Topic 1 -- Understand Multiplication and Division of Whole Numbers

• Use repeated addition, arrays, properties and number lines to understand multiplication and its relationship wtih division

• Use sharing to separate equal groups and repeated subtraction to think about division and its relationship with subtraction

• Think strategically about available tools that can be used to solve problems

Topic 2 -- Multiplication Facts: Using Patterns

• Gain fluency in multiplication when using factors of 2, 5 and 9 and when multiplying by 0, 1 and 10

• Use number relationships, patterns and reasoning strategies to recall basic multiplication facts and represent and solve word problems

Topic 3 -- Apply Properties: Multiplication Facts for 3, 4, 6. 7, 8

• Use the distributive property to break apart unknown facts with 3, 4, 6, 7 or 8 as factors and solve problems involving multiplication within 100

• Use strategies such as bar diagrams and arrays with known facts to solve multiplication problems

• Use the associative property of multiplication to group factors when multiplying 3 factors

• Use repeated reasoning with known facts to make generalizations when multiplying

Topic 4 -- Use Multiplication to Divide: Division Facts

• Use multiplication facts to divide and find related division facts

• Use knowledge of even and odd numbers to find multiplication patterns

• Use properties to understand division involving 0 and 1

• Use patterns and known facts to find unknown multiplication facts

• Use multiplication and division facts to find unknown values in equations

• Use previously learned concepts to find and answer hidden questions to solve problems

Topic 5 -- Fluently Multiply and Divide within 100

• Use the multiplication table and the distributive property to find patterns in factors and products

• Use number sense and reasoning while practicing multiplication and division basic facts

• Use properties such as skip counting and properties of operations to multiply

• Solve multiplication and division problems that involve different strategies and representations

• Use multiplication to write and solve problems real world problems involving equal groups

• Use the structures of multiplication and division to compare expressions

Topic 6 -- Connect Area to Multiplication and Addition

• Use unit squares, standard units and multiplication to find the area of shapes and figures

• Use areas of rectangles to model the distributive property of multiplication and to find the area of irregular shapes

• Solve problems by breaking apart or changing the problem into simpler problems

Topic 7 -- Represent and Interpret Data

• Use graphs, frequency tables and picture graphs to compare and interpret data and to solve problems

• Use scaled bar graphs to represent data sets

• Use words, symbols and numbers to accurately and precisely solve math problems

Topic 8 -- Use Strategies and Properties to Add and Subtract

• Solve real world problems using properties of addition

• Identify patterns in the addition table and explain them using algebraic thinking

• Use mental math to add and subtract

• Use place value and a number line to round numbers

• Use rounding or compatible numbers to estimate sums and differences

• Solve one-step and multi-step problems by modeling with math

Topic 9 -- Fluently Add and Subtract within 1,000

• Add 2 three-digit numbers by breaking apart problems into simpler problems

• Use regrouping to add and subtract 3-digit numbers

• Add three or more numbers using addition strategies

• Subtract multi-digit numbers using the expanded algorithm

• Use strategies to add or subtract multi-digit numbers including subtraction with zeros

• Use addition and subtraction to justify a conjecture

Topic 10 -- Multiply by Multiples of 10

• Use a variety of strategies including the structure of multiplication, place value, patterns and properties of multiplication to find products when one factor is a multiple of 10

Topic 11 -- Use Operations with Whole Numbers to Solve Problems

• Draw diagrams and write equations to solve two-step equations involving addition, subtraction, multiplication and division of whole numbers

• Examine relationships between quantities in a two-step word problem by writing equations. Choose and apply the operations needed to find the answer

• Critique the reasoning of others by asking questions, identifying mistakes and providing suggestions for improvement

Topic 12 -- Understand Fractions as Numbers

• Understand how to read and write unit fractions for equal-sized parts of a region

• Use a fraction to represent multiple copies of a unit fraction

• Determine and draw the whole (unit) given one part (unit fraction)

• Represent fractions less than and greater than 1 on a number line

• Measure length to the nearest fourth inch and half inch and show the data on a line plot

• Determine when a problem has either extra or missing information

Topic 13 -- Fraction Equivalence and Comparison

• Find equivalent fractions that name the same part of the whole

• Represent equivalent fractions on the number line

• Use models such as fraction strips to compare fractions that refer to the whole and have the same denominator or the same numerator

• Use benchmark numbers and number lines to compare fractions

• Use fraction names to represent whole numbers

• Construct math arguments using fractions

Topic 14 -- Solve Time, Capacity and Mass Problems

• Show and tell time to the nearest minute using analog and digital clocks

• Solve word problems using addition and subtraction to measure quantities of times

• Use standard units to estimate and measure liquid volume and estimate the masses of solid objects

• Use a pan balance with metric weights to measure the mass of objects in grams and kilograms

• Use pictures to help solve problems about mass and volume

• Make sense of quantities and relationships in problems

Topic 15 -- Attributes of Two-Dimensional Shapes

• Identify, analyze and compare quadrilaterals, and use attributes to describe, group and classify shapes

• Solve math problems precisely, efficiently and accurately using appropriate tools and mathematics vocabulary

Topic 16 -- Solve Perimeter Problems

• Find the perimeter of different polygons

• Use the given sides of a polygon and the known perimeter to find the unknown side length

• Understand the relationship of shapes with the same perimeter and different areas, and shapes with the same area and different perimeters

• Understand the relationship between numbers to simply and solve problems involving perimeter

Topic 17 -- Step Up to 4th Grade

• Recognize the relationship between adjacent digits in a multi-digit number

• Multiply multiples of 10, 100, and 1,000 using mental math and place-value strategies

• Use models and properties of operations to multiply 2-digit numbers by multiples of 10

• Solve division problems and interpret remainders

• Use fraction strips and number lines to add fractions

• Decompose a fraction or mixed number into a sum of fractions in more than one way

• Recognize and draw lines, rays, and angles with different measures

• Find the measure of an angle that turns through a fraction of a circle

• Draw and identify perpendicular, parallel and intersecting lines