Created by: Kim Marshall, Kathleen Sherrod, Tina Creecy. Edible Equations. A Hands-On Lesson for Introducing Models of Equations
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1 Edible Equations A Hands-On Lesson for Introducing Models of Equations Tina Creecy Kim Marshall Kathleen Sherrod creecytm@lcps.k12.va.us kmarshall@sbo.hampton.k12.va.us Kathleen.allan@nn.k12.va.us The lesson presented today is from a unit on equations that was designed to cover SOL 6.23abc. We have included a copy of the unit outline, today s lesson, and the worksheets that would be needed. Please feel free to any of the presenters to obtain a copy of the complete unit. We want the students to use physical objects to identify, represent and solve algebraic equations. It is also essential to have students understand and apply the correct usage of the equals sign. Students will understand the concept of equations when performing operations on both sides of the equals sign. The students will utilize correct algebraic terminology when identifying and solving equations: equation, variable, term, and coefficient. The students will be assessed on these areas. An activity that will require the students to think at the next level will also be used. Lesson Objectives: The student will model algebraic equations using concrete materials. The student will identify the equation created by model. Key Vocabulary: equation: a mathematical sentence that contains an equals sign term: a number, a variable, or a product of numbers and variables in an equation variable: a letter or symbol used to represent a number coefficient: a number multiplied by a variable in an algebraic expression Materials Needed: - Skittles TM (original red pack/king Size) - Balance Me! worksheet (attachment A-Day2) - Equation flashcards - Modeling equations worksheet (attachment B-Day2) - Colored pencils - Math journals (notebook for reflections)
2 Day Lesson Idea(s) Title of Lesson: Getting to Know Equations Objectives: The student will use the following algebraic terms appropriately: variable, coefficient, term, and equation. Description: This will be the introductory lesson to equations for the students. The vocabulary equation, term, variable, and coefficient will be introduced and discussed through the use of a foldable. The student will then create 5 flashcards on index cards. An equation will be on the front with any vocabulary part circled and on the back will be the vocabulary word that describes the circled part on the front. The students will then play Around-the-word using flashcards created by them. Title of Lesson: Edible Equations Objectives: The student will use physical objects to represent equations. Description: In this lesson, students will use one specific color of skittle to represent variables, (blue) and another color (yellow) to represent whole numbers. They will have work mats to use during this activity. When looking at an equation such as 3x = 12, students will set up the problem with the skittle, at the top of their individual or partner mat. Full sized version will be attached. The object is to have the students model equations. Title of Lesson: Hands on Equations Objectives: Students will be able to model, solve and demonstrate an understanding of algebraic equations, using Hands-On Equations. In using this activity, students will be able to rationalize a solution to a one- step equation, using inverse operations. Description: In this lesson, the teacher will introduce the students to hands-on Equations kits. The kit will allow the students to get a visual understanding on how the balance scale represents an equal value on both sides. The pawns in the kit will be another method of representing an unknown value. Students will be able to model, solve and check algebraic equations using inverse operations. Title of Lesson: Stepping up to Equations Objectives: The student will solve one-step equations with paper and pencil. Description: In this lesson, the students will solve one-step equations using paper and pencil based on their experience from the previous few days. The students will also participate in I have you have game. One student will call out an equation, all students will solve the equation but only one student will have that particular answer. Title of Lesson: Assessment/What s Missing? Objectives: The students will model and solve one-step linear equations. The student will use the following algebraic terms appropriately: variable, coefficient, term, and equation. The students will also create a story and requires the given equation to solve. Description: Students will take an assessment, quiz, on concepts taught the previous days. After quiz, students will complete the What s Missing activity. In this activity the students will develop stories to match equations. The main focus of this lesson will be to design a question, in the story, that matches the variable in the equation.
3 Assesments: Check and correct homework, oral responses and dialogue, written responses, oral prticipation Differentiation Strategies/Activities: flexible grouping, paired activities Initial Activity: 1. Play Around the World from the previous day s lesson using the flashcards that were created by the students for about 5 minutes. 2. Collect homework. Have students share any difficulties they may have had on the previous day s lesson. Allow other students to share ways that could help them understand. Instruction: 3. Edible Equations: Explain to students that you are now going to show them how to make pictures, or models, of equations using skittles. Hand out the Balance Me! Worksheet (attachment A-Day 2) Say to students, This is a picture of a balance and is used to weigh items. (Can show an actual balance if available.) The heavier side lowers while the lighter side rises. When the two sides are the same weight or equal, they are level and the needle at the bottom points straight up. We are going to be dealing with equations that are equal so we know our balances will be level. Each pan of the balance will represent one side of the equation. Now that you know what this is, lets get started! Have students open bag of skittles and place in a pile on desk. Explain that you will identify which color will represent the variable and which will represent the whole number 1 for each example. Instruct students to, Place 3 red skittles on the left hand side of the balance and 6 yellow skittles on the right hand side. If the red skittles are your variable, y, what is the left side of the balance modeling? (3y- lead students to understand that the answer is the term 3y and not y + 3 because the model has 3 times the same variable being represented not the variable AND 3 other items.) Now ask students, If the left side is 3y, what would the right side of the balance be modeling remembering that each yellow skittle represents 1? (6-inform students all they have to do is count each one for a total.) State, Now that we have what each side of the balance is modeling we need one more part to create an equation. Who can tell me the definition of an equation? Ask several students for a definition, place on the board. (A mathematical sentence that contains an equals sign.) Say, Based on this definition, what are we missing from our equation? (The = sign) (Remind students we get the equal sign from the balancing being level/at 0) Write the final equation on the board. 3y = 6.
4 Have students clear balances, move skittles off and back into pile, and explain that the class is going to do several more examples together. Now have the students place one green skittle and 3 red skittles on the left side of the balance. For the right side, have the students place 7 red skittles. Explain that the green skittle is the variable and the red skittles equal 1. Ask the students what difference they notice on the left side of this model compared to the last model. (This model has a variable and 1 s where the last one only had variables.) Have students identify the modeled part of the equation on the left side of the balance. (x + 3) Explain to the students when they see two different items being combined on one side of the equation or balance it represents adding the two together. Have students identify the right side of the model (7). Instruct the class to think, pair, share what equation we have modeled. (Think to themselves, pair with a classmate to discuss, share with the class) (x + 3 = 7) Write the equation on the board. Repeat the previous steps with the students for the following equations. (Teacher or students can choose color of skittles to use-just making sure no more than two colors are used per equation; one for variable and one for 1 whole.) 4t = 12 h + 1 = 5 3r = 3 add more if needed For students who have special needs (instructional strategies and accommodations) 4. Have students get in pairs with the skittles and Balance Me! worksheet. Provide the following directions to the class. As a pair, you will now create your own models of equations for addition and multiplication. First create the model on the Balance Me! worksheet. Then you will draw the model using the balance on the Modeling Equation worksheet. You can use your colored pencils to draw the different colors on the worksheet. Be sure to include a key as to which color is your variable and which color represents on e whole. Once you have drawn the model write the equation that goes with it. Answer any questions then let students begin. When finished, collect students Modeling Equations worksheet and have them return to their desk. Closing: 5. Have students write in Math Journals about what they learned from the lesson today and what they feel they need more instruction on. HOMEWORK: Using colored pencils, create 5 models of equations. Draw the balance, models and write the equation beside each. Write a paragraph about how a multiplication model is different from an addition model.
5 Balance Me!
6 Name Date Class (1) Modeling Equations (2) (3) (4)
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