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Numbers, Relationships Among Numbers, and Number Systems

 

1. Understand base ten place value, number theory concepts (e.g., greatest common factor), and the structure of the whole, integer, rational, and real number systems.

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Lesson 1. Base 10 Place Value;  Base 10 Place Value 2; Standard FormExpanded Form

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Lesson 2. GCF 1; GCF 2; LCM 1; LCM 2; LCM and GCF

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Lesson 3. Prime NumbersComposite Numbers, Prime Factorization

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Lesson 4. Divisibility Tests; Divisibility Tests 2

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Lesson 5. Real Number System; Real Numbers; Properties of Real Numbers;  Real Numbers 2; Rational Numbers 3; 

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Assessment: Test 1; Test 2; Test 3; Test 4; Test 5

 

 

2. Order real numbers, including integers, mixed numbers, rational numbers (e.g., fractions, decimals, percents) and irrational numbers on a number line.

 

Lesson 6. Ordering Rational Numbers

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Lesson 7. Ordering Fractions

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Lesson 8. Comparing Rational Numbers

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Lesson 9. Ordering Rational Numbers Part 2

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Lesson 10. Putting Fractions in Order

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3. Represent and perform operations on numbers in exponential and scientific notation.

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Lesson 11. Scientific Notation;  More Introduction

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Lesson 12. Operations Involving Scientific Notation;  Multiplying and Dividing in SN;  Adding and Subtracting in SN

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4. Describe the relationships between the algorithms for addition, subtraction, multiplication, and division.

 

Lesson 13. Addition 

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Lesson 14. Subtraction; Subtraction

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Lesson 15. Multiplication; Multiplication; Multiplication; Multiplication

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Lesson 16. Division; Division; Division; Division; Division

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5. Understand properties of number systems and their relationship to the algorithms, [e.g., 1 is the multiplicative identity; 27 + 34 = 2 × 10 + 7 + 3 × 10 + 4 = (2 + 3) × 10 + (7 + 4)].

 

Lesson 17. Properties applied to operations

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Lesson 18. Properties applied to operations

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Lesson 19. Properties applied to operations

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Lesson 20. Operations and properties applied to fractions

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Lesson 21. Properties applied to rational number operations

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Lesson 22: Strategies for adding and subtracting whole numbers

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Lesson 23: Properties applied to problems

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6. Perform operations with positive, negative, and fractional exponents, as they apply to whole numbers and fractions.

 

Lesson 24. Exponents 1;  Exponents 2Exponents 3;  Exponents 4;  Exponents 5

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Lesson 25. Simplifying Expressions with Exponents 1

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Lesson 26. Simplifying Expressions with Exponents 2

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Lesson 27. Simplifying Expressions with Exponents 3

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Computational Tools, Procedures, and Strategies

 

7. Demonstrate fluency in standard algorithms for computation and evaluate the correctness of nonstandard algorithms.

 

Lesson 28. Nonstandard algorithms

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Lesson 29. Alternative algorithms

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Lesson 30. Alternative algorithms

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Lesson 31. Alternative algorithms

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Lesson 32. Alternative algorithms

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8. Demonstrate an understanding of the order of operations.

 

Lesson 33. Order of Operations 1

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Lesson 34. Order of Operations 2

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Lesson 35. Order of Operations 3

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Lesson 36: Order of Operations 4

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9. Round numbers, estimate the results of calculations, and place numbers accurately on a number line.

 

Lesson 37. Rounding 1

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Lesson 38. Rounding 2

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Lesson 39. Rounding 3

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Lesson 40. Rounding 4

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Lesson 41. Rounding 5

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Lesson 42: Plotting Points on a Number Line 1

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Lesson 43: Plotting Points on a Number Line 1

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Lesson 44: Plotting Points on a Number Line 1

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Lesson 45: Plotting Points on a Number Line 1

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Assessment

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CSET Math Subtest II Number Sense Questions: 8-9

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Good multiple choice items: Work through problems that deal with the number sense domain.

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NY Grade 3 State Test Questions

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NY Grade 4 State Test Questions

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NY Grade 5 State Test Questions

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NY Grade 6 State Test Questions

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NY Grade 7 State Test Questions

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NY Grade 8 State Test Questions

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Good constructed response items: 

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  • Access the Mathematics Assessment Project website. Work through problems from the Grades 6 & 7 Tests for Middle School that deal with the number sense domain. You may also access the summative tasks page if you want to solve more problems.  

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