Operations with integers can be modeled using two-colored counters. Positive +1 Negative.

Slides:



Advertisements
Similar presentations
Let’s Do Algebra Tiles.
Advertisements

Modeling Adding and Subtracting Integers
ILLUSTRATING INTEGERS
ILLUSTRATING INTEGERS
ILLUSTRATING INTEGERS
11-3: Subtracting Integers
Subtracting Integers with Tiles
ILLUSTRATING INTEGERS September 28, 2011 Mr. Pearson Inman Middle School GPS - M7N1.
Section 1.1 introduction — an exploration into:
Exponent Rules Repeated Multiplication Remember: so and.
ADDING, SUBTRACTING, MULTIPLYING AND DIVIDING INTEGERS By : Katie Kurth and Kateylnn Everhart.
Adding Integers. Adding Integers with the Same Sign Add the absolute values. The sum will have the same sign as the addends. Example 1 Find –2 + (-3)
INTEGERS: adding, subtracting, multiplying, and dividing
Adding Integers with Different Signs
ALGEBRAIC EQUATIONS. EQUATIONS AND SOLUTIONS  A correct equation is like a balance scale.  In order to determine if a given value for a variable is.
ADDING INTEGERS (SAME SIGNS)
INTEGERS AND MULTIPLICATION
Integer Rules. Adding with the same sign Rules Rules Add like normal Add like normal Keep the sign Keep the sign Examples Examples = -22 (all.
ALGEBRA 1 Operations with Integers
Modeling Review.
Wednesday, August 19, 2015 We are learning to…add and subtract positive and negative integers with Algebra Tiles.
Objective How to solve Integer problems
Adding and Subtracting Integers To add integers with the same sign, add their absolute values and then change the sign to the sign of the addends. Positive.
ILLUSTRATING INTEGERS INTRODUCTION TO INTEGERS Integers are positive and negative numbers. …, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, … Each.
Addition, Subtraction, Multiplication, and Division of Integers
Integer Operations. 1) What’s the rule for adding integers? *If both addends are Positive: - Add together and the sum is positive (Ex = 12) *If.
Copyright©amberpasillas2010. Integer Addition Rules If the signs are the SAME Add the numbers. The sign stays the same = =
11-7 Multiplying Integers Warm Up Find each product ,600 14,000.
Copyright © Ed2Net Learning, Inc.1 Integers Grade 6.
Algebra Tiles & Integer Operations. Objectives MA Read, write, and represent integers (-100 to 100) * MA Add, subtract, multiply and.
Definitions Add & Subtract Multiply & Divide ExponentsMixed.
ILLUSTRATING INTEGERS
Adding Integers 7.NS.1. Warm Up 1.What is the relationship of 4 and -4? 2.What happens when we add 4 and then subtract 4 to a number? Show this on a number.
Lesson 6-3 Example Example 2 Find the difference of –2 and –4. Use counters. 1.Write the subtraction expression. –2 – (–4)
Solving One-step Equations Algebraically. The goal of solving equations: -To get one x alone on one side of the equation. The rule for solving equations:
Subtracting Integers Subtracting Integers CCS: 6.NS.2: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
Cougar Time. Adding Negative Numbers  What are the two rules for adding integers?  Same Signs = Add and keep the sign  Different Signs = Find the absolute.
Positive and Negative numbers. Negative numbers A positive or negative whole number, including zero, is called an integer. For example, –3 is an integer.
Interesting Integers! Let’s subtract.. What You Will Learn Rules for subtracting Method for subtracting Are you ready??
Solving Two- Step Equations Lesson 2-2. Rules to Remember When solving an equation, the goal is to get the variable by itself. Addition and Subtraction.
Multiplication and Division of Exponents Notes
One step equations Add Subtract Multiply Divide  When we solve an equation, our goal is to isolate our variable by using our inverse operations.  What.
Solving Equations Inverse operations. INVERSE = Opposite If I am solving an equation using inverses operations, I am solving it using opposite signs.
Adding, Subtracting, Multiplying, and Diving Integers!!!
The University of Texas at Dallas. Red and yellow tiles can be used to model multiplication. Remember that multiplication can be described as repeated.
Multiplying Integers with Tiles Student Expectation: 7 th Grade: 7.1.2C Use models, such as concrete objects, pictorial models, and number lines, to add,
ILLUSTRATING INTEGERS The University of Texas at Dallas.
Addition Multiplication Subtraction Division. 1.If the signs are the same, add the numbers and keep the same sign = = If the.
1.3.2 Multiplication and Division of Real Numbers SWBAT: 1) Multiply and divide real numbers 2) Connect and analyze properties for all basic operations.
Solving 1-Step Equations 2 An Equation is Like a Balance.
ILLUSTRATING INTEGERS The University of Texas at Dallas.
Integers. Definition Positive integer – a number greater than zero
Adding Integers KMS 7 TH GRADE. Adding Integers Rules  To add integers with the same sign: you add the absolute values and keep the sign.  Example A.
 Commutative Property of Addition  When adding two or more numbers or terms together, order is NOT important.  a + b = b + a  =
Adding Integers. Using Two Coloured Counters We can model integer addition with tiles. Represent -2 with the fewest number of tiles Represent +5 with.
Algebra Tiles Practice PowerPoint Integer Computation.
Warm up: Fill in Agenda. Complete the number sort on the board
3. 3 Solving Equations Using Addition or Subtraction 3
Modeling Adding and Subtracting Integers
DIVIDING INTEGERS The University of Texas at Dallas.
Interesting Integers!.
Adding and Subtracting Integers is like …
Integers with Manipulatives
Integers.
Subtracting Integers with Tiles
Integers with Manipulatives
ILLUSTRATING INTEGERS Multiplication and Division
Integers with Manipulatives
INTEGERS INTRO : Zero Pairs.
Review of Integers and Solving Equations
Presentation transcript:

Operations with integers can be modeled using two-colored counters. Positive +1 Negative

The following collections of counters have a value of +5. Build a different collection that has a value of +5.

What is the smallest collection of counters with a value of +5? As you build collections of two-colored counters, use the smallest collection, but remember that there are other ways to build a collection.

The collections shown here are “zero pairs”. They have a value of zero.

Describe a “zero pair”.

Now let’s look at models for operations with integers.

What is addition? Addition is combining one or more addends (collections of counters).

When using two-colored counters to model addition, build each addend then find the value of the collection. 5 + (-3) zero pairs = 2

Modeling addition of integers: 8 + (–3) = 5

Here is another example: -4 + (-3) (Notice that there are no zero pairs.) = -7

Build the following addition problems: 1) = 2) = 3) = 4) -6 + (-3) =

Write a “rule”, in your own words, for adding integers.

What is subtraction? There are different models for subtraction, but when using the two-colored counters you will be using the “take-away” model.

When using two-colored counters to model subtraction, build a collection then take away the value to be subtracted. For example: 9 – 3= 6 take away

Here is another example: –8 – (–2) = –6 take away

Subtract : –11 – (–5) =–6

Build the following: 1) –7 – (–3) 2) 6 – 1 3) –5 – (–4) 4) 8 – 3 = –4 = 5 = –1 = 5

We can also use fact family with integers. Use your red and yellow tiles to verify this fact family: = = = = + 8

Build –6. Now try to subtract +5. Can’t do it? Think back to building collections in different ways.

Remember? +5 = or

Now build –6, then add 5 zero pairs. It should look like this: This collection still has a value of –6. Now subtract 5.

–6 – 5 = –11

Another example: 5 – (–2) Build 5: 5 – (–2) = 7 Add zero pairs: Subtract –2:

Subtract: 8 – 9 = –1

Try building the following: 1) 8 – (–3) 2) –4 – 3 3) –7 – 1 4) 9 – (–3) = 11 = –7 = –8 = 12

Look at the solutions. What addition problems are modeled?

1) 8 – (–3) = 11 = 8 + 3

2) –4 – 3 = –7 = –4 + (–3)

3) –7 – 1 = –8= –7 + (–1)

= ) 9 – (–3) = 12

These examples model an alternative way to solve a subtraction problem.

Subtract: –3 – 5 = –8–8 –3–3 –5 +

Any subtraction problem can be solved by adding the opposite of the number that is being subtracted. 11 – (–4) = = 15 –21 – 5 = –21 + (–5) = –26

Write an addition problem to solve the following: 1) –8 – 142) –24 – (–8) 3) 11 – 154) –19 – 3 5) –4 – (–8) 6) 18 – 5 7) 12 – (–4)8)–5 – (–16)

What is multiplication? Repeated addition!

3 × 4 means 3 groups of 4: 3 × 4 = 12 ++

3 × (–2) means 3 groups of –2: 3 × (–2) = –6 + +

If multiplying by a positive means to add groups, what doe it mean to multiply by a negative? Subtract groups!

Example: –2 × 3 means to take away 2 groups of positive 3. But, you need a collection to subtract from, so build a collection of zero pairs.

What is the value of this collection? Take away 2 groups of 3. What is the value of the remaining collection? –2 × 3 = –6

Try this: (–4) × (–2) (–4) × (–2) = 8

Solve the following: 1) 5 × 6 2) –8 × 3 3) –7 × (–4) 4) 6 × (–2) = 30 = –24 = 28 = –12

Write a “rule” for multiplying integers.

Division cannot be modeled easily using two-colored counters, but since division is the inverse of multiplication you can apply what you learned about multiplying to division.

Since 2 × 3 = 6 and 3 × 2 = 6, does it make sense that - 3 × 2 = - 6 ? Yes + 2 × - 3 = - 6 and - 3 × + 2 = - 6 belong to a fact family: + 2 × - 3 = × + 2 = ÷ + 2 = ÷ - 3 = + 2

If 3 × (–5) = –15, then –15 ÷ –5 = ? and –15 ÷ 3 = ? If –2 × –4 = 8, then 8 ÷ (–4) = ? and 8 ÷ (–2) = ? 3 –5 –2 –4

Write a “rule” for dividing integers.