Web viewStudents will classify two-dimensional shapes based on their attributes such as congruent ... and revise to solve word ... to classify polygons according

2015 - 2016

Mathematics: Fifth GradeIn 5th grade, instructional time will focus on operations with decimals;

operations with fractions; conversion of measurement; and classifying 2-dimensional and 3-dimensional shapes.

Instruction on decimals will focus on comparing and rounding to the thousandths as well as being able to add, subtract, multiply, and divide decimals to the hundredths.

Fraction instruction will involve addition, subtraction, multiplication, and division. The fractions will include like and unlike denominators as well as mixed numbers. Students are expected to simplify their answers.

The students will convert length, capacity, and weight measurements within the customary and metric systems. The problems they encounter will involve multistep conversions.

Students will classify two-dimensional shapes based on their attributes such as congruent angles, congruent sides, right angles, and parallel lines. They will also identify the properties of three-dimension figures such as faces, edges, and vertices.

Course Information:

Frequency & Duration: Daily for 60 minutesText: My Math (2013), McGraw Hill

Mathematics: Fifth Grade v. 2015 - 2016

Content: Place Value/Multiplying Whole Numbers

Duration: 6 weeks (Aug/Sept)

Essential Question:

How does the position of a digit in a number relate to its value?What strategies can be used to multiply whole numbers?

Skills:

Compare and order whole numbers and decimals to the thousandths

Round decimals to the thousandths

Use partial products and distributive property to multiply numbers

Use powers to express numbers

Multiply mentally using basic facts and powers of 10

Develop an understanding that a digit in one place represents 1/10 of what it represents in the place to its left.

Read and write decimals to the thousandths

Estimate products Multiply numbers up to 3-

digit factors

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to estimate products of whole numbers and

decimals to the thousandths Students are able to multiply 3-digit numbers by 3-digit

numbers

Recommended Activity:

Problem of the Day Foldables Games

Standards:

CC.2.1.5.B.1 Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.CC.2.1.5.B.2 Extend an understanding of operations with whole numbers to perform operations including decimals.

Vocabulary: Decimal point; Decimal; Equivalent decimals; Expanded form; Standard formPeriod- each group of three digits on a place value chart; Base-in a power the number used as a factor; Power-a number obtained by raising a base to an exponent; Exponent- in a power, the number of times the base is used as a factor; Compatible numbers-numbers in a problem that are easy to work with mentally; Cubed-a number raised to the third power; Power of 10- a number like 10, 100, 1,000 and so


onComments:


Content: Divide by a One-Digit Divisor Duration: Oct/Nov (4 weeks)

Essential Question: What strategies can be used to divide whole numbers?

Skills:

Understand how division and multiplication are related

Divide with two-digit divisors

Estimate quotients Divide using the

distributive property and partial quotients

Understand how to place the first digit in a quotient

Solve division problems that result in quotients that have zeros

Interpret and explain how to interpret the remainder in a division problem

Identify extra information or missing information needed to solve a problem

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to divide by 2-digit divisors Students are able to estimate quotients Students are able to interpret remainders when answering word

problems


Foldables Scoot Game

Standards: CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.

Vocabulary:

Dividend; Divisor; Fact family; Quotient; RemainderPartial quotient - a method of dividing where you break the dividend into sections that are easy to divide; Unknown - missing value in a number sentence or equation; Variable - a letter or symbol used to represent an unknown quantity


Comments:


Content: Add and Subtract Decimals Duration: November (2 weeks)

Essential Question:

How can I use place value and properties to add and subtract decimals?

Skills:

Round decimals Estimate sums and differences by rounding Solve problems by using an estimate or an exact answer Explore adding decimals using models Add decimals to the hundredths Subtract decimals to the hundredths

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to add and subtract decimals to the

hundredths Students are able to estimate sums and differences Students are able to determine whether an estimate or exact

answer is needed when problem solving


Foldables Use menus from restaurants

Standards:

CC.2.1.5.B.1 – Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals.CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.

Vocabulary: Continue reviewing and reinforcing previous vocabulary.

Comments:


Content: Multiply and Divide Decimals Duration: Nov/ December (2 weeks)

Essential Question:

How is multiplying and dividing decimals similar to multiplying and dividing whole numbers?

Skills:

Estimate products of whole numbers and decimals Multiply decimals by whole numbers Multiply decimals by decimals Use the associative, commutative, and identity properties to

multiply mentally Estimate quotients of decimals and whole numbers Divide decimals by whole numbers Divide decimals by decimals

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to multiply decimals to the hundredths Students are able to divide decimals to the hundredths (no

divisors with decimals) Students are able to estimate products and quotients


Problem of the Day Scoot Review

Standards: CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.

Vocabulary: Continue reviewing and reinforcing previous vocabulary.

Comments:


Content: Expressions and Patterns Duration: December (2 weeks)

Essential Question: How are patterns used to solve problems?

Skills:

Write and evaluate numerical expressions Use the order of operations to evaluate expressions Use numbers and operation symbols to write verbal phrases as

numerical expressions Solve problems by working backwards Generate numerical patterns and identify pattern relationships

between corresponding terms of 2 patterns Identify and extend patterns and sequences Plot points on a grid to solve real-world problems Graph ordered pairs on a coordinate plane

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to evaluate numerical expressions containing

exponents, parentheses, and brackets Students are able to generate numerical patterns and identify

the relationship between corresponding terms in two different patterns

Students are able to graph an ordered pair in the first quadrant on a coordinate plane.


Students create their own patterns Mystery picture (plot points to reveal picture)

Standards:

CC.2.2.5.A.1 – Interpret and evaluate numerical expressions using order of operations.CC.2.2.5.A.4 – Analyze patterns and relationships using two rules.CC.2.3.5.A.1 – Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and mathematical problems.

Vocabulary:

Coordinate plane - a plane that is formed when two number lines intersect; Evaluate - to find the value of an expression by replacing variables by numbers; Numerical expression - combination of numbers and operations; Ordered pair - a pair of numbers that is used to name a point on a coordinate grid order of operations; Origin - the point (0,0) on a coordinate plane where the vertical axis meets the horizontal axis; Sequence - a list of numbers that follow a specific pattern; Term - a number in a pattern

Comments:


Content: Fractions and Decimals Duration: January (2 weeks)

Essential Question: How are factors and multiples helpful in solving problems?

Skills:

Determine the common factors and the greatest common factor of a set of numbers

Generate equivalent fractions by writing a fraction in simplest form

Guess, check, and revise to solve word problems Determine the least common multiples of a set of numbers Compare fractions by using the least common denominators Use fraction equivalence to write fractions as decimals

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to generate equivalent fractions using the

greatest common factor Students are able to compare fractions by using least common

denominators


Factor Trees Provide students with a fraction card; then have students find

their equivalent fraction

Standards:

CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract fractions.CC.2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide fractions.CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals.

Vocabulary:Common factor; Common multiple; Denominator; Equivalent fractions; Fraction; Greatest common factor; Least common multiple; Least common denominator

Comments:


Content: Add and Subtract Fractions Duration: Jan/February (4 weeks)

Essential Question: How can equivalent fractions help me add and subtract fractions?

Skills:

Add like fractions including mixed numbers Subtract like fractions including mixed numbers Use models to add unlike fractions including mixed numbers Add unlike fractions including mixed numbers Subtract unlike fractions including mixed numbers Solve problems by determining reasonable answers

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students will be able to add and subtract like fractions including

mixed numbers. Students will be able to add and subtract unlike fractions

including mixed numbers.

Recommended Activity: Use models to add and subtract fraction

Standards:

CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract fractions.CC.2.2.5.A.1 – Interpret and evaluate numerical expressions using order of operations.

Vocabulary: Like fractions; Unlike fractions

Comments:


Content: Multiply and Divide Fraction Duration: February/March (3 weeks)

Essential Question: What strategies can be used to multiply and divide fractions?

Skills:

Estimate products of fractions Multiply whole numbers and fractions Multiply fraction by a fractions Multiply mixed numbers Multiplication as scaling Divide whole number by fraction Divided fractions by a whole number

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to multiply whole numbers, fractions, and

mixed numbers Students are able to divide whole numbers and fractions using

models


Create foldable math skills practice sheet Compare fractions and decimals using a Venn Diagram

Standards: CC.2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide fractions

Vocabulary:

Unit fractionScaling - the process of resizing a number when it is multiplied by a fraction that is greater than or less than one; Fair share - an amount divided equally

Comments:


Content: Measurement Duration: March (2 weeks)

Essential Question: How can I use measurement conversions to solve real-world problems?

Skills:

Convert measurements of length within the customary system Convert measurement of weight within the customary system Estimate and measure the capacity of liquids Convert measurements of capacity within the customary system Display measurement data in fractions of a unit on a line plot

and solve real-world problems Convert measurements of length within the metric system Convert measurement of mass within the metric system Convert measurement of capacity within the metric system

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students will be able to compute multi-step conversions within

the same measurement system Students will be able to display fractional data on a line plot and

determine the fair share


Have students stand and use hand motions showing large to small means multiply.

Graph measurement data on a line plot.

Standards:

CC.2.4.5.A.1 – Solve problems using conversions within a given measurement system.CC.2.4.5.A.4 – Solve problems involving computation of fractions using information provided in a line plot.

Vocabulary:Capacity; Centimeter; Convert; Cup; Customary system; Fair share; Fluid ounces; Foot; Gallon; Gram; Inch; Kilogram; Kilometer; Length; Liter; Mass; Meter; Metric system; Mile; Milligram; Milliliter; Ounce; Pint; Pound; Quart; Ton; Weight; Yard

Comments:


Content: Polygons Duration: April (4 weeks)

Essential Question: How does geometry help me solve problems in everyday life?

Skills:

Classify two-dimensional figures based on properties Classify triangles based on attributes Measure the sides and angles of quadrilaterals Classify quadrilaterals based on attributes, such as congruent

sides, parallel sides, and right angles Build nets and explore properties of three-dimensional figures Describe properties of three-dimensional figures Use volume formulas to find the volume of rectangular prisms

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to classify polygons according to their

attributes Students are able to use volume formulas to calculate volume of

rectangular prisms and composite figures


Quadrilateral sort Cut out and build nets

Standards:CC.2.3.5.A.2 – Classify two-dimensional figures into categories based on an understanding of their properties.CC.2.4.5.A.6 – Apply concepts of volume to solve problems and relate volume to multiplication and to addition.

Vocabulary:

Congruent angles; Congruent figures; Congruent sides; Hexagon; Octagon; Parallelogram; Polygon; Prism; Rectangle; Regular polygon; Rhombus; Square; TrapezoidAttribute- the characteristic of a figure; Base - any side of a parallelogram; Composite figure - a figure made up of 2 or more 3 dimensional figure; Cube - a rectangular prism with 6 faces that are congruent squares; Cubic unit - a unit of measuring volume; Edge - line segment where 2 faces of a 3 dimension figure meet; Face - a flat surface; Net - a two dimensional pattern of a 3 dimensional figure; Three-dimensional figure - a figure that has length, width, and height; Triangular prism - a prism that has triangular bases; Unit cube - a cube with a side length of 1 unit; Vertex - the point where two rays meet in an angle where three or more faces meet on a 3-D figure; Volume - the amount of space inside a 3-D figure

Comments:



Content: Prime Factorization Duration: May (1 week)

Essential Question: What strategies can be used to multiply whole numbers?

Skills: Identify and explore patterns in prime factorization

Assessment:

Pre- and Post-Assessments Performance Tasks Quiz Students will be able to break down a number into its prime

factorization

Recommended Activity: Develop factor trees

Standards: There is no PA common core standard aligned to this content.

Vocabulary: Prime factorization - a way of expressing a composite number as a product of its prime factors

Comments:


Content: Adding and Subtracting Fractions (with renaming)

Duration: May (1 week)

Essential Question: How can equivalent fractions help me add and subtract fractions?

Skills: Adding mixed numbers with renaming Subtract mixed numbers with renaming

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to add and subtract mixed numbers with

renaming

Recommended Activity: Use fractions bars to demonstrate renaming

Standards: CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract fractions.

Vocabulary: Continue reviewing and reinforcing previous vocabulary

Comments:


Content: Polygons Duration: May/June (2 weeks)

Essential Question: How does geometry help me solve problems in everyday life?

Skills: Measure the sides and angles of triangles Measure sides and angles of quadrilaterals

Assessment:

Pre- and Post-Assessments Performance Tasks Mid-Chapter (formative) Quiz Students are able to classify triangles based on their angles and

length of sides

Recommended Activity: Measure lengths of sides and measure angles of triangles

Standards: CC.2.1.5.C.2 – Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Vocabulary:

Acute triangle- a triangle with three acute angles; Obtuse triangle- a triangle with one obtuse angle; Equilateral triangle- a triangle with three congruent sides; Isosceles triangle- a triangle with at least 2 sides the same length; Scalene triangle- a triangle with no congruent sides; Right triangle- a triangle with one right angles

Comments:

Documents

Web viewStudents will classify two-dimensional shapes based on their attributes such as congruent ... and revise to solve word ... to classify polygons according