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- Math in Focus: 5A (2013)

# Math in Focus: 5A (2013)

### 1: Whole Numbers

1.4: Rounding and Estimating

Rounding Whole Numbers (Number Line)

Place points on a number line. Round these values to the nearest ten or hundred. Visualize rounding by showing the number line as a hill or series of hills. These hills cause the points to roll to the nearest valley (nearest multiple of ten or one hundred). 5 Minute Preview

### 3: Fractions and Mixed Numbers

3.1: Adding Unlike Fractions

Fractions with Unlike Denominators

Find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. 5 Minute Preview

3.4: Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview

### 4: Multiplying and Dividing Fractions and Mixed Numbers

4.1: Multiplying Proper Fractions

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview

4.4: Multiplying Mixed Numbers and Whole Numbers

Multiplying Mixed Numbers

Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

4.7: Real-World Problems: Multiplying and Dividing with Fractions

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

### 5: Algebra

5.1: Using Letters as Numbers

Using Algebraic Expressions

Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview

5.2: Simplifying Algebraic Expressions

Addition and Subtraction of Functions

Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview

5.3: Inequalities and Equations

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

Modeling and Solving Two-Step Equations

Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview

### 6: Area of a Triangle

6.2: Finding the Area of a Triangle

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

### 7: Ratio

7.1: Finding Ratio

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

7.4: Ratio in Fraction Form

Proportions and Common Multipliers

Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview

7.6: Real-World Problems: More Ratios

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

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