Resources for Teaching Grades 6-7 Number Sense
- Power Up- Using old batteries and a voltage sensor, students get a real feel of the meaning of negative and positive numbers. Students explore addition of signed numbers by placing batteries end to end (in the same direction or opposite directions) and observe the sum of the batteries’ voltages.
- The Math Forum: Internet Mathematics Library- This site has many electronic resources to choose from including Mathematics Topics, Resource Types, Mathematics Education Topics, and Educational Levels.
- Fraction Game- This applet allows students to individually practice working with relationships among fractions and ways of combining fractions. For a two person version of this applet see the Fraction Track E‑Example.
- Proportioner- This applet allows students to investigate and compare ratios, area, and perimeter of various objects.
- Greatest Common Factor- This lesson is intended to be used for review after students have learned about GCF. It takes about 30 minutes to complete.
- Budgeting with Percents- This resource is a full lesson plan on using percents in a real life application.
- Grid and Percent It- In this lesson, students use a 10 × 10 grid as a model for solving various types of percent problems. This model offers a means of representing the given information as well as suggesting different approaches for finding a solution. This lesson is adapted from "A Conceptual Model for Solving Percent Problems," which originally appeared in Mathematics Teaching in the Middle School, Vol. 1, No. 1 (April 1994), pp. 20-25.
- Math 6 Spy Guys- Interactive lessons that covers multiple standards from the Mathematics Framework for California Schools. Includes a glossary, strategies, and operations.
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Title Power Up URL http://illuminations.nctm.org/LessonDetail.aspx?id=L699 Materials needed Voltage sensors
A collection of old batteries (all the same size)
Masking tape
Ruler (with ridge, to hold the batteries)
Graphing calculators (optional; will be needed if using the TI CBL 2TM or the Casio EA‑100 Data Analysis System, or some other calculator‑based technology)
Battery Lab Activity Sheet
Power Up Activity Sheet
Volt Meter ToolLearning Objectives Students will:
- Discover and apply the rules for addition of sign numbers.
Grade Levels Grade 6, Grade 7, Algebra I
CA 97 Standards Grade 6: NS 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations
Grade 7: NS 1.2 Add, subtract, multiply, and divide rational numbers and take positive rational numbers to whole number powers Algebra I: 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable
CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning6.EE.3: Apply the properties of operations to generate equivalent expressions. 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. How could you use this resource? Students can use this resource in a lab to discover how positive and negative integers work by using hands on manipulatives or an applet. Teachers can use this resource as an introduction to positive and negative integers.
EL and Special Needs Has students work in a group, uses hands-on manipulatives or applet.
Lesson Plans Teacher Comments Cost Free Copyright (c)2000-2009 NCTM
Title The Math Forum: Internet Mathematics Library URL http://mathforum.org/library/ Materials needed Computer to view links. Other links may vary on material, usually requires JAVA app.
Learning Objectives Each type of resource has its own set of objectives.
Grade Levels Grade 6, Grade 7, Middle School, High School, College
CA 97 Standards Covers multiple standards.
CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoningCovers multiple standards. How could you use this resource? This resource can be used to find lessons and other information on mathematical topics.
EL and Special Needs Teacher will have to adapt resources to fit specific needs of the students.
Lesson Plans Teacher Comments Cost Free Copyright (c) 1994-2009 Drexel University
Title Fraction Game URL http://illuminations.nctm.org/ActivityDetail.aspx?id=18 Materials needed Computer to view applet. Other links may vary on material, usually requires JAVA app.
Learning Objectives Students will:
Add fractions
Use equivalent fractions
Simplify fractions
Grade Levels Grade 6, Grade 7, Algebra I
CA 97 Standards Grade 06: NS 1.0 Students compare and order fractions, decimals, and mixed numbers. They solve problems involving fractions, ratios, proportions, and percentages.
Grade 07: NS 2.2 Add and subtract fractions using factoring to find common denominators. Algebra I: 12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to lowest terms.
CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoningGrade 6 RP (Cluster Statement) Understand ratio concepts and use ratio reasoning to solve problems. Grade 6 NS (Cluster Statement) Apply and extend previous understandings of numbers to the system of rational numbers. A-APR. 6; Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system How could you use this resource? This resource can be used by students to practice adding fractions, simplifying fractions, and determining sums of fractions that will add up to a given fraction. This resource can be used by teachers to have students practice adding fractions, simplifying fractions, using equivalent fractions, and using combinations of fractions.
EL and Special Needs This is a hands-on activity that allows students to practice using fractions in multiple ways. The game is fun and can be reset instantly by a click of a button.
Lesson Plans Teacher Comments Cost Free Copyright (c) 2000-2010 NCTM
Title Proportioner URL http://seeingmath.concord.org/resources_files/Proportioner.html Materials needed Computer
JavaLearning Objectives Students will:
- Investigate and compare ratios, area, and perimeter
Grade Levels Grade 6, Grade 7, Geometry CA 97 Standards Grade 6: NS 1.2 Interpret and use ratios in different contexts to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).
Grade 7: MG 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangle, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Geometry: 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.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. 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.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. Geometry-GPE.7; Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. How could you use this resource? Students can use this resource as a method of studying ratios and how ratios vary based on the two objects being compared. Students can also compare ratios, find the area, and find the perimeter of a given object. Teachers can use this resource as an introduction tool to ratios and geometric figures. Since the applet does the computations, it should be used to demonstrate the effects of ratios, perimeter, and area instead of how to find them.
EL and Special Needs This is a very visual applet that can help students link the concept to real life problems.
Lesson Plans Teacher Comments Cost Free Copyright (c) 2005 Concord Consortium
Title Greatest Common Factor URL http://www.lessonplanspage.com/
MathGCFPosterTalkShowReviewIdea69.htmMaterials needed Computer,
poster paper,
task cardsLearning Objectives Students will:
- Review what is the Greatest Common Factor
- Use what they know about GCF and use it to find the GCF of two numbers
Grade Levels Grade 5 CA 97Standards Grade 5: NS 1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor. CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning4 OA 4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite. 5 OA 2.1 Express a whole number in the range 2-50 as a product of its prime factors. For example, find the prime factors of 24 and express 24 as 2x2x2x3. 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. For example, express 36 + 8 as 4 (9 + 2). How could you use this resource? This resource can be used by teachers to help prepare a lesson on Greatest Common Factors. The resource provides a sample lesson plan with what materials will be needed. EL and Special Needs This is a hands on activity for students to work on as a group. Students will also need to present to the class so it is improtant that they work with the other students to understand what they must be doing and what they need learn. Lesson Plans Teacher Comments Cost Free Copyright © 1996-2010
Title Budgeting With Percents URL http://www.lessonplanspage.com/MathCIBudgetingWithPercents78.htm
Materials needed pencils
markers
calculator
large manila construction paper
protractor
compass
ruler
A computer can be used to create an Excel graph.Learning Objectives Students will:
- use percents
- calculate percents
- visually represent percentage values.
Grade Levels Grade 5, Grade 6, Grade 7 CA 97 Standards Grade 5 NS 1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Grade 6 NS 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Grade 7 NS 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with Mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning4.NF Understand decimal notation for fractions, and compare decimal fractions.
5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using the number line or another visual model.6.RP 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
c. 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.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. How could you use this resource? This resource can be used by teachers to help prepare a lesson on using percents in a real life situation. The resource provides a sample lesson plan with what materials will be needed, vocabulary used, questions, and homework. EL and Special Needs This resource allows students to choose their real life scenario allowing all students to relate to the problem. Students practice hands on how to compute percents and use technology to make graphs to make their work more visual. Lesson Plans Teacher Comments Cost Free Copyright © 1996-2010
Title Grid and Percent It URL Materials needed Grid Worksheet
Dry-erase, water-based, or grease markersLearning Objectives Students will:
- Shade 10 × 10 grids to represent percent, and determine the percent of a grid that is shaded
- Determine the value represented by one square in a 10 × 10 grid, and determine the value of a grid given the value of one square
- Use a 10 × 10 grid to solve percent problems
Grade Levels Grade 5, Grade 6, Grade 7 CA 97 Standards Grade 5 NS 1.2 Interpret percents as part of a hundred; find decimal and percents equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Grade 6 NS 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages. Grade 7 NS 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoningGrade 6 RP (Cluster Statement) Understand ratio concepts and use ratio reasoning to solve problems. Grade 6 NS (Cluster Statement) Apply and extend previous understandings of numbers to the system of rational numbers. 7.NS.2: Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers: present addition and subtraction on a horizontal or vertical number line. 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 rule for multiplying signed numbers. Interpret products of rational 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.EE.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities are related. 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 or estimation strategies.How could you use this resource? The worksheet provided can be used for homework or lessons. This resource is very easy to use. EL and Special Needs This resource gives a very visual way to understand fractions, decimals, and percentages. It address the needs of EL students and other students with special learning needs. Lesson Plans Teacher Comments Cost Free Copyright © 2000-2010 NCTM
Title Math 6 Spy Guys URL http://www.learnalberta.ca/content/mesg/html/math6web/math6shell.html#
Materials needed Computer with high speed internet
Adobe Flash PlayerLearning Objectives Learning objectives vary by lesson selection and concept.
Grade Levels Grade 6 CA 97 Standards Multiple Grade 6 standards from the Mathematics Framework for California Public School. CA Common Core State Standards Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Covers multiple Grade 6 and some Grade 7 standards from the California Common Core State Standards.
How could you use this resource? Students can use this resource to clarify concepts not understood in class, interact with virtual manipulatives, and see virtual representations of concepts. This resource could be used by a teacher to show to a class as a demonstration or an introduction. This is a fairly simple site to use EL and Special Needs Visual graphics display concepts and are interactive. Lesson Plans Teacher Comments Cost Free Copyright © 2003 Alberta Education