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Exploring Input/Output Tables in Patterns – Discovering patterns with tables – Patterns help predict the next numbers in a sequence – Using addition in patterns – Add the same number to get the next output – Applying subtraction to find patterns – Subtract a constant to find the preceding number – Multiplication & division in patterns – Use these operations to see patterns grow or shrink quickly | This slide introduces the concept of input/output tables and how they relate to understanding patterns in math. Emphasize the importance of recognizing patterns as a way to predict future numbers in a sequence. Show how addition can be used to continue a pattern by consistently adding the same value. Similarly, demonstrate subtraction as a method to determine previous numbers in a pattern. Highlight how multiplication and division can create patterns that grow or reduce more rapidly than those created by addition or subtraction. Provide examples of each operation within an input/output table and encourage students to practice creating their own tables with different operations.

Exploring Input/Output Tables – What are Input/Output tables? – Tables that show how a rule applies to an input number to produce an output. – Everyday examples of Input/Output – Like recipes: ingredients (input) and the final dish (output), or saving money: deposit (input) and balance (output). – Understanding ‘rules’ in tables – The ‘rule’ is a math operation applied to the input to get the output, such as add 2, subtract 1, multiply by 3, or divide by 4. – Practice with math operations – We’ll use addition, subtraction, multiplication, and division to fill in tables. | This slide introduces the concept of Input/Output tables, which are fundamental in understanding functions and algebraic thinking. Start by defining Input/Output tables as a way to represent how a function takes an input, applies a ‘rule’ (which is a mathematical operation), and gives an output. Provide relatable examples to make the concept tangible for fourth graders, such as following a recipe or tracking weekly allowance. Emphasize the importance of the ‘rule’ which dictates how the input is transformed into the output. Conclude with interactive examples using the four basic math operations to solidify their understanding. Encourage students to think of their own examples and share how they use rules to find outputs in everyday life.

Addition in Input/Output Tables – Understanding addition for output – Use addition to find the output value in a table – Example: Adding 2 to a number – Starting with 0, if we add 2 each time: 0, 2, 4, 6… – Practice: Input 3, 5, 7; Add 2 – Apply the rule: Add 2 to each input to get the output | This slide introduces the concept of using addition to determine the output in input/output tables. Start by explaining that input/output tables help us understand patterns and sequences in math. Show how adding a consistent number to the input values results in a sequence of outputs. Use the example provided to illustrate this concept: if we start with 0 and add 2, we get a sequence of even numbers. For the practice problem, guide students to apply the rule of adding 2 to each input number (3, 5, 7) and ask them to find the corresponding outputs. Encourage students to verbalize their thought process as they work through the problem. This activity will help solidify their understanding of addition within input/output tables and prepare them for more complex operations.

Subtraction in Input/Output Tables – Understanding subtraction in tables – Example: Subtracting 3 from inputs – If input is 7, and we subtract 3, output is 4 – Practice with given inputs – Inputs are 10, 8, 6; what are the outputs? – Discover the outputs together | This slide is focused on teaching students how to use subtraction within input/output tables. Start by explaining that an input/output table is a way to organize information so that a rule can be applied to each input to get an output. Use the example provided to show how subtracting a number from the input gives us the output. For the practice problem, guide the students to apply the rule of subtracting 3 to each input (10, 8, 6) and determine the outputs. Encourage the students to work through the problem together and discuss how the rule applies to each input to find the corresponding output. This exercise will help solidify their understanding of how rules function in input/output tables and the concept of subtraction within them.

Multiplication in Input/Output Tables – Understanding multiplication – Example: Multiply inputs by 4 – If input is 1, output is 4 (1×4). Continue the pattern. – Practice with a set rule – Use the rule ‘Multiply by 4’ for each input number. – Find outputs for 2, 4, 6 – Calculate outputs: 2×4=8, 4×4=16, 6×4=24 | This slide introduces students to the concept of using multiplication in input/output tables. Start by explaining that multiplication is a quick way of adding the same number several times. Show an example where each input number is multiplied by 4 to find the output. For the practice problem, provide students with the inputs 2, 4, and 6, and guide them to apply the rule of multiplying by 4 to find the corresponding outputs. Encourage students to share their answers and explain their process. This activity helps solidify their understanding of multiplication within the framework of patterns and sequences.

Division in Input/Output Tables – Understanding division in tables – Example: Divide inputs by 5 – If we input 10, dividing by 5 gives us 2 as the output – Practice: Inputs 25, 50, 75 – Apply the rule: Divide by 5 to find the output for each input – Discover outputs using division – Outputs are the results after division | This slide introduces the concept of using division in input/output tables, a key component of understanding patterns and sequences in mathematics. Start by explaining that division is one way to find a relationship between input and output values. Use the example to show how dividing an input number by 5 yields the output. For the practice problem, guide students to apply the rule of division to each input value (25, 50, 75) to find the corresponding outputs (5, 10, 15). Encourage students to verbalize their thought process as they divide. This exercise will help solidify their understanding of division within the context of input/output tables and prepare them for more complex patterns and sequences.

Creating Input/Output Tables – Choose the right operation – Decide if we add, subtract, multiply, or divide – Fill in tables with numbers – Input a number, apply the rule, and write the output – Group Activity: Secret Rule Table – Each group makes a table with a hidden rule for others to guess – Discuss results with class – Share your table and see if classmates can find the rule | This slide introduces the concept of creating input/output tables using basic arithmetic operations. Start by explaining how to choose the correct operation based on the pattern observed. Then, guide students through filling in the tables with inputs (starting numbers) and calculating the outputs (results after applying the rule). For the group activity, have students work in small teams to create their own input/output table with a secret rule. Other groups will try to identify the rule based on the inputs and outputs provided. This activity encourages critical thinking and understanding of mathematical operations. After the activity, facilitate a discussion where students can explain their reasoning and how they determined the rules of other groups’ tables.

Class Activity: Secret Rule Table Game – Pair up with a classmate – Exchange tables with secret rules – Guess your partner’s table rule – Discuss how you found the rule – Think about the operations used: addition, subtraction, multiplication, or division | This interactive class activity is designed to help students understand input/output tables and the rules that govern them. Start by explaining how input/output tables work with examples of addition, subtraction, multiplication, and division. Then, have the students create their own tables with a secret rule. After exchanging tables with their partners, they will try to guess the rule based on the inputs and outputs provided. Encourage them to look for patterns and use logical reasoning. Once they’ve guessed the rule, ask them to share their thought process with the class. This will help them articulate their understanding and learn from others’ strategies. Possible activities for different pairs could include tables with single operations, mixed operations, or even two-step operations to cater to varying levels of difficulty.

Review: Input/Output Tables – Recap on Input/Output tables – We learned how to use addition, subtraction, multiplication, and division in tables. – Real-life application of tables – Use tables to plan a party budget or keep track of sports scores. – Open floor for questions – Share interesting observations | This slide aims to consolidate the students’ understanding of Input/Output tables and their practical applications. Begin by reviewing the concept of Input/Output tables and how they incorporate basic arithmetic operations. Emphasize the importance of these tables in organizing information and solving problems efficiently. Encourage students to think of ways they could use these tables in their daily lives, such as budgeting for a family event or tracking points in a game. Open the floor for any questions the students might have, allowing them to clarify their doubts. Finally, ask them to share any interesting observations or insights they’ve gained from the lesson. This interactive discussion will help reinforce their learning and ensure they can apply the concept beyond the classroom.