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*Slope
*Writing equations of lines
*Graphing equations of lines
*Transforming forms of equations
*Solving Systems of Equations
*Exponents/Roots

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Operations with Fractions and Mixed Numbers

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*Understanding of fractions & mixed numbers, what they represent, and how to move back and forth between the two
*How to find common denominators & simplify
*Some understanding of positive and negative integers and how they relate on a number line.

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- Understanding of how to add and subtract + unit fractions
- Place Value Understanding
- Recall of Multiplication Facts

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Operations on Fractions and Decimals
Exposure to Operations on Integers
One step equations
Basic Order of Operations

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~Basic math facts (+, -, x, /)
~Place Value/Number Sense (Add/Subtract decimals and understand "rules" and why)
~Fraction concepts and add/subtract fractions

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*Solid understanding of all operations with decimals and fractions.
* Able to plot a point on a coordinate plane.

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conceptual understanding of fractions (equivalent  fractions , fraction addition/subtraction/multiplication)

Understanding of place value & rounding

conceptual understanding of multi-digit multiplication

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*Understanding of equivalent fractions and how to reduce
*Multiply fractions and cross simplifying
*Understanding of variables (what they are)

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*Integer Operations/Order of Operations
*Solve 1 & 2 Step Equations with inverse operations
*Graphing coordinate points in 4 quadrants

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Problem Solving and Word Problem strategies/vocabulary

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Problem Solving and Word Problem strategies/vocabulary

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and the bravery to try and have flexible thinking when problem solving

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1. Adding and Subtracting within 10.
2. Count, write, and identify numbers up to 20.
3. Ability to identify and use different partners up to 10.

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-fraction operations (+,-, x)
-add/subtract, compare/order decimals
-fluency in math facts

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Fractions- what do they represent, how to find common denominators

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Fractions- what do they represent, how to find common denominators

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Decimals.

Multiplication facts

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Order of operations
Integers
Solve 1-and 2-step equations
Fractions

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1. 1:1 Number Correspondence
2. Rote Counting to 10
3. Recognizing Numbers to 10
4. Writing Numbers (0-9)
5. Subitize or recognizing numbers (more/less)
6. Recognizing shapes (circle, square, triangle, rectangle)
7. Patterning/Patterns
8. Knowing 13 & 14 are not same (teen numbers)

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Understanding how to read and understand word problems and the vocabulary that goes with them.

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Understanding how to read and understand word problems and the vocabulary that goes with them.

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1. Ability to count according to count sequence, identify and write numbers (1-20).
2. Difference between addition and subtraction (addition being putting together/adding to, subtraction being pulling apart/taking away).
3. Fluency in partners up to 10 (understanding that you can switch number order and still get same total).

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Equivalent Fractions
Simplifying fractions
Adding and Subtracting Fractions
Decimal place values
Multiplication/Division fact fluency

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Operations with fractions and mixed numbers

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* Solid understanding of  what fractions and decimals are from a conceptional standpoint and how to solve basic operation problems
* Solving one-step equations
* Measurement knowledge and skills

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All

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Identify numerals to 10
Count to 10
identify 2D shapes

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Multiplication math facts
Basic fraction information - how to build, deconstruct, etc.
Place value and number sense( single digit division and multi-digit multiplication)

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ER/WO: Fundamental Understanding of What a Fraction Represents

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ER/WO: Fundamental Understanding of What a Fraction Represents

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ER/WO Repeated addition (makes multiplication a natural next step)

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ER/WO Repeated addition (makes multiplication a natural next step)

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- multiplication facts to recall
- equivalent fractions
- adding and subtracting fractions
- general understanding of how decimals and fractions work
- how to use a ruler

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Solve a 2 step equation using inverse operations, write steps going down the page

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*Operations with Fractions & Decimals
*Intro to Integers
*Multiplication facts!

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flexibility with strategies for basic addition and subtraction through 12.

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Count to 10
Identify and write numbers to 5 (to 10)
Identify 2D shapes

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1. Math Facts (multiplication/division)
2. Fraction concepts and knowledge
3. Place Value and Number Sense

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ER/WO: Understanding of Place Value for Expanded Notation Purposes

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ER/WO: Understanding of Place Value for Expanded Notation Purposes

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A good understanding of place value (how to take put together and take apart numbers)

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A good understanding of place value (how to take put together and take apart numbers)

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* Conceptual understanding of fractions (benchmark fractions, fraction models for operations)
* Knowledge of fraction & decimal operations
* Quadrant 1 of Coordinate plane
Concepts of volume & formulas

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From Challenge 7 Math Prerequisites plus:

Conceptual and procedural mastery of...

Integer operations      (+, -, x, ÷)

Simplifying expressions

Solving equations using inverse operations

Inequalities (writing, graphing, solving)

Proportions

Direct Variation

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From Math 6
Prerequisites plus:
* Conceptual: integers, exposure to adding integers
* Conceptual: inequalities on a number line
* Solving 1 step Equations
Distributive Property w/ variables

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Operations with integers
Solve basic 1 and 2 step equations
Ability to accurately plot points

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identify coins

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3 most critical prerequisite math skills and knowledge

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Place Value

Fractions on a number line
Basic fraction knowledge, parts of a whole

Problem solving steps

Number sense

Common Math Language

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*Integer operations
*Graphing on a Coordinate Grid
*Solving 2-step Equations
*Fraction Operations
*Order of Operations