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 Assessment

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

STANDARDS

Understands the Place Value System

• 5.NBT.A.1 - Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represents in the place to its left.
• 5.NBT.A.2 - Explain patterns in the number of zeros in the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
• 5.NBT.A.3 - Read, write, and compare decimals to thousandths.
• 5.NBT.A.3.a - Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
• 5.NBT.A.3.b - Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• 5.NBT.4 - Use place-value understanding to round decimals to any place.
• 5. OA. 1 - Use parentheses, brackets or braces in numerical expressions, and evaluate expressions with these symbols.
• 5. OA. 2 - Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them.

Write and interpret numerical expressions.

Additional Standards to be covered throughout the year.

• 5.MD.1 - Convert among different-sized standard measurement units within a given measurement system( e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

BIG IDEAS / UNDERSTANDINGS

• Deep understanding of place value is needed to understand and use multi-digit numbers (whole numbers, fractions, decimals).
• Converting and using measurement quantify and represent daily tasks (distance, time, volume, mass, money).

CONTENT / CONCEPTS

The student will be able to . . .

• read and write decimals to the thousandths place in word form, base-ten form, and expanded form.
• identify the powers of ten.
• compare two decimals to the thousandths place.
• How to round decimals to any place.
• understand the relationship between the value of digits in different places in a multi-digit number.
• simplify expressions using the order of operations.
• interpret math expressions.
• understand the difference between an expression and an equation.
• write an expression for different math situations.
• compare two expressions without evaluating them.

STANDARDS

Perform operations with multi-digit whole numbers and with decimals to hundredths.

• 5.NBT.B.5 - Fluently multiply multi-digit whole numbers using the standard algorithm.
• 5.NBT.B.6 - Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.
• 5.NBT.B.7 - Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties or operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Additional Standards covered throughout the year.

• 5.MD.A.1 - Convert among different-sized standard measurement units within a given measurement system( e.g., convert 5cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

BIG IDEAS / UNDERSTANDINGS

• Fractions are numbers where the operations on whole numbers can be applied.
• Converting and using measurement quantify and represent daily tasks (distance, time, volume, mass, money).

CONTENT / CONCEPTS

The student will be able to . . .

• fluently use an algorithm to multiply multi-digit numbers.
• divide up to 4 digit dividends and 2-digit divisors using place value strategies.
• interpret remainders.
• explain the division process using models.
• add and subtract decimals using strategies based on place value.
• correctly place the decimal point when multiplying and dividing decimals.
• multiply a decimal by a whole number and a decimal.
• divide a whole number by a decimal, a decimal by a whole number and a decimal by a decimal.

STANDARDS

Use equivalent fractions as a strategy to add and subtract fractions

• 5.NF.A.1 - Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
• 5.NF.A.2 - Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Additional Standards covered throughout the year.

• 5.MD.1 Convert among different-sized standard measurement units within a given measurement system( e.g., convert 5cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

BIG IDEAS / UNDERSTANDINGS

• Adding and Subtracting Fractions provide a process to share and split things equally.
• Converting and using measurement quantify and represent daily tasks (distance, time, volume, mass, money).

CONTENT / CONCEPTS

The student will be able to . . .

• find a common denominator to find equivalent fractions.
• add and subtract fractions using strategies including finding a common denominator.
• model fractions as division and explain how fractions represent division.

STANDARDS

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

• 5.NF.B.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
• 5.NF.B.4 - Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4.a - Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).
  • 5.NF.B.4.b - Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
• 5.NF.B.5 - Interpret multiplication as scaling (resizing), by:
  • 5.NF.B.5.a - Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  • 5.NF.B.5.b - Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
• 5.NF.B.6 - Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• 5.NF.B.7 - Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
  • 5.NF.B.7.a - Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
  • 5.NF.B.7.b - Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
  • 5.NF.B.7.c - Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Additional Standards covered throughout the year.

• 5.MD.A.1 - Convert among different-sized standard measurement units within a given measurement system( e.g., convert 5cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

BIG IDEAS / UNDERSTANDINGS

• Fractions are numbers where the operations on whole numbers can be applied.
• Converting and using measurement quantify and represent daily tasks (distance, time, volume, mass, money).

CONTENT / CONCEPTS

The student will be able to . . .

• multiply fractions, including mixed numbers, by a whole number or fraction.
• use models to multiply fractions.
• interpret the product when multiplying fractions.
• identify unit fractions.
• divide a unit fraction by a whole number using models.
• divide a whole number by a unit fraction using models.

STANDARDS

Geometric Measurement: Understand concepts of volume (relate volume to multiplication and addition)

• 5.MD.C.3 - Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
• 5.MD.C.3.a - A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
• 5.MD.C.3.b - A solid figure which can be packed without gaps or overlaps using unit cubes is said to have a volume of cubic units.
• 5.MD.C.4 - Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
• 5.MD.C.5 - Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.
  • 5.MD.C.5.a - Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
  • 5.MD.C.5.b - Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.
  • 5.MD.C.5.c - Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding volumes of the non-overlapping parts, applying this technique to solve real-world problems.

Supporting Standards

• 5.MD.A.2 - Make a line plot to display a data set of measurements in fractions of a unit ( ½ , ⅛ ). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Additional Standards covered throughout the year.

• 5.MD.A.1 - Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

BIG IDEAS / UNDERSTANDINGS

• Converting and using measurement quantify and represent daily tasks (distance, time, volume, mass, money).
• Volume is an attribute of solid figures (that can describe patterns and reason in the physical world) that can be measured.

CONTENT / CONCEPTS

The student will be able to . . .

• create line plots with units in halves, fourths, eighths.
• use data from line plots to solve problems.
• volume is measured in cubic units and why.
• find volume in a rectangular prism.
• find volume in complex figures.
• recognize the x-axis and y-axis on a coordinate plane.
• solve problems involving ordered pairs.
• identify and classify shapes based on their attributes.