Patternsare everywhere! You may have noticed them in pine cones, flowers, stacks of cans in the grocery store, or many other places. Patterns are interesting partly because of the many ways that you can see or interpret how the parts of a pattern are changing. In this course, you will often be asked to look for multiple ways of seeing a pattern or concept. As you study the pattern in this lesson, work with your team to find multiple ways to see and describe the pattern and how it is growing. The following questions can help guide your discussion.
How can we describe the pattern?
Is there another way to see or describe it?
Does anyone see it differently?
1-15. DOT PATTERN
1. Copy the dot pattern below onto graph paper.
2. What should the 4th and 5th figures look like?
3. Draw them on your paper.
4. How can you describe the way the pattern is growing?
5. Can you find more than one way?
6. Draw the 10th figure.
7. What would it look like?
8. How many dots would be in the 10th figure of the pattern?
9. How many dots would be in the 30th figure?
10. 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.
1-16.With your team, prepare a stand-alone poster. It should show your description of the dot pattern in problem 1-15 and your prediction. “Stand-alone” means that anyone looking at your poster should be able to understand your thinking without any further explanation. Your poster should include:
Clear drawings of the 4th and 5th figures of the pattern.
Use color to help you show how you see the pattern.
An explanation of the different ways that you see the pattern you found.
Find ways to help your classmates understand how you saw the pattern.
Your prediction for the 30th figure with a clear explanation.
1-17.To generalize means to make a statement or conclusion about the common properties of a set of items. Work with your team to generalizethis pattern by finding a way to describe any figure in the pattern. In other words, if you knew a figure number, how could you decide what the figure looks like even if you cannot draw it? Be ready to share your ideas with the class.
1-18.Additional Challenge: Study the dot pattern below.
1. Sketch the 4th and 5th figures.
2. Predict how many dots will be in the 10th figure. Show how you know.
3. Predict how many dots will be in the 100th figure. Show how you know.
4. Make a list of ways this pattern is different from others in this lesson.
Place Value
The number assigned to each place that a digit occupies is called the place value. In our number system, the place values are all powers of ten.
Starting from the left side of the decimal point, the place values are: ones, tens, hundreds, thousands, ten thousands, and so on.
On the right side, the place values are tenths, hundredths, thousandths and so on.
In the example below, the place occupied by 8 has the value of 100, so the value of the digit8is 800.
The number above is read, “nine thousand, eight hundred seventysix and five hundred fortythree thousandths.”
The number 64.3 is read, “sixtyfour and three tenths.”
The number 7.17 is read, “seven and seventeen hundredths.”
The only time the word “and” is said when reading a number is at the location of the decimal point.
1-19. Study the dot patterns in parts (a) and (b) below. Assume that each pattern continues to increase by the same number of dots and in the same locations for each figure.
1. For each pattern, sketch the 4th and 5th figures.
2. Predict how many dots will be in the 100th figure.
3. For each pattern, explain how you made your prediction for the 100th figure.
1-20.The value of a decimalbecomes clearer when the place valueis spoken or written as the number it names. For example, 0.1 makes more sense if it is read as “one-tenth” rather than “zero point one.”
1. Write the following numbers in words so that the place value can be identified.
0.4 1.3 0.56 2.008
2. Now reverse your thinking. Write the decimals that go with the following words.
thirty-five hundredths three and two-tenths six-hundredths
1-21.
1.Findthe perimeter of each figure below. The arrows mean that the lines are parallel. The slashes mean that the lines are equal in length. As you find each perimeter, be sure to show your work.
1-22.
1. For each shape drawn above, choose one of the labels below that best describes that shape. Be as specific as you can.
right triangle / scalene triangle / obtuse triangleisosceles triangle / rhombus / rectangle
Square / trapezoid / hexagon
1-23. Use the bar graph below to answer the following questions.
1. How many people attended the fair on Tuesday?
2. Which day had the largest attendance?
3. What was the total attendance for the week?