This Math Talk focuses on the meaning of numbers and symbols in expressions. It encourages students to relate repeated addition to multiplication and to relate repeated multiplication to exponents. The numbers are selected to discourage students from computing the values of the expressions. Instead, they prompt students to rely on what they know about operations and exponents to mentally make comparisons. The understanding elicited here will be helpful later in the lesson when students write expressions to represent the surface area and volume of cubes.
To decide, without calculations, which of two expressions has the greater value, students need to look for and make use of structure (MP7). In explaining their reasoning, students need to be precise in their word choice and use of language (MP6).
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
Keep all previous problems and work displayed throughout the talk.
Decide mentally which expression has a greater value.
To involve more students in the conversation, consider asking:
To support students in upcoming work, highlight the following ideas if they are not already mentioned by students:
Math Community
Display the Math Community Chart and a list of 2–5 revisions suggested by the class in the previous exercise for all to see. Remind students that norms are agreements that everyone in the class shares responsibility for, so everyone needs to understand and agree to work on upholding the norms. Briefly discuss any revisions and make changes to the “Norms” sections of the chart as the class agrees. Depending on the level of agreement or disagreement, it may not be possible to discuss all suggested revisions at this time. If that happens, plan to discuss the remaining suggestions over the next few lessons.
Tell students that the class now has an initial list of norms or “hopes” for how the classroom math community will work together throughout the school year. This list is just a start, and over the year it will be revised and improved as students in the class learn more about each other and about themselves and math learners.
When given an expression with an exponent, students may misinterpret the base and the exponent as factors and multiply the two numbers. Remind them about the meaning of the exponent notation. For example, show that 5⋅3 = 15, which is much smaller than 5 ⋅5 ⋅5, which equals 125.
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This Math Talk focuses on the meaning of numbers and symbols in expressions. It encourages students to relate repeated addition to multiplication and to relate repeated multiplication to exponents. The numbers are selected to discourage students from computing the values of the expressions. Instead, they prompt students to rely on what they know about operations and exponents to mentally make comparisons. The understanding elicited here will be helpful later in the lesson when students write expressions to represent the surface area and volume of cubes.
To decide, without calculations, which of two expressions has the greater value, students need to look for and make use of structure (MP7). In explaining their reasoning, students need to be precise in their word choice and use of language (MP6).
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
Keep all previous problems and work displayed throughout the talk.
Decide mentally which expression has a greater value.
To involve more students in the conversation, consider asking:
To support students in upcoming work, highlight the following ideas if they are not already mentioned by students:
Math Community
Display the Math Community Chart and a list of 2–5 revisions suggested by the class in the previous exercise for all to see. Remind students that norms are agreements that everyone in the class shares responsibility for, so everyone needs to understand and agree to work on upholding the norms. Briefly discuss any revisions and make changes to the “Norms” sections of the chart as the class agrees. Depending on the level of agreement or disagreement, it may not be possible to discuss all suggested revisions at this time. If that happens, plan to discuss the remaining suggestions over the next few lessons.
Tell students that the class now has an initial list of norms or “hopes” for how the classroom math community will work together throughout the school year. This list is just a start, and over the year it will be revised and improved as students in the class learn more about each other and about themselves and math learners.
When given an expression with an exponent, students may misinterpret the base and the exponent as factors and multiply the two numbers. Remind them about the meaning of the exponent notation. For example, show that 5⋅3 = 15, which is much smaller than 5 ⋅5 ⋅5, which equals 125.