Students have been using hands on activities to learn about and apply their knowledge of volume. To start the unit, students used pattern blocks to build towers. They were able to find the volume of one prism, and then discovered that they could multiply the volume of one block by the number of blocks in their tower to find the tower's volume. Using this, students were able to generalize and determine that the volume of any prism is the area of its base times its height. Using what they learned from the pattern block towers, students made the conclusion that the same procedure could work for cylinders. Students watched a video in which an 8.5 by 11 piece of paper was used to create two different cylinders, one with a height of 8.5 in and one with a height of 11 inches. The cylinders were then filled with popcorn. Students made predictions about whether or not the two cylinders would hold the same amount of popcorn, and if not, which would hold more. They then created these cylinders and poured popcorn in to determine if their predictions were correct.
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Students have been learning about solid shapes and have been determining their surface areas. First, students looked at the different types of solids and determined what shapes made up their surfaces. Next, students looked at the nets of three dimensional shapes. They used what they knew about the shapes that made up the surfaces of the solids to draw a these two dimensional representations of them. To further investigate nets, students traced Rubik's Cubes, flipping from one side to another and keeping track of which sides they had traced. They then cut out the resulting net they had created and folded it into a cube. Students then looked at surface area by finding the dimensions of various solids and determining the areas of each of their sides. They found the surface area of rectangular prisms, triangular prisms, trapezoidal prisms, cylinders, square pyramids, triangular pyramids, and cones.
Students have been combining their knowledge of circles and angles with their understanding of percents to create circle graphs. First, students collected data from students in the upper school to answer a survey question they had selected. Using what they have previously learned about percents, students then determined what percent of the students they surveyed selected each choice. Combining this understanding of percents with their knowledge that a circle has a total of 360 degrees, students then determined what angle measure would be that percent of 360 degrees to determine how big the sections in their circle graphs would need to be. Next, students practiced making circles with compasses and measuring angles in them with protractors. Finally, students were ready to put together all that they had done and create a final copy of their graph. Here are their graphs:
Students have been learning a lot about right triangles. First, they started by looking at the Pythagorean Theorem. Students drew right triangles with squares on each side, and cut and rearranged the squares to show that the area of the largest one was equal to the areas of the smaller two combined. Students used the Pythagorean Theorem to answer questions involving right triangles in real life, such as determining how far a catcher would need to throw a ball to catch a player stealing second base.
Students then applied the Pythagorean Theorem to points in a coordinate plane to find the distance between two points. We played a game, entitled "Save the Hikers." The premise was that they were doctors trying to decide in what order to attend to 3 hurt hikers so they would get to each of them as quickly as possible. Students determined the distances between each hiker's location. After a few rounds, some students decided to try to find the longest route possible instead of the shortest. Here are the rules for this activity: Save the Hikers To wrap up our unit on right triangles, students looked at trigonometric ratios. They started by looking at the ratios of sides in similar triangles, and determining that the ratios were the same regardless of the triangles' sizes. Students then learned the names for the ratios and used their understanding of these ratios to determine the missing length of a side in a right triangle using a given side and angle. They applied their knowledge of trigonometric ratios to determine how tall a ladder can reach if it is placed at a safe angle with the ground, and thought about how long a firetruck's ladder would have to be to reach the top of a building. Students have been spending the past few weeks working with percents. After learning these fundamental concepts of percents, students started to look at where percents are used in real life. They calculated the total cost of a meal given the prices of various items and the percentage for tax and tip. Students also applied their understanding of percentages to find the prices of items after they are on sale. Finally, students learned about simple and compound interest and were able to determine how much money would be in a bank account given the principal amount, the annual interest rate, and the amount of time it was being saved.
Students had the opportunity to utilize the skills they developed throughout this unit for their final project. Students chose between basketball and hockey and answered questions based on provided information regarding players' statistics. Students then needed to research a team of their choice and record data for players on that team for two seasons. They then compared the two seasons and found the percent change in either their free throws or their shots made. Here are their finished projects: Students began this unit by reviewing what they have already learned about ratios. They knew how to write ratios to represent a given situation, and also knew how to write equivalent ratios. Using their knowledge of ratios, students were able to find unit rates to compare two prices to determine which was a better deal. They applied this understanding of unit rates to play a game of unit rate "go-fish," in which they asked their partners for the unit rates of the rates they had on their cards. Next, students learned different ways to solve proportions, applying the algebra they learned earlier in the year. They looked at how the different methods are similar, and discussed when each method would be best. Finally, students are applying their knowledge of proportions to similar figures. They are using proportions to determine the ratio of corresponding sides of similar shapes and using that ratio to find the value of missing lengths. Students playing unit rate "go-fish"
Students have been working for the past week on reviewing previously learned topics, and also on problem solving. They have been looking at challenging problems, coming up with a strategy, and trying to implement their strategy to find a solution. These problems have also required students to work together cooperatively and share their ideas with one another. One problem that students enjoyed was this brain teaser. In this problem, a teacher is buying chocolate letters to spell the names of each of her students. Different letters cost different amounts, as some are more common than others. The names and prices for each student is given. The pre-algebra students looked at the information that was given, and noticed that a lot of the names were very similar. They used this information to create a plan to determine the cost of each letter. Working together, students were able to find out how much each letter costs, and they then calculated the total costs for their full names.
Students have been learning about Greatest Common Factors, Least Common Multiples, and exponents. We started with a review of what students had learned last year about GCF and LCM. Next, students were introduced to a new way of finding the GCF and LCM of 2 numbers, and also learned how to find the GCF and LCM of more than 2 numbers. Students were then introduced to monomials. They used their knowledge of finding the GCF and LCM of numbers to find the GCF and LCM of monomials. Next, students helped establish rules for multiplying and dividing powers, as well as determine what negative exponents are. Students were then able to put together all that they had learned in this unit to simplify fractions that have monomials as their numerators and denominators.
Students have been working on solving inequalities. We started by solving one step inequalities involving adding and subtracting, and graphing the solutions. When multiplying and dividing, students took a look at what happens when multiplying or dividing by a negative number. Students are now working on solving multi-step inequalities, using the skills they learned when solving multi-step equations and using their knowledge of inequalities. Today, students worked on a puzzle together. Each piece matched an inequality with its answer. Here are some pictures of them working together, as well as their final puzzle in the shape of a heart.
Students have begun learning how to solve algebraic equations. They started by learning about the distributive property and simplifying expressions. In order to develop the distributive property, students used algebra tiles to model what multiplying by a variable expression would look like. They were then able to generalize based on the answers they got in the examples we did. Students then used their understanding of combining like terms to simplify algebraic equations that then required one step to solve. We then used algebra tiles again to figure out how to solve two step problems. Again, students were able to generalize from the examples we did to determine how to solve two step equations. Here's how we solved the equation 3x + 6 = 12 using algebra tiles: |
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