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The third grade map shows the shift in teaching strategies from a traditional method focusing on rote skills to building a growth mindset and conceptual understanding. The primary focuses for third grade are multiplication, division and unit fractions. Students must begin to work with multiplication and division at or near the very start of the year to allow time for understanding and fluency to develop. Students will be building on second grade skills of patterns, skip counting, and repeated addition to help build their multiplication knowledge. In 3rd grade, students develop an understanding of fractions as numbers which is essential for future work with the number system. In the map, you will find compelling questions and essential vocabulary that will better organize and guide your instruction.
Big ideas in third grade:
(1) developing understanding of multiplication and division and strategies for multiplication and division within 100
(2) developing understanding of fractions, especially unit fractions (fractions with numerator 1)
(3) developing understanding of the structure of rectangular arrays and of area
(4) describing and analyzing two-dimensional shapes.
Instructional Time Guidance for Third Grade:
Printables:
Printables:
learning targets, year at a glance, report card correlation, & resource list
learning targets, year at a glance, report card correlation, & resource list
3rd grade learning targets printable list click here.
Year at a Glance printable version click here
3rd gr Number talk guide click here
Report Card Standards Correlation click here
Standards Based Report Cards 3rd grade ENGLISH SPANISH ARABIC parent information
K-5 Math Framework click here & Vertical Coherency overview click here
3rd grade Classroom Inventory list click here
Ready Teacher Toolbox math templates printables
Third Grade Fluency
Third Grade Fluency
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.
By the end of Grade 3, know from memory all products of two one-digit numbers. Proficiency Rubric 3.OA.7
By the end of Grade 3, know from memory all products of two one-digit numbers. Proficiency Rubric 3.OA.7
**Timed tests do NOT measure all components of fluency, only speed and accuracy. It takes the focus away from phase 2, building reasoning strategies, and ultimately creates fast counters and memorizers. If we want fluent kids, we need to give them time to build fluency with strategies.
**Timed tests do NOT measure all components of fluency, only speed and accuracy. It takes the focus away from phase 2, building reasoning strategies, and ultimately creates fast counters and memorizers. If we want fluent kids, we need to give them time to build fluency with strategies.
More information and Resources on the fluency tab.
All Print Resources from Mastering the Basic Facts Multiplication and Division: x÷facts
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
*The standard algorithm is a 4th grade standard.
Essential Questions
Essential Questions
Year at a Glance
Year at a Glance
Click here for a printable version of Year at a Glance.
You will find that content in our curriculum maps have been given a priority designation; however, lower priority is not meant to imply exclusion. These priorities are meant to help guide the focus of teachers as they allocate their limited time for planning and instruction. Teachers should always use their best judgment for what works for them and their students.
🟩 Major content identifies those areas where students should spend the large majority (65-85%) of instructional time and focus on the major work of the grade.
🔷 Supporting content is designed to strengthen the areas of major emphasis, as these pieces are closely connected to the major clusters of the grade.
🟡 Additional content covers material that does not connect tightly or explicitly to the major work of the grade, but still engages students in grade-level conceptual learning.
Starting out the year
Starting out the year
Growth Mindset Lessons, Activities and Videos to use as you lay the groundwork for a Mathematical Mindset connected to The 8 Standards for Mathematical Practice. Good Group Work-setting norms
Begin launching Guided Math:
For assistance on structuring guided math, click here. Guide to the first 20 days here.
T1
1 week
What is multiplication and division?
What is multiplication and division?
🟩 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
🟩 3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
🟩 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
T1
2-3 weeks
*Begin with foundational facts 2, 5,10, 1, 0 FACTS ONLY the first 5 -6 weeks.
Build on foundational facts next using facts 3, 4, 8, 6, 9, 7 AFTER covering compelling question 2 standards.
What is the relationship between place value and addition and subtraction?
What is the relationship between place value and addition and subtraction?
T1
3-4 weeks
Continue to focus on foundational facts
x/÷ 2, 5, 10, 1, 0
What is area and perimeter? What are strategies used to solve area and perimeter?
What is area and perimeter? What are strategies used to solve area and perimeter?
🔷 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
🟩 3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.
3.MD.5a A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
3.MD.5b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
🟩 3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
🟩 3.MD.7 Relate area to the operations of multiplication and addition.
3.MD.7a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
3.MD.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
3.MD.7c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
3.MD.7d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
🟩 3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
🟡 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
T1/2
6-7 weeks
Continue to practice x/÷ foundational facts.
Extend to x/÷3, 4, 8, 6 when introducing the distributive property.
What is multiplication and division and how are they related?
What is multiplication and division and how are they related?
Continue 3.OA.1-9 as needed
🟩 3.OA.1, 3.OA.2, 3.OA.3 from Q1
🟩 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
🟩 3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
🟩 3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
🟩 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
🟩 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding
🟩 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
🟡 3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (eg. 8 x 90, 5 x 60) using strategies based on place value and properties of operations.
T2
5-6 weeks
Continue to practice x/÷ foundational facts and x/÷3, 4, 8, 6
What is a fraction? What are different ways to represent fractions?
What is a fraction? What are different ways to represent fractions?
🔷 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
🟩 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
🟩 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
3.NF.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
🟩 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
🔷 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
🟩 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
T2/3
6-7 weeks
Continue to practice x/÷ foundational facts and x/÷3, 4, 8, 6
Extend to x/÷7, 9
How do we measure time and how are time and fractions related?
How do we measure time and how are time and fractions related?
🟩 3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
🟩 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
T3
2-3 weeks
Continue to practice x/÷ foundational facts and x/÷3, 4, 8, 6
Extend to x/÷7, 9
How do we choose the appropriate units of measurement?
How do we choose the appropriate units of measurement?
🟩 3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
🟩 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
T3
2 weeks
Continue to review all multiplication and division fact sets
How do we use data to create, interpret and analyze a picture graph or bar graph?
How do we use data to create, interpret and analyze a picture graph or bar graph?
🔷 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
🟩 3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding
🟩 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
T3
1-2 weeks
Continue to review all multiplication and division fact sets
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