### 1. Place value up to billions.

Concept that helps students understand the magnitude of very big numbers. Place value is based on powers of ten, and it can help students comprehend large numbers, such as 1 billion or 10 billion. In place value notation, 1 billion is written as 1 x 10^9 (1 followed by nine zeros).

### 2. Compare and order whole numbers and decimals to the thousandths place.

Students learn how to compare, arrange, or rank numbers in numerical order. For example, they can determine which number is greater: 0.735 or 0.573? Or they can identify the middle value between 2 numbers (median). They also learn how to compare decimal numbers that are written as far out as the thousandths place.

### 3. Add and subtract whole numbers and decimals to the thousandths place.

Helps students with basic addition and subtraction at an advanced level such as calculating sums of money with decimal values or adding multiple fractional amounts together accurately. It is important for students to be able to identify and use the proper place value when solving these types of equations.

### 4. Multiply whole numbers by 10, 100, 1000, and decimal equivalents thereof.

Makes sure students can accurately measure out objects or items that come in standard sizes. This skill teaches students how to multiply whole numbers such as 1x10 (1 times ten) or 2x1000 (2 times a thousand). Students should be able to convert decimals into fractions as part of this skill too.

### 5. Divide whole numbers by 10, 100, 1000, and decimal equivalents thereof.

Allows students to divide fractions, mixed numbers and decimals with accuracy and precision. They must understand how to use long division for larger divisors than ones and twos. They also must be able to identify the quotient when dividing whole numbers.

### 6. Identify prime and composite numbers.

Helps students learn how to tell whether a number is divisible by other numbers (divisibility rules) as well as recognizing which numbers are prime or composite. Prime numbers are only divisible by themselves and one, while composite numbers are divisible by many different factors.

### 7. Square whole numbers between 0-100.

Makes sure that students understand how to square a number, or multiply it times itself, up to 100. Squaring a number involves multiplying it by itself, such as 3x3=9 or 5x5=25.

### 8. Convert fractions to decimals and percentages.

Students should be able to convert fractions into decimals accurately. For example, 1/4 is 0.25 or 25%. They should also learn how to convert decimal numbers into fractions such as 0.75 being 3/4.

### 9. Convert decimals to fractions and percentages.

Helps students understand how to take a number like 0.72 and turn it into an exact fraction (72/100) or what percent that number would be (72%). Students should have an understanding of the place value when converting these types of numbers.

### 10. Understand concepts of geometry including lines, angles, basic shapes, area, perimeter and volume.

Gives students a foundation in basic geometric principles applicable in everyday life. Geometry includes concepts such as lines, angles, basic shapes (circle, triangle and square), area, perimeter and volume. Students learn to measure these objects using a ruler or other measuring tools. They also learn how to calculate the area of a shape or figure by counting the number of squares inside it. Additionally, students are exposed to more complex geometric principles such as Pythagorean Theorem. This helps them understand how to determine the length of one side of a right triangle when given two sides that form the right angle. Finally, students learn about volume; they must be able to calculate 3D measurements such as the amount of water in a fish tank or cubic feet in a room.