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

Instruction: All 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

Generalize place-value understanding for multi-digit whole numbers.

• 4.NBT.A.1 - Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
• 4.NBT.A.2 - Read and Write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• 4.NBT.A.3 - Use place value understanding to round multi-digit whole numbers to any place.

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

• 4.NBT.B.4 - Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Additional Standards to be addressed all year.

• 4.OA.C.5 - Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.
• 4.MD.A.1 - Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.

BIG IDEAS / UNDERSTANDINGS

• Deep understanding of place value is needed to understand and use multi-digit whole numbers (operations, equations, rectangular arrays, area models).

CONTENT / CONCEPTS

The student will be able to . . .

• read and write multi-digit numbers to one million using standard form, expanded form and word form.
• round numbers to any place.
• add and subtract multi-digit numbers using place value strategies and the standard algorithm.

STANDARDS

• 4.NBT.B.5 - Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Use the four operations with whole numbers to solve problems.

• 4.MD.A.3 - Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
• 4.OA.A.1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• 4.OA.A.2 - Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

BIG IDEAS / UNDERSTANDINGS

• Deep understanding of place value is needed to understand and use multi-digit whole numbers (operations, equations, rectangular arrays, area models)

CONTENT / CONCEPTS

The student will be able to . . .

• multiply a whole number of up to 4 digits by a 1 digit whole number using strategies based on place value and properties.
• multiply 2-digit numbers by 2-digit numbers using strategies based on place value and properties.
• solve problems by finding the area or the perimeter of a shape including irregular shapes.
• find missing information when given the area or the perimeter of a shape.

STANDARDS

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

• 4.NBT.B.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Gain familiarity with factors and multiples.

BIG IDEAS / UNDERSTANDINGS

• Deep understanding of place value is needed to understand and use multi-digit whole numbers (operations, equations, rectangular arrays, area models).
• Numbers can be used in various ways through factors, multiples and patterns. Factors, numbers and multiples help to develop varied uses for numbers.

CONTENT / CONCEPTS

The student will be able to . . .

• identify prime numbers and composite numbers.
• find multiples and factors of given numbers.
• divide a multi-digit number by a 1 digit divisor using models and strategies based on place value.
• interpret remainders in division word problems.

STANDARDS

Extend understanding of fraction equivalence and ordering.

• 4.NF.A.1 - Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. *Only use denominators 2, 3, 4, 5, 6, 8, 10, 12, 100
• 4.NF.A.2 - Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

• 4.NF.B.3 - Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
• 4.NF.B.4 - Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

BIG IDEAS / UNDERSTANDINGS

• Models help explain how fractions are equivalent and comparable by size.
• Fractions are numbers where the operations on whole numbers can be applied.

CONTENT / CONCEPTS

The student will be able to . . .

• to find equivalent fractions for a given fraction.
• prove two fractions are equivalent using models, reasoning or computations.
• compare and order fractions.
• decompose a fraction into a sum of fractions with the same denominator.
• add and subtract fractions with LIKE denominators by drawing models and using an understanding of fractions as numbers.
• add and subtract mixed numbers with like denominators.
• solve addition and subtraction word problems using models and equations.
• understand non-unit fractions like ⅚ as products of unit fractions - e.g., ⅚= 5 x ⅙.
• find the product when multiplying a fraction by a whole number.
• solve word problems that call for multiplying a fraction by a whole number by using visual models.

STANDARDS

Understand decimal notation for fractions, and compare decimal fractions.

• 4.NF.C.6 - Use decimal notation for fractions with denominators 10 or 100.
• 4.NF.C.7 - Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.

BIG IDEAS / UNDERSTANDINGS

• How do I know when fractions are equivalent?
• Fractions are numbers where the operations on whole numbers can be applied

CONTENT / CONCEPTS

The student will be able to . . .

• compare and combine decimal fractions with denominators of 10 and 100.
• write a fraction with a denominator of 10 or 100 as a decimal.
• understand decimal notation and compare decimals to the hundredths place.

STANDARDS

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

• 4.G.A.1 - Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
• 4.G.A.2 - Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence of absence of angles of a specified size. Recognize right triangles as a category, and identify right angles.
• 4.G.A.3 - Recognize a line of symmetry for a two dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Represent and interpret data.

• 4.MD.B.4 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

Geometric measurement: understand concepts of angle and measure angles.

• 4.MD.C.5 - Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.
• 4.MD.C.6 - Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
• 4.MD.C.7 - Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

BIG IDEAS / UNDERSTANDINGS

• Real world problems are solved using the four operations, formulas, plots and units of measurement. Units of measurement quantify and represent daily tasks (distance, time, volume, mass, money): Angles are geometric shapes that describe patterns and reason in the physical world.
• Lines and angles form shapes that describe patterns and reason in the physical world.

CONTENT / CONCEPTS

The student will be able to . . .

• draw and identify various types of lines and angles.
• identify angles as acute, obtuse and right.
• measure angles with a protractor and draw angles of a specified measurement.
• understand that angle measurement is additive.
• classify shapes by properties of their lines and angles including classifying triangles.
• recognize a line of symmetry and identify figures that have line symmetry.