Algebraic Ideas

• Identify the coordinates of a given point on a grid.
• Identify the missing number in equations.
• Introduction to the order of operations.
• Use and apply the distributive property.
• Identify the set of numbers that make an inequality statement true.
• Select the operation symbol to complete number sentences.
• Explain number sentences with variables represented by symbols.
• Recognize and use concept of variable in expressions.

Fractions, Decimals, and Percents

• Relate decimals to money concepts.
• Round decimals.
• Estimate decimals.
• Solve addition and subtraction problems using decimals.
• Estimate sums and differences of decimals.
• Add and subtract decimals mentally: whole numbers and tenths.
• Add and subtract decimals and solve story problems.
• Add and subtract decimals using a calculator.
• Relate decimals to fractions using models.
• Convert a decimal to a fraction with a denominator of 10 or 100 and write the decimal number as the new numerator.
• Convert improper fractions and mixed numbers.
• Identify numerator and denominator of fractions using models.
• Use models to identify and solve problems about fractional parts of whole.
• Introduction to understanding lowest term fractions.
• Relate addition and subtraction operations to models and solve problems using like denominators.
• Understand and find equivalent fractions.
• Understand, compare and order fractions with like denominators.
• Estimate fractions and size of regions.
• Find sums and differences of like fractions and solve word problems.
• Find fractional part of a number.
• Understand lowest term fractions.
• Find least common denominator.
• Understand, add, and subtract fractions with unlike denominators.
• Understand, compare and order mixed numbers.
• Add mixed numbers.
• Subtract mixed numbers.

Geometry

• Estimate distances and positions in the coordinate plane to the nearest whole number.
• Solve problems using positions, concepts, and notations.
• Visually compare the measures of segments, angles, and plane regions.
• Recognize straight, right, acute, and obtuse angles.
• Recognize and define a circle's center, radius and diameter.
• Recognize and define triangular, rectangular and square pyramids and prisms.
• Recognize and define isosceles, right, scalene and equilateral triangles.
• Recognize and define polygon, pentagon and quadrilateral.
• Identify and illustrate relations among figures (congruency, similarity, intersection, parallelism, and perpendicularity).
• Name points, lines and line segments using letters.
• Find distance between two points on a line.
• Recognize and define parallel, perpendicular, and intersecting lines.
• Find perimeter of square given length of one side and of a rectangle given lengths of two adjacent sides.
• Identify shapes (triangle, rectangle, square, rectangular prism, cube, cylinder, sphere, and cone) and their properties (angle, face, edge, and point).
• Identify and solve problems based on relations among figures and shapes.
• Identify lines of symmetry in geometric figures.
• Identify geometric figures that have been flipped, turned, shrunk, or stretched.
• Predict the next figure in a sequence of geometric figures.
• Recognize and define congruent and similar geometric figures.
• Identify the line or lines of symmetry in complex 2-dimensional geometric figures.
• Identify and illustrate properties of geometric shapes.

Measurement

• Identify the concept of volume-customary and metric.
• Solve one-step word problems using volume-customary and metric.
• Identify and measure inches, feet, and yards for length of familiar objects.
• Estimate length of familiar objects using inches.
• Measure length of lines using inches, feet, and yards.
• Measure length of objects using inches, feet, and yards.
• Solve one-step word problems using inches, feet, and yards.
• Choose appropriate measure for length using inches, feet, and yards.
• Convert among measures of length from one customary unit to another.
• Solve two-step word problems using inches, feet, and yards.
• Choose appropriate measure of length using meters and centimeters.
• Estimate length of familiar objects using meters and centimeters.
• Measure length of familiar objects using meters and centimeters.
• Solve one-step word problems using meters and centimeters.
• Develop personal referents for standard units of measurement-metric.
• Read ruler using millimeters, centimeters, decimeters, and meters.
• Choose appropriate measure for length-metric.
• Convert among measures of length-metric.
• Solve one-step word problems using kilometers.
• Estimate liquid capacity using cups, pints, quarts, and gallons.
• Measure liquid capacity using cups, pints, quarts, and gallons.
• Solve one-step word problems using liquid capacity-customary.
• Choose appropriate unit to measure liquid capacity-customary.
• Estimate liquid capacity using cups, pints, quarts, half-gallons, and gallons.
• Measure liquid capacity using cups, pints, quarts, half-gallons, and gallons.
• Solve two-step word problems using liquid capacity-customary.
• Choose appropriate unit to measure liquid capacity using liters and milliliters.
• Estimate liquid capacity of familiar objects using liters and milliliters.
• Read units of measurement of liquid capacity using liters and milliliters.
• Solve one-step word problems using liquid capacity using liters and milliliters.
• Choose appropriate unit to measure liquid capacity using liters, milliliters, and kiloliters.
• Identify the monetary value of coins.
• Identify the monetary value of bills up to $5.
• Identify combinations of coins and bills; all coins plus $1 and $5.
• Identify $10 bill and count money using combinations of $1, $5, and $10 bills.
• Identify $20 bill and count money up to $20 using combinations of $1, $5, $10 and $20 bills.
• Estimate money, rounding to the nearest dollar.
• Choose appropriate measure for weight-customary.
• Estimate weight of familiar objects using ounces and pounds.
• Read appropriate measure of weight using ounces and pounds.
• Solve word problems using weight-customary.
• Choose appropriate measure weight-metric.
• Estimate weight of familiar objects using grams and kilograms.
• Read weight of familiar objects using grams and kilograms.
• Solve one-step word problems using grams and kilograms.
• Estimate and calculate perimeter of familiar objects-customary.
• Solve one-step word problems using perimeter-customary.
• Estimate perimeter of familiar objects-metric.
• Calculate perimeter of familiar objects-metric.
• Solve one-step word problems using perimeter-metric.
• Differentiate between a.m. and p.m.
• Tell time to five-minute intervals using analog and digital clocks.
• Tell time to one-minute intervals using analog and digital clocks.
• Make reasonable time estimations.
• Solve one-step word problems involving elapsed time.
• Read Celsius scales to nearest degree.
• Read Fahrenheit scales to nearest degree.
• Estimate temperatures using Celsius scales.
• Estimate temperatures using Fahrenheit scales.
• Solve one-step word problems using Celsius and Fahrenheit scales.

Number Concepts

• Explore the concept of number line.
• Explore the four steps to solving word problems.
• Explore the concept of place value using base ten blocks.
• Estimate sums of 2-digit numbers.
• Use models to show addition algorithm with regrouping.
• Add three 2-digit numbers with regrouping.
• Add two 3-digit numbers.
• Add two 2-digit numbers mentally.
• Add multiples of 1,000 and 10,000 mentally.
• Estimate sums using two 3-digit or three 2-digit numbers.
• Add three 3-digit numbers.
• Solve word problems using addition: three 2-digit or two 3-digit numbers.
• Add any whole numbers using a calculator.
• Count forward and backward by 1s, 2s, 5s, and 10s.
• Arrange up to 3-digit numbers in order.
• Recognize and write names for whole numbers through 9,999.
• Arrange numbers in order up to 5 digits.
• Write numbers given the written word and the word given the number up to 5 digits.
• Understand division by using models.
• Understand relationship between multiplication and division using fact families.
• Identify strategies for division and recall basic division facts from memory.
• Divide 2-digit dividend by 1-digit divisor without a remainder.
• Divide 1- or 2-digit dividend by 1-digit divisor with a remainder.
• Divide 3- or 4-digit dividend by 1-digit divisor with and without a remainder.
• Divide 2-digit dividend by 2-digit divisor with and without a remainder.
• Solve simple word problems involving 3- or 4-digit dividends divided by 1-digit divisor and 2-digit dividend by 2-digit divisor without remainders.
• Divide whole numbers using a calculator: 2- or 3-digit dividend and 1- or 2-digit divisors without a remainder.
• Estimate sums when adding 2-digit numbers.
• Estimate differences subtracting two 2-digit numbers.
• Estimate sums when adding two 3-digit numbers.
• Estimate differences subtracting two 3-digit numbers.
• Estimate products using multiples of 10.
• Estimate quotients with 1-digit divisors and 2-digit dividends.
• Estimate the sum of 2-, 3-, 4-, and 5-digit numbers using front-end strategy.
• Identify factors and product in a multiplication sentence.
• Understand meaning of common factor and find common factors of two numbers up to 40.
• Understand meaning of multiple.
• Understand meaning of common multiple.
• Understand and differentiate meanings of prime and composite numbers.
• Identify the greater/less than number up to 1,000.
• Compare whole numbers that have up to and including 5 digits (>, <, or =).
• Write number sentences represented by a picture.
• Identify strategies for basic multiplication and recall basic multiplication facts from memory.
• Rewrite a horizontal multiplication problem vertically.
• Multiply two numbers (1 digit, 0 to 9, times 2 and 3 digits with no regroupings).
• Solve word problems involving multiplication by 0 through 9.
• Use models to show multiplication algorithm: 1 digit times 2 digit with regrouping.
• Multiply 1-digit times 3-digit numbers with regrouping.
• Multiply two 2-digit numbers and 2-digit times 3-digit numbers with regrouping.
• Multiply any whole numbers using a calculator.
• Identify meaning of odd and even numbers less than 10.
• Identify meaning of odd and even numbers greater than 10.
• Predict when sums, differences, products and quotients are odd or even.
• Recognize ordinal numbers first through twentieth.
• Introduction to choosing the correct operation (appropriate symbol +, -, x, or ÷).
• Recognize and state place value up to 9,999.
• Regroup numbers using place value to 4 digits.
• Recognize and state place value of each digit up to 99,999.
• Regroup numbers using place value through 5 digits.
• Write numbers in standard and expanded form.
• Regroup numbers using place value up to 3 digits.
• Use models to show the addition algorithm with regrouping.
• Add three 2-digit numbers horizontally and vertically with regrouping.
• Use models to teach the subtraction algorithm and test subtraction using 2-digit or 3-digit numbers with one or two regroupings.
• Solve word problems involving up to 3-digit subtraction with one regrouping.
• Add three or more whole numbers.
• Add and regroup numbers using place value up to 6 digits.
• Find differences of 3-digit numbers involving regrouping including zero in middle.
• Multiply 1- and 2-digit numbers with regrouping.
• Multiply 2 numbers up to a 3-digit by 2-digit number.
• Round numbers to nearest 10 using the number line.
• Round numbers to nearest 100 using the number line.
• Round numbers to nearest 1000 using the number line.
• Round numbers to nearest 10000.
• Round numbers to nearest 100000.
• Relate subtraction to addition.
• Recall basic subtraction facts through 18.
• Understand and use models representing 2-digit subtraction, no regrouping.
• Subtract multiples of 10 and 100 mentally.
• Use models to show the subtraction algorithm with regrouping and subtract 2-or 3-digit numbers with one or two regroupings.
• Estimate differences using 2-digit numbers that are within 3 of a multiple of 10.
• Solve one-step word problems using up to 3-digit subtraction with one regrouping.
• Subtract whole numbers using a calculator with regrouping.
• Subtract multiples of 1000 and 10000 mentally.
• Estimate to find differences using 3-digit numbers.
• Estimate to find differences using 4-digit numbers.
• Find differences of 3-digit numbers involving 2 regroupings with zero in middle.
• Find differences of 4-digit numbers involving 2 regroupings with zero in middle.
• Solve multi-step word problems using 2- and 3-digit numbers involving 2 regroupings with zero in middle.
• Introduction to solving word problems using addition, subtraction, multiplication, and division.
• Solve grade appropriate word problems using four basic operations.

Statistics and Probability

• Make comparisons among graphs.
• Determine appropriate scales for graphs.
• Understand probability by predicting and determining trends, patterns, and outcomes and identify the number of combinations that can be made from 2-10 objects.
• State the number of possible outcomes and figure the probability of each outcome when tossing a coin (1 out of 2) or rolling a die (1 out of 6).
• Compare probabilities of occurrence of given events.
• Calculate number of times an event is expected to happen based on the probability of it happening.
• Use probability devices to simulate world events.
• Calculate mean of a group of numbers, rounding to nearest whole number.
• Find median of a group of numbers.
• Calculate range of a group of numbers.
• Determine frequency as a number in a category.
• Read tables and interpret data from tables.
• Complete a table by inserting data using tally marks.
• Understand the effects of change on data.