Fourth Grade Number Sense and Algebraic Concepts 2015-11-23 - PDF document

Slide 1 / 308 Slide 2 / 308 Fourth Grade Number Sense and Algebraic Concepts 2015-11-23 www.njctl.org Slide 3 / 308 Slide 4 / 308 Table of Contents Click on a topic Vocabulary words are identified with a dotted underline. to go to that section Algebraic Equations/Number Sentences Sometimes when you subtract the fractions, you Problem Solving find that you can't because the first numerator is Place Value/Number Sense Through the Millions smaller than the second! When this happens, you need to regroup from the whole number. Read and Represent Multi-Digit Numbers (Click on the dotted Analyze Number Lines Using Number Sense underline.) Compare numbers How many thirds are in 1 whole? Order Numbers How many fifths are in 1 whole? Round Numbers How many ninths are in 1 whole? ------------- Patterns Glossary The underline is linked to the page in the presentation's glossary containing the vocab chart. Slide 5 / 308 Slide 6 / 308 The charts have 4 parts. Its meaning 2 (as used in the 1 Vocabulary Factor lesson) Word Algebraic Equations/ A whole number that A whole number that multiplies with can divide into Number Sentences another number to another number with make a third number. no remainder. 5 1 R 15 ÷ = 3 5 3 x 5 = 15 16 3 3 and 5 are 3 is a 3 is not a factors of 15 factor of 15 factor of 16 3 Examples/ 4 Back to Counterexamples Link to return to the Return to Table Instruction of Contents instructional page.

Slide 7 / 308 Slide 8 / 308 What is an Equation/Number Sentence? ----------- 6 + y = 10 Brainstorm the important parts of an equation and record results below: equals sign (relation symbol) To understand equations, we also need to know what operations are. Use the green box on the left to list the ideas you brainstormed. Four basic symbols/signs: Click for answers + addition subtraction x ÷ An equation is another name for a number sentence that contains an EQUALS symbol, an operation(s), number(s), and/or variable(s). multiplication division An equation says that two things are equal. Click for Definition What is on the left is equal to what is on the right. = LEFT RIGHT Definition of OPERATION: ------------ Therefore, an equation is like a statement "this equals that". Slide 9 / 308 Slide 10 / 308 Let's Review Some Vocabulary 6 + y = 10 operation equals sign (relation symbol) Use this equation to help you define the important terms: 6 + Y = 10 Finally, let's brainstorm what we know about a variable. First, without using the word 'equal', what does the equal sign mean? Use the gray box on the left to list the ideas you brainstormed. Use the red box below to list the ideas you brainstormed. Click for answers A symbol (LETTER) used in the place of a number ( examples: y, a,n, w) is are was were will be The same value as The solution is the number that Click for answers total comes to sold for equivalent to The same as ---------- fits in the place of the variable. Definition of the EQUAL sign: Definition of VARIABLE : ----------- Slide 11 / 308 Slide 12 / 308 Review operation 6 + y = 10 Why are equations/number sentences important? What is this What is the name of this equals sign (relation symbol) symbol? symbol? Let me introduce you to QUIGLEE the equation! variable Identify this Please click inside the oval. symbol QUIGLEE will tell us why equations (number sentences) are This type of equation is called an algebraic equation. so important and review some important vocabulary. Algebraic Equation: An equation that includes one or more variables. ----------------- Please click the microphone on Quiglee's mouth. Knowing how to create sentences by correctly organizing words helps you understand and learn a language. Equations are a way to organize numbers to help you understand math and learn how to problem solve.

Slide 13 / 308 Slide 14 / 308 An EXPRESSION in math is like a phrase/sentence fragment. It can ------------ contain numbers, operators, and variables. It is a part of an equation. An EQUATION in math is like a sentence. It is a mathematical sentence in which two things are the same and are joined by an equal sign. It can only be true or false. Expressio Expressio Equatio n n n 7 + 8 4 + 11 7 + 8 = 4 + 11 Is QUIGLEE's equation true or false? True Click for Answer How do you know? Both sides of the equation are equal. Click for Answer Slide 15 / 308 Slide 16 / 308 1 Which choice best explains what a variable is? 2 Choose the algebraic equation below. A A symbol that tells you to add. A 8 + 2 = 10 B It is a sign that tells you two items are the same. B 6 - h = 4 C It replaces a number in an equation. C 18 = 9 x 2 D It can be also called a relation symbol. D 78 + y Slide 17 / 308 Slide 18 / 308 3 Which of the following are expressions? 4 What would be needed to make the expression below a complete equation. A 8 - b A a variable 7 - p B m + 4 = 9 B an equals sign C 4 + y = 7 + 6 C an operation symbol D 2y + 7 D a solution E 2 x 3

Slide 19 / 308 Slide 20 / 308 5 Is the equation below true or false? Determining the Solutions to ---------------- Algebraic Equations 8 - 6 = 2 x 2 A solution/answer to an algebraic equation is a number that makes the equation true. True In order to determine if a number is a solution, replace the variable with the number and evaluate/solve the equation. False If the number makes the equation true, it is a solution. If the number makes the equation false, it is not a solution. Slide 21 / 308 Slide 22 / 308 Determining the Solutions to Algebraic Equations The algebraic equation is TRUE if the two expressions (left side and right side) are balanced with an equal sign. Algebraic Equation or What number would replace the Open Number Sentence -------------------- variable and make this algebraic equation TRUE (Balanced)? 7 + 8 = v + 6 Slide 23 / 308 Slide 24 / 308 Evaluate the following expression and balance the algebraic 6 Choose the equation below that is balanced. equation. Use QUIGLEE'S Magic Mirror to check your answer. A 7 + 3 = 5 x 2 1. Evaluate the expression: (14 - n) for n = 8 B 5 x 2 = 7 + 2 6 Solution: 22 148 C 8 - 5 = 15 - 10 17 + y = 2 x 10 D 3 + 2 + 4 = 10 Simplify equation Click for strategy 2. Balance the algebric equation: 17 + y = 20 for #2 17 + y = 2 x 10 To be balanced the left = right. The variable y is: 37 20 3 20 = 20 So, y = 3.

Slide 25 / 308 Slide 26 / 308 7 Evaluate the expression below when t = 5. 8 In order for the algebraic equation below to be true, what whole number must replace the variable w? 3 x t 9 + w = 12 + 9 Slide 27 / 308 Slide 28 / 308 9 Choose the answers that would make the algebraic 10 Choose the algebraic equations that are true when g = 3. equation false. A 6 x g = 9 A p = 3 B 4 + g = 6 + 1 3 x p = 9 + 9 B p = 18 C g + g = 9 C p = 6 D 8 - g = 5 D p = 9 E 20 - g = 18 Slide 29 / 308 Slide 30 / 308 11 What value of k would make the algebraic equation below true? 5 + k = 3 x 3 Problem Solving Return to Table of Contents