions are whole numbers

Data Analysis
- represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions
- solve problems using data in whole number, decimal, and fraction form in a frequency table, dot plot,
or stem-and-leaf plot

Measurement
- identify relative sizes of measurement units within the customary and metric systems
- convert measurements within the same measurement system, customary or metric
- solve problems that deal with measurements of length, intervals of time, liquid volume, mass,
and money using addition, subtraction, multiplication, or division

Personal Financial Literacy
- fixed vs variable expenses
- calculate profit in a given situation