Number Relationships and Computation (Multiplication)

Multiplication involves counting groups of like size and determining how many are in all. There are patterns and relationships in basic facts. You can figure out new or unknown facts from the ones that you already know. All facts can be learned with the help of efficient strategies.

Administer the Number Relationships and Computation: Multiplication and Division Unit Pretest, when appropriate. Then administer the Number Relationships and Computation: Multiplication and Division Unit Posttest at the end of the unit.

Instructional Objective(s)
The students will be able to:

1. Use models, manipulatives, and arrays to represent multiplication.
   
   
   
   

1. Use basic facts up to
   9 x 9 = 81 using number sentences, pictures or drawings (No Calculator).
   

1. These next three objectives should be taught together making connections between each. Stress the relationship between multiplication and division. This can be done in a variety of ways including repeated addition, repeated subtraction, rectangular arrays, and by the inverse relationship between multiplication and division. Division is simply introduced here to develop a conceptual understanding.
   

1. Array
   
   x x x
   x x x =   2 x 3
   (The first factor indicates the number of rows; The second factor indicates the number of objects in each row.)
   

1. Use the hundred chart and constant key on the calculator to show skip counting and its relationship to multiplication.
   
   
   

1. Facts That Last Multiplication
   * This resource may be used with (a-e).
   
   
1. Developing Number Concepts Book 3 (169-175)
   
   

1. Number Sense 3-4
   (59-61)
   
   
1.  Rectangle Multiplication
   
   
1. Illuminations Lesson -Multiplying Meanings
   
   
1. BCR | Rubric
   

2. Identify the factor and product in a multiplication sentence.

2. Use basic facts of no more than 9 x 9 = 81.
   

2. Review as a warm-up and combine with other objectives.

2. Factors are 3 and 4
   Product is 12

2. Nimble with Numbers 3-4 (115-128)
   
   
2. The Product Game
   
   
2. Illuminations Lesson - The Product Game
   
   

3. Apply the zero, identity, and commutative properties to basic multiplication facts.

3. Use the properties of commutative, identity or zero for multiplication with whole numbers 0 – 20.

3. Zero property- Any number
   multiplied by zero equals zero.
   (5 x 0 = 0)
   

3. Identity Property- Any number
   multiplied by one equals itself.
   (9 x 1 = 9)
   

3. Commutative Property-
   Changing the order of factors
   does not change the product.
   3 x (2 x 4) = (3 x 2) x 4

3. Nimble with Numbers 3-4 (115-128)
   
   
3. Navigating Through Algebra 3-5 (48-50)
   
   
3. Illuminations Lesson - It's in the Cards
   

4. Explore strategies for multiplication basic facts (i.e., number times ten, number times five, doubles, splitting fours, number times three, number times six, number times nine).

4. Use basic facts of no more than 9 X 9 = 81
   

4. Use "Strategies at Work" for Multiplication. Differentiate instruction for varying levels of mastery. This is an ongoing program.

4. "Strategies at Work!" For Multiplication
   
   
4. Developing Number Concepts Book 3 (136-168)
   

4. Strategies Multiplication.xls
   
   
4.  Multiplication - An Adventure in Number Sense
   
   
4. Arithmetic Four
   
   
4. Illuminations Lesson - Times Six, Times Seven
   
   
   

5. Use patterns to multiply a one-digit number by multiples of ten using mental computation.

5.     4 x 10 = 40
     4 x 100 = 400
   4 x 1000 = 4000

5. Base Ten Blocks 3-4 (54-57)

Number Relationships and Computation (Fractions)

Digits in fractions have different meanings than they do in whole numbers. Two equivalent fractions are two ways of describing the same amount using different sized fractional parts.

Administer the Number Relationships and Computation: Fractions Unit Pretest, when appropriate. Then administer the Number Relationships and Computation: Fractions Unit Posttest at the end of the unit.

Instructional Objective(s)
The students will be able to:

1. Represent a variety of fractions for a region or a set using manipulatives and/or drawings.
   
   
   
   
   

1. Use fractions with denominators of 2, 3 or 4.
   
   
   
   
   

1. Show 2/3 using pattern blocks, fraction bars, fraction circles, drawings, etc.

1. Region               Set    

1. Super Source - Color Tiles (46-49)
   
   
1. Twenty Thinking Questions for Fraction Circles Grades 3-6
   
   * Above resources can be use with objectives (a-g)
   
1. Read It! Draw It! Solve It!
   
   
1.  Tour of Fractions
   
   
1.  Parts of a Square
   
   
1. BCR | Rubric
   
   
1. BCR | Rubric
   
   

2. Identify and define numerator and denominator.

(This concept should be incorporated into fraction lessons throughout the unit. The concept should not be the focus for the entire day's lesson.)

3. Read and write a fraction for a given region (halves, thirds, fourths, fifths, sixths, eighths, and tenths).

3. Use fractions with denominators of 2, 3 or 4 using symbols, words or models.
   
3. VSC Number Relationships A.2.a Sample Assessment

3. Write a fraction to show the shaded part.
   
        
   
   

3. Super Source - Color Tiles 3-4 (34-37)
   
   
3.   Fraction Visualizing
   
   
3.   Fractions - Naming
   
   
3. Who Wants Pizza?
   
   
3. Fraction Finder
   
   
3.  Building a Fraction Book
   
   
3. Illuminations Lesson - Fun with Fractions: A Unit on Developing the Region Model
   
   
   

4. Read and write a fraction for a part of a set (halves, thirds, fourths, fifths, sixths, eighths, and tenths).

4. Use fractions with denominators of 2, 3 or 4 which have the same number of items as the denominators using symbols, words or models.

4. What fraction of this set are triangles?
   
   
   
   
   
   

4.  Fun with Fractions | TRS 1
   
   
4. Illuminations Lesson -
   Fun with Fractions: A Unit on Developing the Set Model
   
   
   

5. Compare and order like fractions from least to greatest and greatest to least.

5.  Fractions - Comparing
   
   
5.  Fraction City
   
   
5. Illuminations Lesson - Fun with Fractions: Length
   
   
   

6. Represent equivalent fractions using manipulatives and/or drawings equal to one whole and one half.

6. 1 = 2/2, 3/3, 4/4, 5/5 ...

6. 1/2 = 2/4, 3/6, 4/8, 5/10 ...

6. Super Source - Cuisenaire Rods 3-4 (26-29)
   
   
6.  Fractions - Equivalent
   
   
6. Mars Fraction Hunt
   
   
   

7. Plot points to represent fractions with denominators of 2,3, and 4 on a number line.

7. Use fractions that have denominators of 2, 3, and 4.

7. Use a number line to show where the fractions fall. Show where 3/4 belongs.
   
    
      
   
   

7. Fraction Line

8. Estimate the value of a fraction as being close to zero, one-half, or one.

8. Use a number line to represent fractions.
   
   
   
   Is 1/3 closer to 0 or 1/2? How do you know? (I know because 1/4 is smaller than 1/3 and so 1/3 is closer to 1/2 than to 0.)

Probability

The possible occurrence of a future event compared to the chance of its nonoccurrence can be characterized as impossible, less likely, equally likely, more likely, or certain. To determine the likelihood of an event along this continuum is to determine the probability of it happening.

Administer the Probability and Algebra, Patterns, and Functions Unit Pretest, when appropriate. Then administer the Probability and Algebra, Patterns, and Functions Unit Posttest after the Algebra, Patterns, and Functions Unit has been taught.

Instructional Objective(s)
The students will be able to:

1. List possible outcomes for an event.
   
   
   

1. A spinner has three equally divided sections. In one section there is a square, another section a triangle, a third section a circle. List the possible outcomes if you spin the spinner. (triangle, circle, or square)
   
   
   
   

1. Exploring Statistics Book 1 (69-88) Obj. a-d
   
   
1. About Teaching Mathematics (261-271)
   (For use with a & b)
   
   
1. Understanding Experimental Probability
   
   

2. Describe the likelihood of an event by using certain, impossible, more likely, less likely, and equally likely.

2. Use probability terms more (or most) likely, less (or least) likely, or equally likely.
   
   
2. VSC Probability B.1.a Sample Assessment
   

2. Of 6 cubes in a bag, three cubes are red, 1 cube is yellow, 1 cube is green and 1 cube is orange. It is more likely that you will draw a red cube and it is impossible to draw a blue cube.

2. Engage students in probability experiments to determine the likelihood of an event.
   

2. Math By All Means 3-4 (24, 38, 54, 67)
   
   
2. Interactive Probability Chart
   
   
2. Probability Power Point
   

2. BCR | Rubric
   

2. BCR | Rubric
   

2. BCR | Rubric
   

2. BCR | Rubric
   
   
   

Algebra, Patterns, and Functions

Numbers can be taken apart in a variety of ways. Numbers can be easily recombined when these parts are recognized. The equal sign represents the same quantity. Functions are relationships or rules that uniquely associate members of one set with members of another set.

Administer the Algebra, Patterns, and Functions Unit Posttest at the end of this unit.

Instructional Objective(s)
The students will be able to:

1. Represent numeric relationships using the following symbols: +, -, <, >, or =.
   
   
   
   

1. Use operational symbols (+ or -) using whole numbers 0 – 50.
   
   
1. When using <, >, or =, use operational symbols
   (+ or -) on either side, using whole numbers 0 to 1,000.
   
   
1. VSC Algebra B.1.a Sample Assessment
   
   

1. Jeff had nine pretzel sticks. He ate seven of them. How many pretzel sticks does he have left? Write an expression to show how many pretzel sticks Jeff has leftover.
   
      9 - 7
   

1. 9 + 7 > 8 + 4
   
   
   
   
   
   

1. Number Sense 3-4 (73-79)
   
   
1. Groundworks Grade 3 (88-104)
   

2. Explain the meaning of the equal sign in a number sentence.

2. Emphasize the meaning of the equal sign as a balance. Write problems that have the answer to the left of the equal sign. Include problems that ask students to show number relationships.

2. ____ = 7 + 1 or 3 + 5 = 7 + ____

3. Find the missing number in a number sentence (addition, subtraction, multiplication, and division) using a variety of strategies.

3. Find the missing number (unknown) in a number sentence (equation) with one operation (+ or -) using whole number (0-100) on one or both sides of the equation.
   

3. 24 = 3 x _____
   
   42 = 6 x ____

3. Include story problems that ask students to write a number sentence with the missing number.

3. Groundworks Grade 3
   (88-104)
   
   
3. Nimble with Numbers 3-4
   (100-104)
   

3.  Mystery Operations