Expressions and Equations Grade 7
Hook 1 7.EE.A.1
Prompt: Fill in the blanks.
This hook presents students with a geometric representation of the distributive property. For some classes, it may be helpful to replace the variables with numbers and to fill in the width of the rectangle with a value. Other classes may be ready for the challenge of the algebraic representation. Many teachers and curricula use this exact model to teach the distributive property. Providing the model to students as a hook before instruction does not need to change anything about the content delivery. The rearranged order merely gives your students a chance to think about the model themselves before you explain it to them. If we allow for inquiry before instruction, students may have ideas or questions about the concept your presenting, an opportunity for dialogue is created and students have a window to share ideas, which is exactly what we want in a math class.
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Hook 1 7.EE.A.2
Prompt: Calculate the total in 4 different ways.
It's important to let students know that they do not need to write their equations in the order given in the hook. I'd expect most students, who can calculate the total, to use the 2-step model, 90 x 0.2 + 90. Others may find it easier to think of it in 4 steps, 90 x 0.1 + 90 x 0.1 + 90. The objective is for students to understand that all of these calculations are equivalent. Of course, for some students, finding the tip will be difficult. Kids at this level can discuss the meaning of a tip, how they believe it is calculated and how that effects the total. In short, they can discuss the real-world application in depth before you begin the needed review of percents. Connecting their work to the real world will, hopefully, help them to begin to connect the different methods of calculating the tip.
Hook 1 7.EE.B.3
Prompt: Who won the election? Provide proof.
This hook provides valuable formative assessment in terms of students' understanding of the connections between percents, fractions and decimals. One aspect of this standard is "the reasonableness of answers using estimation". Perhaps, students will notice that these numbers do not add exactly to 100%. You may want to discuss this and the "reasonableness" of the actual sum. What sums would seem to be unreasonable to them?
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Hook 1 7.EE.B.4
Prompt: Create an equation to model the cost of the date.
In this hook, the table acts as tape diagram to provide students with a visual to help them create their equation. Depending on the level of your class, this hook may provide a opportunity to discuss what exactly an equation is with your students. Although equality seems self-evident, these kind of discussions can be illuminating for both students and teachers. Students will also need to find a way to represent a ticket's cost. If they're familiar with variables, great. If not, there's another valuable discussion. It's important to help students see the logic in equations and variables so that they will later grasp the logic and utility of solving equations.
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Hook 2 7.EE.B.4
Prompt: Complete. Fill boxes with numbers and variables. Fill spaces in between boxes with a single symbol.
The fact that the visual in this hook is not a tape diagram like the previous hook may confuse some students. However, it also offers an opportunity to discuss the difference between equations and inequalities and how that difference prevents us from presenting the data in a tape diagram. Some student groups may need to discuss the meaning of a budget and the less than sign while others may focus on solving the inequality. In either case, allow your students to share their ideas about a shopping trip and how to represent that transaction algebraically.
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