Standards: Connecticut has adopted the Common Core State Standards (CCSS) as the Connecticut State Standards (CSS).

Instruction: students will engage the Standards of Mathematical Practice when problem solving and thinking mathematically. Mathematics Instruction will follow the C-P-A pedagogy of concrete, pictorial and abstract components when solving mathematical problems. Mathematical instruction focuses heavily on visual representation as a strategy to support mathematical thinking. Strategies such as number bonds for composing and decomposing numbers, bar models, and open number lines to support problem solving and mental math, are ongoing strategies students are encouraged to use.

Personalized Learning Resources: DreamBox, NWEA Assessments

Standard Assessments: Students take the NWEA Assessment three times a year and Smarter Balanced Assessment in the Spring.

STANDARDS

Use place-value understanding and properties of operations to perform multi-digit arithmetic.

• 3.NBT.A.1 - Use place-value understanding to round whole numbers to the nearest 10 or 100.
• 3.NBT.A.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.

BIG IDEAS / UNDERSTANDINGS

• Deep understanding of place value is needed to use the 4 operations and perform arithmetic problems

CONTENT / CONCEPTS

The student will . . .

• understand and practice how to use place value strategies to add and subtract 3-digit numbers.

STANDARDS

Represent and solve problems involving multiplication and division.

• 3.OA.A.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.A.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.A.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.
• 3.OA.A.4 - Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Understand properties of multiplication and the relationship between multiplication and division.

• 3.OA.B.5 - Apply properties of operations as strategies to multiply and divide. (Commutative, Associative, and Distributive property)
• 3.OA.B.6 - Understand division as an unknown-factor problem.

Multiply and Divide within 100.

• 3. OA.C.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.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

• 3. OA.D.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.D.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.A.3 - Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 8.0 , 5 60 ) using strategies based on place value and properties of operations.

BIG IDEAS / UNDERSTANDINGS

• Multiplication and division are related operations.
• An unknown quantity can be determined quickly using the four operations and patterns in arithmetic.

CONTENT / CONCEPTS

The student will be able to . . .

• understand concepts of multiplication and division.
• use concrete objects and drawings to represent multiplication and division problem situations.
• create and interpret equations to represent multiplication and division problems.
• understand that division is the inverse of multiplication.
• build an understanding of the commutative, associative, and distributive properties of multiplication.
• investigate and explore these properties through concrete models and drawings.
• develop understanding of multiplication and division math facts.
• gain fluency with multiplication and division math facts through focus on strategies and games.
• recognize problem structure that indicate when to add, subtract, multiply, or divide to solve math problems and build appropriate equations.
• understand problems through retelling, discussing and constructing models to represent the problem.
• explore strategies for solving two step problems.

STANDARDS

• 3.NF.A.1 - Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into equal parts; understand a fraction a/ b as the quantity formed by a parts of size 1/b.
• 3.NF.A.2 - Understand a fraction as a number on the number line; represent fractions on a number line diagram.
• 3.NF.A.3 - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

BIG IDEAS / UNDERSTANDINGS

• Fractions are numbers that are part of a whole.

CONTENT / CONCEPTS

The student will be able to . . .

• understand what fractions are.
• represent fractions using models, number lines and set models.
• understand the meaning of numerator and denominator in reading and writing fractions.
• explore fraction equivalence.
• understand that whole numbers can be expressed as fractions.
• compare fractions with like denominators and numerators.
• understand when comparing fractions the whole must be the same

STANDARDS

Solve problems involving measurement and estimation.

• 3.MD.A.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.MD.A.2 - Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 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.MD.C.5 - Recognize area as an attribute of plane figures and distinguish between linear and area measures.

BIG IDEAS / UNDERSTANDINGS

• Measurement and estimation help with daily tasks (time, volume, mass).
• What we measure influences how we measure.

CONTENT / CONCEPTS

The student will be able to . . .

• tell and write time to the nearest minute.
• use addition and subtraction to solve problems about time.
• solve problems using elapsed time.
• understand units of measure for mass and volume.
• estimate and measure mass and volume.
• solve one step problems involving mass and volume using any operation.

STANDARDS

Represent and interpret data.

• 3.MD.B.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.
• 3.MD.B.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.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

• 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

Geometric measurement: recognize perimeter.

Reason with shapes and their attributes.

BIG IDEAS / UNDERSTANDINGS

• Graphs and plots are used to represent measured and estimated data.

CONTENT / CONCEPTS

The student will be able to . . .

• draw a scaled picture graph and bar graph.
• solve problems (1-2 step) using data from graphs.
• measure to the nearest half AND quarter inch.
• create line plots with the horizontal scale marked in wholes, halves, and fourths.
• understand and determine area by counting square units.
• use multiplication to determine area.
• decompose complex figures to determine area.
• determine perimeter using addition.
• determine missing side length of a figure given perimeter.
• explore the relationship between area and perimeter.