Mathematics Curriculum Guide
Number Sense and Number Systems
Grade 6 In the Area of: Number Sense & Number Systems |
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| Calculate, compute, use whole numbers,
fractions, decimals fluently.
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Have students work in groups then present drawing on board or
overhead to show fractional parts of a whole.
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A Trip to Benny's Bakery.
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Conclusion of unit. Students write a report that explains their understanding of rational numbers. | Students, "cut," rectangular cake into unusual shapes which tessellate. | - Understanding Rational Numbers and Proportions, pp.
13-31, NCTM Addenda.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 2
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| Demonstrate an understanding of place value to millionths. | Students work in groups to determine what a millionth of,
"something," could be.
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Exploring the Size of One Millionth.
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Developing Number Sense, NCTM Addenda, p. 24.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 3
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| Demonstrate an understanding of
exponents.
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Use words such as, "base," "power,"
"square," "cube." Model examples of each.
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Use dot paper to draw square numbers. Relate to area of a
perfect square. Build cubes to show number raised to 3rd power.
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Check student designs and construction. Make tables to show progression such as 2 , 2 , 2 , etc. |
Writing: Describe how the size of a motion picture is related
to distance of the projector to the screen. Ex: 20 ft = 20 = 400 ft.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 4
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| Develop rational, whole, integer number
systems.
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Use manipulatives such as circles, fraction bars.
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Identify fractions near 0, 1/2, and 1. | Sort fractions into categories such as: between 0 and 1/4;
1/4 and 1/2, etc.
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- Draw pictures illustrating fractional parts of a whole. - Get with the System activities. |
-Developing Number Sense, Pg. 30, Addenda Series. -Zounds!, p.96.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 5
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| Demonstrate concepts of prime and composite numbers, divisibility rules, squares and powers, square roots. | Ask questions such as: How are the dimensions of a rectangle related to the factors? | Build rectangles using a specified number of
tiles. Ex.: Using 18 tiles, how many different rectangles can you build?
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Students draw rectangles on grid paper. Observe students using tiles. | Build perfect squares. Identify the square root. Build cubes; identify the cube root. | ||
Grade 6 In the Area of: Number Sense & Number Systems
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| 6
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| Develop, use percents, ratios and
proportions through real world applications and problems.
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Review connections between fractions, decimals and percents.
Using M&M's demonstrate ratio and proportion.
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M&M Experiment.
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Use activity sheets in unit with student input.
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Use computer spreadsheet to graph selected data. | Understanding Rational Numbers and Proportions, NCTM
Addenda Series, Grades 5-8,pp.49-56.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 7
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| Compare, develop percents, ratios and
proportions through their relationships.
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Extend concepts taught through M&M experiment through
application to another population and set of data as provided by the teacher.
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Devise their own version of the M & M experiment with
choice of product, investigation and reporting of percents, ratios and proportions related
to the product. Share in report and diagram form with appropriate audience.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 8
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| Demonstrate understanding of relationship between mathematical operations. (addition, subtraction, multiplication, division) | Discuss, elicit solutions from students of sequences and
mathematical operations involved.
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Explore patterns, determine sequence : Examples: Fibonacci
numbers and the Golden Ratio, Pascal's Triangle. After sufficient class time for
exploration with or without a partner, student can then solve pattern puzzle provided by
teacher.
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Take a Number activity.
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- A Mathematical Mystery Tour: Higher Thinking Math Tasks. - Zounds!, p.97.
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Grade 6 In the Area of: Number Sense & Number Systems
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| 9
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| Develop other non base ten number
systems. (binary, roman, etc.)
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- Review place value concepts (regrouping, expanded notation,
absolute value) via another base. - Teacher models with overhead and beans and cups.
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Create their own mathematical language with a unique system
of symbols and values. Devise problems within this number system. Invite others to solve.
Share with appropriate audience.
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Beans, cups, place value charts | |
Grade 6 In the Area of: Number Sense & Number Systems
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| 10
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| Convert from fractions to decimals and to percents regularly and understand the, "connectedness," of these numbers, including the fact that the fraction bar represents division to percents. | Model common fractions and their decimal equivalents. Explain
and relate use of calculator for fractions such as 3/16, 7/11, etc.
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Work in groups to conduct surveys on diverse topics: ex.
favorite fast foods or musical groups. Show data as fractions, decimals, percents.
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Prepare a final table showing fractions, decimals, percents;
write an essay about their relationships.
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Use spreadsheet software to rewrite fractions as decimals. | ||
Grade 6 In the Area of: Number Sense & Number Systems
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| 11
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| Summarize and explain in writing
reasons for mathematical computations/ solutions.
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Review samples of student's writing about math ( anonymous)
on overhead. Ask students to evaluate for depth/accuracy of mathematical thinking.
Discussion can then generate a rubric to be used to evaluate further math writing
assignments.
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Write regularly in math journals as directed by teacher.
Reflect on this writing and what it says about the level of student's understanding.
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Student writing should clearly illustrate grasp of number
sense as well as appropriate expression and usage.
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Justify yourself activity. | Zounds!, p.98. | |
Grade 6 In the Area of: Number Sense & Number Systems
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| 12
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| Describe how the four mathematical operations are affected by the order of operations and significantly different solutions obtained. | Illustrate examples of solutions to an equation without using order of operations. Then show the correct solution using order of operations. Invite students to compare/contrast. | - Connect dots in two different ways to show different
outcomes. Students calculate an expression first without order of operations and then with
to show two different outcomes. Compare - Use scientific calculator to demonstrate competency in order of operations.
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- Students correctly solve equations using the order of
operations. - Journal writing: explain how the order of operations can provide opportunities in certain situations. |
Create a personal mnemonic device that will help them
remember the order of operations. Diagram and share with class.
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The Textbook Series: Order of Operations* | |
Return to Grade 6 Curriculum Preface
Return to Grade 6 Curriculum Guide
Return to Mathematics Curriculum Frameworks