Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.
Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.Īn introductory card sort activity matches students with their partner for the week. Identify and use the properties of operations.
Use parentheses to evaluate numerical expressions. Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems. Students use the multiplication property of equality to justify solutions to real-world ratio problems. The mathematical work of the unit focuses on ratios and rates, including card sort activities in which students identify equivalent ratios and match different representations of an equivalent ratio. Students then work on Gallery problems, to further explore the resources and tools and to learn how to organize their work. Students learn how to present their work to the class, the importance of students’ taking responsibility for their own learning, and how to effectively participate in the classroom math community. Then over the course of the week, students learn about the routines of Opening, Work Time, Ways of Thinking, Apply the Learning (some lessons), Summary of the Math, Reflection, and Exercises. This unit introduces students to the routines that build a successful classroom math community, and it introduces the basic features of the digital course that students will use throughout the year.Īn introductory card sort activity matches students with their partner for the week. Identify and use the multiplication property of equality. Use ratio and rate reasoning to solve real-world problems. Understand ratio concepts and use ratios. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. Recognize the first quadrant of the coordinate plane. Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line. Plot positive rational numbers on a number line. The answers that you get by these two approaches won’t be identical, since one will be a log base $4$ and the other a log base $2$, but they’ll be equal, and you can use the relationship $\log_2x=2\log_4x$ to verify this.Solve problems with positive rational numbers. Going back to $\log_2x=2\log_4x$, if you happen to notice that $2\log_4x=\log_4x^2$, you simply replace $5\log_4x^2$ by $5\log_2x$ to get Use the result of the first paragraph to change $\log_2(2x+1)$ to $2\log_4(2x+1)$ and $\log_2x$ to $2\log_4x$ then you haveĪnd you can use the usual properties of logs to express this as the log base $4$ of a single expression. Now you have $\log_2(2x+1)-5\log_4x^2+4\log_2x$, which mixes logs base $2$ with logs base $4$ it would be much easier to simplify if all of the logs were to the same base. In other words, we’ve just demonstrated that for any $x>0$, $\log_2x=2\log_4x$.
Suppose that $x>0$ is some number, and $\log_4x=y$.
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