Printables

 We have attached several documents, provided many resources, and lesson plans you can implement in your classroom. If you have a document, resource, and/or lesson plan you think will help other teachers, please share: wanda@mathconcentration.com - subject ((Printable)). Great teachers never stop learning and honing their skills.

Jump to Implementing Effective Differentiated Instruction

Jump to Classroom Organization and Management Printables

Jump to Multi-Lingual Aids for ESL Students

Jump to Rewards and Incentives

Jump to Math Pizzazz Puzzles

Jump to PowerPoint Presentations

Jump to Math Vocab Cards

Jump to Math Student Surveys

Jump to Common Core Math Standards Freebies and Ideas

Pretest Printables:

6th Grade Math Pretest -Please email us if you would like the answer key(free): wanda@mathconcentration.com

7th Grade Math Pretest-Please email us if you would like the answer key (free): wanda@mathconcentration.com

Lesson Planning Printables:

Lesson Plans - Acrobat Lesson Plan Template
Lesson Plans- Lesson Plan Template
Lesson Plans- Lesson Plan Template
Lesson Plans- Lesson Plan Template
Lesson Plans -Lesson Plan Template
Lesson Plans-Lesson Plan Template
Common Core Planning Sheet- Common Core Math Lesson Planning Sheet
Pick A Number - Students pick a number before and after the lesson: (4): I understand it very well and can teach it (3): I can do it without help (2): I have some understanding (1): I have little understanding with help (0): I don't understand
Ticket Out the Door- A way of knowing whether or not your students understood the lesson for that day.
Implementing Effective Differentiated Instruction
4MAT-2: These are a collection of resources that explain the 4MAT approach to going through a lesson - good for differentiating by interest and learning style.  
7MR-1:An example of a tiered lesson for mathematics for a 7th grade class.
Agendas: This is the entire agenda handout taken from Tomlinson's Book. Agendas are a great way to slit up the classroom into multiple paths for learning where individual or groups of students have their learning agendas to accomplish.  
Cubing: This is the ASCD handout on Cubing. Cubing is an easy way to give students 6 different choice of questions to answer, problems to solve, or to create different levels of activities for your students while they kinesthetically roll the dice.  
Choice Board Explanation:A quick Word explanation of what a choice board is.  
Choice Board Handout:A more simple version of a choice board to have.  
Differentiated Instruction Workshop For Middle School Teachers Session 1: The powerpoint from the Middle School session. 
Differentiated Instruction Workshop for High School Teachers Session 1: The powerpoints from the High School session - there are slight differences from the Middle School group.
Flexible Grouping: This is a nice summary of the ways you would choose to have flexible grouping in your classroom as well as a nice summary of many of the strategies on this page.  
Monitor Student Progress:

Rubistar

  • Create your own rubrics from available templates and categories; can be personalized

Rubrics for Educators

  • Wide variety of ready-to-use rubrics and resources

RAFT: This is the ASCD handout on RAFT. RAFT is an excellent strategy to give students choice on the ROLE they want to take, the AUDIENCE they want to respond to, the FORMAT and the TOPIC they would like to write about, act out, or whatever you choose.  
Sternberg Intelligences: This is an ASCD packet on Sternberg's Intelligences. This is a great method to tap into the 3 types of learning styles that Sternberg proposes each student has certain inclinations for.  
Tier Planning Process:This is a diagram from Tomlinson that proposes a method to go about planning a tiered lesson.
Tiered Lesson Sample:This is an example of a lesson that has been broken up into 3 separate tiers, especially the products the students need to make. This gives a real in depth example of how to break up a common essesntial understanding in three different levels based on readiness.  
Tiered Lesson ELA-7th Grade:This is an example of a 7th grade ELA lesson that has been tiered.
Quick Summary of Multiple Intelligences:A brief run down of Howard Gardner's 8 intelligences. Useful for the 2nd task.  
Classroom Organization and Management
Bathroom Sign Out Sheet - Documents how many times a student used the restroom
Bathroom Sign Out Sheet- Documents when a student uses the restroom
Bathroom Sign Out Sheet - Documents when a students uses the restroom
Behavior Evaluation Report- Anecdotal record of student behavior
Book Check Out Sheet- Keep track of your classroom library books
Classroom Rules_ - A list of my classroom rules
Consequences - A list of consequences for breaking classroom rules
Detention Individual Assignment - An assignment for students to complete when serving a detention
First Day Letter- A welcome letter that I distribute on the first day of school
Heading- The way I require my students to head their papers.
Math Supply List - A list of math supplies required for my class.
Policies and Procedures - A list of policies and procedures for my class
parent/teacher communication log -  log parent communication
Seating Chart-A seating chart
Seating Chart with Rows - A seating chart for a classroom set up in rows
Seating Chart with Groups of Two - A seating chart for a classroom set up in groups of two
Seating Chart for Groups - A seating chart for a classroom set up in groups
Student Behavior/Parent Contact Log-Track a students behavior and parent contact log all on one document.
Student Classroom Expectation Contract - Student Classroom Expectation Contract to create a positive learning environment where students feel safe and comfortable learning and asking questions. Contract holds students accountable for their actions. I place this contract in their folder and if they choose to break a rule I pull this out as a reminder and verbal warning before giving the student a consequence.
Student Information Sheet- A great way for gaining and maintaining student-teacher rapport. Also contains a student interest survey to help differentiate instruction.
Tardy Log - Document the number of tardies accumulated over the school year
Tardy Log- A different version from the above
Think Sheet - Students can reflect back on what they did wrong and write what they can do to prevent this type of behavior from occurring again
Voice Level Chart - Simple way to visually explain the concept of volume. This voice level chart has 5 volume levels- 1: no talking 2: whisper voice 3: speaking voice 4: Loud Voice 5: Screaming and Shouting Voice.

Guidelines for Writing and Acting Upon Student Discipline Referrals by Creative Concern Publications

 
Multi-Lingual Aids for ESL Students
Use Multi-lingual Multiplication Tables Desktop Helpers to:
Present tested skills for reference and practice
Aid ESL students
laminate and place on student desks or wall
Our Multi-lingual Set includes:
Set of three multi-lingual tables in English, French, and Spanish
Size: 8 1/2” by 11” each
CLICK Here
Rewards and Incentives

Free Homework Pass

Rewards- A list of rewards students receive for appropriate behavior

Ideas for Incentives - A list of 49 Ideas for Low-Cost/No Cost Incentives

Stuff Happens Card -This is a "One Time Only" Forgiveness Pass. If you do not use this Pass You can trade it in the last week of the quarter for 20 bonus points!!!
Smiley Stamper- Students can earn the smiley stamp if they turn homework in on time, complete warm-up, and copy their notes. Every student should receive an smiley stamp card. When a student has earned 30 smiley stamps on their card they can go into the smiley stamp card box and pick a prize: book marks, pencils, pencil sharpener and free homework passes.
 
Math Pizzazz Puzzles
Designed to provide practice with skills and concepts taught in today's middle school classroom. Math with Pizzazz Book AMath With Pizzazz Book BMath with Pizzazz Book CMath with Pizzazz Book D ,
Math with Pizzazz Book EPre-Algebra with PizzazzAlgebra with Pizzazz for FREE!!!

 
Power Point Presentations
Who Wants to be Skeleton - Classroom version of who wants to be a millionaire
Collins Classroom Procedures - PowerPoint presentation covering my classroom rules and procedures

Open House PowerPoint- PowerPoint presentation covering how the purpose of open house is to inform parents of my expectations of their child and to help them better assess and assist their child with learning math. Also covers my classroom policies, curriculum goals and opportunities for them to get involved.

 
Math Vocab Cards

Math Vocab Cards

Math Vocab Cards 5

Math Vocab Cards

Visual Math Word Wall

 
Math Student Surveys
 
General Mathematics and Teaching Resources
Journal Articles and More
 
Common Core Math Standards Freebies and Ideas

Write and interpret numerical expressions
5.OA1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Possible Activities:
Target Number Dash
Numerical Expressions Clock

Pan Balance -- Expressions

Pan Balance -- Numbers

5.OA2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Possible Activities:
Verbal Expressions

Running Races

Speed of Ascent

Analyze patterns and relationships
5.OA3 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 pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Possible Activities:
Function Table and Graph Template
Function Table and Coordinate Plane Paper
Addition on the Coordinate Plane 
Subtraction on the Coordinate Plane

5th GRADE NUMBER ACTIVITIES: NUMBER AND OPERATIONS IN BASE TEN

Understand the place value system
5.NBT.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 **New

Count on Math

Making Your First Million

5.NBT.2 Explain patterns in the number of zeros of 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.
Multiplying a Whole Number by a Power of 10
Multiplying a Decimal by a Power of 10
Dividing a Whole Number by a Power of 10
Dividing a Decimal by a Power of 10

5.NBT.3 Read, write and compare decimals to thousandths.
5.NBT.3a read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347.392 = 3x100 + 4x10 + 7x1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000)
Possible Activities:
Representing Decimals with Base 10 Blocks
Representing Decimals in Different Ways
Hunt for Decimals

Numbers and Language

Post-Office Numbers

5.NBT.3b. Compare two decimals to thousandths based on meanings of the digits in each place, using>, =, and < symbols to record the results of comparisons.
Possible Activities:
Comparing Decimals

5.NBT.4 Use place value understanding to round decimals to any place.
Rounding Decimals to the Nearest Hundredth

Perform operations with multi-digit whole numbers and with decimals to hundredths
5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
Possible Activities:
Make the Largest Product
Make the Smallest Product

5.NBT.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.
Estimating Quotients **New
Creating and Solving a Division Problem

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used.
Possible Activities:
Decimals of the Week **New Use as morning work or for homework!
Base 10 Pictures with Decimals
Base 10 Buildings with Decimals
Base 10 Decimal Bag Addition
Base 10 Decimal Bag Subtraction
Total Ten
Decimal Cross Number Puzzles
Decimal Subtraction Spin
Decimal Addition to 500
Decimal Addition Bingo
Decimal Race to Zero
Decimal Magic Triangle
Magic Squares (adding decimals)

5th GRADE NUMBER ACTIVITIES: NUMBER AND OPERATIONS - FRACTIONS

Fractions of the Week **New Use as morning work or for homework!

Use equivalent fractions as a strategy to add and subtract fractions
5.NF.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 differences of fractions with like denominators.
Fraction Word Problems (unlike denominator)
Mixed Number Word Problems (unlike denominators)
Closest to 25
Magic Squares (adding fractions)
Mixed Number Sum 
Mixed Number Difference 

Communicating about Mathematics Using Games: Playing Fraction Tracks

5.NF.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 + ½ = 3/7 by observing that 3/7 < ½.

Possible Activities:
Using Equivalent Fractions to Subtract Fractions 
Addition Word Problems with Fractions 
Subtraction Word Problems with Fractions 

A Brownie Bake

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

5.NF3 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, e.g. by using visual fraction models or equations to represent the problem.

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.4a. 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 axq÷b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd)
Possible Activities:
Multiplying Fractions by Dividing Rectangles
Fraction x Fraction Word Problems

5.NF.4b. 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.
Area Word Problems with Fractional Side Lengths 

5.NF.5 Interpret multiplication as scaling (resizing) by:
5.NF.5a. 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.5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; 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= nxa)/(nxb) to the effect of multiplying a/b x 1

5.NF.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.
Fraction x Mixed Number Word Problems 
Whole Number x Mixed Number Models
Mixed Number x Fraction Models

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.7a. 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) x 4 = 1/3.
Divide a Unit Fraction by a Whole Number

5.NF.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 x (1/5 )=4.
Dividing a Whole Number by a Unit Fraction 
Divide a Whole Number by a Unit Fraction

5.NF.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 1/2lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Division of Fractions Word Problems

Measurement and Data

Convert like measurement units within a given measurement system.

Represent and Interpret Data

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

5.MD.2.Make a line plot to display a data set of measure- ments in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving in- formation presented in line plots. For example, given dif- ferent 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.

Aluminum Cans

Let's Compare

Mathematics and Environmental Concerns: Unit Overview

 

Measurement and Data

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

5.MD.3.Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.MD.3aA 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 vol- ume.

5.MD.3b A solid figure which can be packed without gaps or overlaps us- ing n unit cubes is said to have a volume of n cubic units.


Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition

5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical

problems involving volume.

5.MD.4aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cu- bes, 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 vol- umes, e.g., to represent the associative property of multiplication.

5.MD.4b 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.4c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rec- tangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.5th Grade Common Core State Standards

Geometry

Graph points on the coordinate plane to solve real-world and mathematical problems.

5.G.1.Use a pair of perpendicular number lines, called axes, to define a coordinate 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 coordi- nates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Dynamic Paper Tool


5.G.2. Represent real world and mathematical problems by graphing points in the first quad- rant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Geometry

Classify two-dimensional figures into categories based on their properties..

5.G.3.Understand that attributes belonging to a cat- egory of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.


5.G.4.Classify two-dimensional figures in a hierarchy based on properties.

6th Grade Common Core Activities
Ratios and Proportional Reasoning:
Understand ratio concepts and use ratio reasoning to solve problems.

6RP.1 Understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities.
 
6RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship.
 
6RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, i.e., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
 
6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
 
6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed. 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
 
6.RP.3d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
 
Ratio Freebies and Ideas:
Games: Ratios and Proportional Reasoning
 
Thinking Blocks Ratios Modeling Tool Scale Factor X Ratio Stadium Ratio Blaster
Ratio Martian Dirt Bike Proportions

 
Number System:
 

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

Games: Number System

 


6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Freebies:

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

 

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

 
6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.7 Understand ordering and absolute value of rational numbers.


6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Expression and Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.


6.EE.3 Apply the properties of operations to generate equivalent expressions.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).


Reason about and solve one variable equations and inequalities.

6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Represent and analyze quantitative relationships bewteen dependent and independent variables.

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.


Games: Expressions and Equations

Weigh the Wangdoodles Algebra Puzzle Math on Planet Zog Algebraic Reasoning Modeling Tool
Geometry
Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.G.4 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

 

Statistics and Probability

Develop understanding of statistical variability.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Summarize and describe distributions.

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.5. Summarize numerical data sets in relation to their context, such as by:

  • Reporting the number of observations.
  • Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
  • Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
  • Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
  • * * Mean, Mode, Median, Range Dice Practice

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7th Grade Common Core Activities

Ratios and Proportional Relationships


Analyze proportional relationships and use them to solve real-world and mathematical problems
Games:

 

Visualize Percentages
See the relationship between different shapes filled to the same proportion.

 
Math at the Mall
Learn about interest and discounts while playing at the mall.

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.


7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.


7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.


Ratio/Rate/Proportion Foldable
Entire Direct Variation Task
7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Learning about Rate of Change in Linear Functions Using Interactive Graphs: Constant Cost per Minute
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

The Number System


Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
 
Games:
 
Fruit Shoot Number Line
Practice moving along the number line using integers.
Two Digit Integer Addition Equations
Practice adding 2-digit integers.

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Integer Addition
7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
7.NS.1b Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
7.NS.1c Understand subtraction of rational numbers as adding the additive inverse, pq = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.2 Apply and extend previous understandings of multiplication and division andhttp://www.mathconcentration.com/forum/topics/printables-1/edit of fractions to multiply and divide rational numbers.

7.NS.2a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real world contexts.
7.NS.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.ional numbers by describing real-world contexts.
7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers
7.NS.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.NS.3a Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
"Switch the Sign": An Algebra Song
Use properties of operations to generate equivalent expressions.
7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Fun with Baseball Stats
7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Geometry


Draw construct, and describe geometrical figures and describe the relationships between them.
 
Games:
 
Geometry Quiz Show
7th Grade Geometry Quiz Show Game -- multiple topics
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Scale Factor
7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Visualizing Geometry Lesson
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Statistics and Probability


Games:
Probabilities Quiz Show
Multiple teams can play this quiz show game with probabilities.
Probability Practice
Practice simple probability statements given desired and possible outcomes.
Bamzooki Zooks
Practice probabilities with the Zooks!
7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
How Much is a Million?
7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Draw informal comparative inferences about two populations.
7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Investigate chance processes and develop, use, and evaluate probability models.
7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Random Drawing Tool
7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Chances Are: Talking Probability
7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
8th Grade Common Core Activities

The Number System

Games:

 Square Root Cannon

 

Rational BIns
Identify rational and irrational numbers.

Know that there are numbers that are not rational, and approximate them by rational numbers.

   8.N.S.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
   8.N.S.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Expressions and Equations

Work with radicals and integer exponents.  

Games:

 

 

Powers Memory
Nice matching game focusing on exponents... and fish!
Square Root
Answer these square root questions "Be a Millionaire"
Exponents Game
Practice the exponents rules.
Exponents Quiz Show
Play this quiz show game covering 8th Grade math topics.

8.E.E.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

8.E.E.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
   8.E.E.3 Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
Cell Size and Scale
8.E.E.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Understand the connections between proportional relationships, lines, and linear equations.
Games:
IXL Practice - Proportional releationship
Write an equation for a proportional relationship or the slope of a line.

8.E.E.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.E.E.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
 
Games:
 
Save the Zogs
Pick the correct linear equation to save your Zog friends.
8.E.E.7 Solve linear equations in one variable.
8.E.E.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
8.E.E.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.E.E.8   Analyze and solve pairs of simultaneous linear equations.
8.E.E.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.E.E.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8.E.E.8c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Functions
Define, evaluate, and compare functions.
Games:
Function Machine
Learn about inputs and outputs using the Function Machine!

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.
 
Games:
 
Basketball Slope-Intercept Game
Determine the slope of the line or the intercept and score hoops.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Geometry


Understand congruence and similarity using physical models, transparencies, or geometry software.
Games:
Transformations Workshop
Experiment with geometric transformations with this fun interactive tool.
8.G.1   Verify experimentally the properties of rotations, reflections, and translations:
8.G.1a  Lines are taken to lines, and line segments to line segments of the same length.
8.G.1b  Angles are taken to angles of the same measure.
8.G.1c  Parallel lines are taken to parallel lines.
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
Visualizing Transformations
   8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Understand and apply the Pythagorean Theorem.
Games:
 
Pythagorean Explorer
Use the Pythagorean theorem to determine the length of triangle legs.
Math Apprentice
Use the Pythagorean theorem to find the distance to capture the criminal.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.


8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Games:
IXL Practice - Volume of pyramids and cones 
Determine the volume of the pyramid using the given information.

8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Scaling Away

Statistics and Probability

Investigate patterns of association in bivariate data.

Games:

 

IXL Practice - Scatter Plots
Interpret the scatter plot and determine trend.

 

8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.


8.SP.2  Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
America on the Move Classroom Activity Guide - Unit 5: 1970s - 2000 The World's People and Products on the Move - Taking a Deeper Look
8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
On Fire
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
 

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