Math Notes

Entry 1: Birthday Bonanza About 18,000,000 people on Earth share your birth date (unless you were born on February 29). Do you think one of them might be in your class? Place a sticky note with your initials above the month of your birthday on the histogram (a graph of data) on the wall.  If there are sticky notes already above your month, place yours directly above them so that all of the notes form a neat “tower” over that month. Which month has the most birthdays in your class?  Which has the fewest?  How can you tell by looking at the histogram? Can you tell by looking at the graph whether anyone shares the same birthday as you?  Why or why not? As a class, discuss how you could find the other students in class who were born in the same month that you were.  Look for an organized way to accomplish this.   Ask the name and birth date for each student born in the same month as you.  Did you find a "birthday twin"? If you are the only student in class born in your month, find the students born in the month just before or just after yours.

Entry 2: Sleepy Time 1-2. SLEEPY TIME To help you work together today, each member of your team has a specific job, assigned by your first name (or last name if team members have the same first name).  Read the Team Roles information further below, and then continue with this problem. How much sleep do you get at night?  On a sticky dot, write the time you usually go to bed and the time you usually get up.  For example, the dot below shows that a student goes to bed at 10:00 p.m. and wakes up at 6:00 a.m. On the scatterplot poster on the wall, find the time that you go to bed on the horizontal axis (the line that lies “flat”).  Then trace straight up from that point high enough to be even with the time that you get up on the vertical axis (the line that stands straight up) and place your sticky dot on the graph. When all the data is collected, work with your team to answer the questions below.  Be sure to use the team role descriptions following this problem in your text. What is the most common bedtime for your class members?  How can you tell? Which dots represent the students who get the most sleep?  The least sleep?  How much sleep does each of these students get? If you were to go to bed an hour earlier, how would your sticky dot move?  What if you were to get up an hour earlier? In general, how much sleep do students in your class get?

Entry 3: 1-5 1-5. TOOTHPICKS AND TILES Cruz, Sophia, and Savanna are using toothpicks and tiles to describe the attributes of the shapes below.  Cruz made a pattern and told the girls the number of tiles he used.  Then Sophia and Savanna each tried to be the first to see who could call out how many toothpicks, or units of length, were on the outside. Explore using: Area Tiles and Toothpicks (CPM). Cruz made the tile pattern shown below and said, “There are six tiles.” Savanna quickly said, “There are ten toothpicks.”  Copy the tile pattern on your paper and show where Savanna counted the 10 toothpicks.  Justify your answer with words, numbers, or pictures. Cruz put down the pattern as shown below, but he ran out of toothpicks.  How would you describe this shape using toothpicks and tiles? Get a set of tiles from your teacher or use the Area Tiles and Toothpicks (CPM) and work with your team to: Make a pattern so that there are four more toothpicks than tiles. Draw your tile pattern on your paper Label the number of toothpicks and tiles on your drawing. Is there more than one answer?

Entry 4: 1-8 1-8. Does changing the number of toothpicks always change the number of tiles?  Does changing the number of tiles always change the number of toothpicks?  Think about these two questions as you look at the following tile shape. Explore using: Area Tiles and Toothpicks (CPM). Write a fact statement that includes information about the number of tiles and toothpicks that would describe the tile shape below. How can you add a tile to the shape in part (a) but not change the number of toothpicks?  Justify your response.

Entry 5: Math Notes The perimeter of a shape is the total length of the boundary (around the shape) that encloses the interior (inside) region on a flat surface.  The area is a measure of the number of square units needed to cover a region on a flat surface.    rectangle is a quadrilateral (four sides) with four right angles. 

Entry 6: 1-11 HW 1-11. In the “Toothpick and Tiles” game, you looked at the number of square tiles and the number of toothpicks used to form shapes. The math words that describe the number of tiles and toothpicks are area and perimeter. Read the Math Notes box for this lesson to review how area and perimeter are related to tiles and toothpicks. Then follow the directions below. Find the area and perimeter of the tile figure at right. Find the area and perimeter of the rectangle at right. Now design your own shape with 5 square tiles. Record the perimeter and the area.

Entry 1-12 HW Consider the first three figures of the pattern below. On your own paper, draw what Figure 4 of this pattern should look like. Using words, describe what Figures 5 and 6 should look like. Using words, describe how the pattern is changing.

Entry 8: 1-13 HW  Vi is trying to figure out how a square can be divided into four equal parts.  Show her at least three different ways to divide a square into four equal parts.

Entry 9: 1-15 Copy the dot pattern below onto graph paper. What should the 4th and 5th figures look like?  Draw them on your paper. How can you describe the way the pattern is growing?  Can you find more than one way? How many dots would be in the 10th figure of the pattern?  What would it look like?  Draw it. How many dots would be in the 30th figure?  How can you describe the figure without drawing it?  Can you describe it with words, numbers, and a diagram?  Be ready to explain your ideas to the class.

Entry 10: 1-8 Study the dot pattern below. Sketch the 4th and 5th figures. Predict how many dots will be in the 10th figure.  Show how you know. Predict how many dots will be in the 100th figure.  Show how you know. In what ways is this pattern different from others in this lesson?

Entry 11: 1-25 1-25. Different ways of presenting data can tell you different things.  For example, some of your questions might have been easy to answer with an organized table of data.  However, other questions can be easier to answer if the data is arranged in a different way, such as in a histogram like the one shown below. Look carefully at the graph.  Use it to try to answer the questions below. Between which two numbers on the graph did the most frogs jump? Typical frogs jump between what two jump lengths? Were there any unusually long or short jumps? How many frogs are represented on this histogram? Half the frogs jumped less than how many inches?

Entry 12: Math Notes Rounding Sometimes you want an approximation of a number.  One way to do this is to round the number.  For example, 4,738 is 5,000 when rounded to thousands.  The number 5,000 is said to be rounded “to the nearest thousand.”  To round a number:   Find the place to which the number will be rounded.  Examine the digit one place to the right.  If the digit is 5 or greater, add 1 to the place you are rounding. If the digit is less than 5, keep the digit in the place you are rounding the same. In the example 4,738, the number 4 is in the thousands place.  If you check the hundreds place, you see that 7 is greater than 5.  This means the 4 needs to be increased by 1.  Here are some other examples: Round 431.6271 to the nearest tenth. (1)  Focus on the 6 in the tenths place. (2)  The number to the right (in the hundredths place) is 2.  This is less than 5. (3)  431.6 is the answer. Round 17,389 to the nearest hundred. (1)  Focus on the 3 in the hundreds place. (2)  The number to the right (in the tens place) is 8.  This is more than 5. (3)  17,400 is the answer.

Entry 13: 1-35 Learning Log In this course, you will often be asked to reflect about your learning in a Learning Log.  Writing about your understanding will help you pull together ideas, develop new ways to describe mathematical ideas, and recognize gaps in your understanding.  Your teacher will tell you where your Learning Log entries should go.  For your first entry, you will consider the process by which you worked with your team and your class to make sense of “Trail Mix” (problem 1‑33).  Write a reflection in your Learning Log that addresses the following questions:  What did people say or what questions did they ask that helped you to make sense of this problem? What did you say or what questions did you ask that helped you to make sense of this problem? What would you advise another student to do to make sense of this problem?

Entry 14: Math Notes Conjecture and Justify A conjecture is a statement that appears to be true.  It is an educated guess. To justify a conjecture is to give reasons why your conjecture makes sense.  In this course you will justify conjectures by using observations of a pattern, an algebraic validation, or some other logical method.