Fifth Grade Standards
number and operations-fractions
apply and extend previous understandings of multiplication and division to multiply and divide fractions
5.NF.B.7
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients EXAMPLE
b. Interpret division of a whole number by a unit fraction and compute such quotients. EXAMPLE
c. Solve real world problems involving division of unti fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g. by using visual fraction models and eqations to respresent the problem. EXAMPLE
5.NF.B.6
Solve real world problems using multplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem.
5.NF.B.5
interpret multiplication as scaling(resizing) by:
a. comparing the size of a priducts to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given product.
5.NF.B.4
Apply and extend previous understandings of multplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) x q as "a" parts of a partition of "q" into "b" equal parts; equivalently, as the result of a sequence of operations, a x q/ b.
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the approriate unit fraction side lengths, and show that the unit area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and prepresent fraction products as rectangular areas.
5.NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a divided by b). Solve wor problems involving devision of whole numbers leading to answers in the form of fractions or mixed numbers, e.g. by using visual fraction models or equations to represent the problem.
Relating fractions to division
use equivalent fractions as a strategy to add and subtract fractions.
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 eqations to represent the problem. Use benchmarks fractions and number sense of fractions to estimate mentaly and assess the reasonableness of answers.
Addition word problems with fractions
5.NF.A.1
Add and subtraction 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.
Class Activity:
-Closest to 25!-
1. Students will pair up with one another and take turns rolling a die twice to form a fraction.
2. With given table, student will decide if they want to add or subtract the given fractions keeping in mind that:
-goal is to be the player closest to 25 after ten rounds
-you may only use each operation five times.
3. Player 2 repeats above steps
geometry
Classify two dimensional figures into categories based on their properties
5.G.B.4
Classify two dimensional figures ina hierchy based on properties.
5.G.B.3
Understand that attributes belonging to a category of two-dimensional figures also belong to subcategories of that category.
Idenifying Quadrilaterals
Graph points on the coordinate plane to solve real-world and mathematic problems .
5.G.A.2
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.G.A.1
Use a pair of perpendicular lines, called axes, to define a coordinated system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers , called its coordinates.
Coordinate shapes
Measurement and data
Geometric measurement: understandin concepts of volume and relate volume to multiplication and to addition.
Subtopic
5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
a. volume of right rectangular prism with whole number side lengths
b. Apply the formulas V = / x w x h and V = b x h for rectangular prisms to finf volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
c. Recognize volume as additive.
create a sculpture
5.MD.C.4
Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and improvised units.
3D structure
5.MD.C.3
Recognize volume as an attribution of solid figures and understand concept of volume measurement.
a. A cube side length 1 unit , called a "unit cube," is said to have "one cubic unit" of volme, and can be used to measure volume.
b. A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a value of n unit cubic units.
Class Activity:
-Build a cubic meter using rolled up newspaper-
represent and interpret data
5.MD.B.2
Make a line plot to diplay a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Using operations on fractions for this to grade solve problems involving information presented in line plots.
Fractions on a line plot
convert like measurement units within a given measurement system
5MD.A.1
Convert among different-sized standard measurement units within a given measurement system (e.g., covert 5cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
number and operations in base ten
Perfom operations with multi-digit whole numbers and with decimals to hundredths
5.NBT.B.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawingd ans strategies based on place value, properties of operations and/or the realtionship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Class Activity:
Decimal Addition Bingo
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 thre calculation by using equations rectangular arrays and/or area models.
Create and Solve a Division Problem
5.NBT.B.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
Class activity:
-Make the Smallest Product-
Work with a partner.
1. Shuffle the cards and place face down in a pile.
2. Take four cards each and arrange them to make a two digit multiplication problem. Aim to make the smallest products possible
3. Write problem out and solve.
4.player with smallest product wins.
5.keep going until one of you reaches 10 points.
understand the place value system
5.NBT.A.4
Use place values understanding to round decimals to any place
5.NBT.A.3
Read, write, and compare decimals to thousandths
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form
b.Complare to decimals to thousandths based on meaning of the digits in each place, using >,=, and < to record the results of comparisons.
347.392 = 3x100 + 4x10 + 7x1 + 3x(1/10) +9x(1/100) + 2x(1/1000)
5.NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explains patterns in 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.
multiplying a whole number by a power of ten
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 1/10 of what it represents in the place to its left.
comparing digits
Operations and Algebraic thinking
analyze patterns and relationships
5.OA.B.3
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairson a coordinate plane.
Class activity:
-Addition on the coordinate plane-
Students will be given graphing paper and rules to find terms in sequences, graph ordered pairs on a coordinate plane, and find the nth term in sequences
write and interpret numerical expressions
5.OA.A.2
Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them.
Class activity:
-Verbal Expressions-
Working with a partner, cut out cards and match each verbal equation with its corresponding algebraic equation.
5.OA.A.1
Use parenthesis, brackets, orbraces in numerical expressions with these symbols.
