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Instructional Focus:
Instructional Focus:
In Grade 3, instructional time should focus on four critical areas:
Developing understanding of multiplication and division and strategies for multiplication and division within 100.
Developing understanding of fractions, especially unit fractions (fractions with numerator 1).
Developing understanding of the structure of rectangular arrays and of area.
Describing and analyzing two-dimensional shapes.
Readiness Standards:
Readiness Standards:
Students extend their understanding of base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing.
Students use their understanding of addition to develop fluency with addition and subtraction within 100.
Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units.
Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes.
(See Second Grade Instructional Focus in Appendix)
Grade 3 Mathematical Content Standards
Grade 3 Mathematical Content Standards
Domain: Operations and Algebraic Thinking
Domain: Operations and Algebraic Thinking
Strand: Represent and solve problems involving multiplication and division.
Strand: Represent and solve problems involving multiplication and division.
Standard:
(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).
(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).
(3.OA.3) Use multiplication and division numbers up to 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).
(3.OA.4) Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
Examples & Resources:
(3.OA.1) Show objects in rectangular arrays or describe a context in which a total number of objects can be expressed as 5 × 7.
(3.OA.2) Deconstruct rectangular arrays or describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
(3.OA.4) Determine the unknown number that makes the equation true in each of the equations (8 x ? = 48, 5 = ? ÷ 3, 6 x 6 = ?).
Strand: Understand properties of multiplication and the relationship between multiplication and division.
Strand: Understand properties of multiplication and the relationship between multiplication and division.
Standard:
(3.OA.5) Make, test, support, draw conclusions, and justify conjectures about properties of operations as strategies to multiply and divide (students need not use formal terms for these properties).
Commutative property of multiplication: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known.
Associative 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.
Distributive property: 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.
Inverse property (relationship) of multiplication and division.
(3.OA.6) Understand division as an unknown-factor problem.
Examples & Resources:
(3.0A.6) Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Literature Connections:
The I Hate Mathematics! Book by Marilyn Burns
The King's Chessboard by David Birch
Strand: Multiply and divide up to 100.
Strand: Multiply and divide up to 100.
Standard:
(3.OA.7) Fluently multiply and divide numbers up to 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.
Examples & Resources:
Use:
counters
graph paper
arrays
Literature Connections:
Hershey’s Mik Chocolate Multiplication Book by Jerry Pallotta
M&M’s Brand Chocolate Candies Math by Barbara McGrath
Movin’ Through Multiplication by Karen Allen
Strand: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Strand: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Standard:
(3.OA.8) Solve and create two-step word problems using any of the four operations. Represent these problems using equations with a symbol (box, circle, question mark) 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.
Examples & Resources:
(3.OA.9) Observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Literature Connections:
Who Sank the Boat? by Pamela Allen
Domain: Number and Operations in Base Ten
Domain: Number and Operations in Base Ten
Strand: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Strand: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Standard:
(3.NBT.1) Use place value understanding to round whole numbers to the nearest 10 or 100.
(3.NBT.2) Use strategies and/or algorithms to fluently add and subtract with numbers up to 1000, demonstrating understanding of place value, properties of operations, and/or the relationship between addition and subtraction.
(3.NBT.3) Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 10 x 60) using strategies based on place value and properties of operations.
Examples & Resources:
Literature Connections:
The Best of Times by Gregory Tang
Anno's Mysterious Multiplying Jar by Masaichiro & Mitsumasa Anno
If You Made a Million by David M. Schwartz
Domain: Number and Operations - Fractions
Domain: Number and Operations - Fractions
(Limited in this grade to fractions with denominators 2, 3, 4, 6, and 8.)
Strand: Develop understanding of fractions as numbers.
Strand: Develop understanding of fractions as numbers.
Standard:
(3.NF.1) Understand a fraction 1/b (e.g., 1/4) as the quantity formed by 1 part when a whole is partitioned into b (e.g., 4) equal parts; understand a fraction a/b (e.g., 2/4) as the quantity formed by a (e.g., 2) parts of size 1/b (e.g., 1/4).
(3.NF.2) Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b (e.g., 1/4) on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b (e.g., 4) equal parts. Recognize that each part has size 1/b (e.g., 1/4) and that the endpoint of the part based at 0 locates the number 1/b (e.g., 1/4) on the number line.
b. Represent a fraction a/b (e.g., 2/8) on a number line diagram or ruler by marking off a lengths 1/b (e.g., 1/8) from 0. Recognize that the resulting interval has size a/b (e.g., 2/8) and that its endpoint locates the number a/b (e.g., 2/8) on the number line.
(3.NF.3) Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent if they are the same size (modeled) or the same point on a number line.
b. 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).
c. Express and model whole numbers as fractions, and recognize and construct fractions that are equivalent to whole numbers.
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).
Examples & Resources:
(3.NF.3c) 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.
Literature Connections:
Eating Fractions by Bruce McMillan
Lao Lao of Dragon Mountain by Margaret Bateson Hill
Domain: Measurement and Data
Domain: Measurement and Data
Strand: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Strand: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
Standard:
(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 or hours (e.g., by representing the problem on a number line diagram or clock).
(3.MD.2) Estimate and measure liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve and create 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). (Excludes multiplicative comparison problems [problems involving notions of “times as much.”]).
(3.MD.3) Select an appropriate unit of English, metric, or non-standard measurement to estimate the length, time, weight, or temperature.
Strand: Represent and interpret data.
Strand: Represent and interpret data.
Standard:
(3.MD.4) 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.
(3.MD.5) Measure and record lengths using rulers marked with halves and fourths of an inch. Make a line plot with the data, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.
(3.MD.6) Explain the classification of data from real-world problems shown in graphical representations. Use the terms minimum and maximum.
Examples & Resources:
(3.MD.4) Draw a bar graph in which each square in the bar graph might represent 5 pets.
Literature Connections:
How Big Is a Foot? by Rolf Myller
Millions to Measure by David M. Schwartz
A Million Fish… More or Less by Patricia C. McKissack
Anno's Magic Seeds by Mitsumasa Anno
On Beyond a Million: An Amazing Math Journey by David M. Schwartz
Strand: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Strand: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Standard:
(3.MD.7) Recognize area as an attribute of plane figures and understand concepts of area measurement.
a. A square with side length 1 unit is said to have “one square unit” and can be used to measure area.
b. Demonstrate that a plane figure which can be covered without gaps or overlaps by n (e.g., 6) unit squares is said to have an area of n (e.g., 6) square units.
(3.MD.8) Measure areas by tiling with unit squares (square centimeters, square meters, square inches, square feet, and improvised units).
(3.MD.9) Relate area to the operations of multiplication and addition.
a. 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.
b. 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.
c. Use area models (rectangular arrays) to represent the distributive property in mathematical reasoning. 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.
d. 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.
Examples & Resources:
(3.MD.9a) After tiling rectangles, develop a rule for finding the area of any rectangle.
(3.MD.9d) The area of a 7 by 8 rectangle can be determined by decomposing it into a 7 by 3 rectangle and a 7 by 5 rectangle.
Literature Connections:
Ben Franklin and the Magic Squares by Frank Murphy
Math-terpieces: The Art of Problem-Solving by Greg Tang
Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander
Strand: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Strand: Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Standard:
(3.MD.10) Solve real world and mathematical problems involving perimeters of polygons, including:
finding the perimeter given the side lengths,
finding an unknown side length,
exhibiting rectangles with the same perimeter and different areas, and
exhibiting rectangles with the same area and different perimeters.
Examples & Resources:
Use:
geo solids
geo boards
graph paper
Literature Connections:
The Art of Shapes: For Children and Adults by Margaret Steele
Cubes, Cones, Cylinders, & Spheres by Tana Hoban
Domain: Geometry
Domain: Geometry
Strand: Reason with shapes and their attributes.
Strand: Reason with shapes and their attributes.
Standard:
(3.G.1) Categorize shapes by different attribute classifications and recognize that shared attributes can define a larger category. Generalize to create examples or non-examples.
(3.G.2) Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
Examples & Resources:
(3.G.2) 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.
Suggested Activities for Grade 3:
Suggested Activities for Grade 3:
Foldables
Kagan Structures
Thinking Maps
Math Games
Odyssey Math
iPad Apps
Elementary Competency Checklist
Elementary Competency Checklist
Math Curriculum - K-5 Competencies - Adopted June 2022.pdfK-12 Math Sequence
K-12 Math Sequence
K-12 Math Sequence _ rev Feb 2017.pdfPage updated
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