Here is a list of the first ten multiples of 5:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

1. Circle the multiples of 10 in the list.

2. What do you notice about where the multiples of 10 are on the list?

3. Why do you think that is?

Find the value of each expression.

1. \(14 \times 7\)
2. \(13 \times 6\)
3. \(23 \times 4\)
4. \(85 \div 5\)

There are 418 students at Jada’s school. There are 135 fewer students at Noah’s school. How many students are there at Jada’s and Noah’s schools together? Explain or show your reasoning.

1. What is the value of the digit 6 in each of the numbers?

   • 165

   • 18,622

   • 675,219

2. Complete this statement so that it is true:

   The value of the 6 in 675,219 is _______________ times that of the 6 in 165.

Find the value of each sum and difference.

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1. Mai follows a rule to create a pattern of square blocks. Her rule is to keep adding 1 square to the top of her L design and 1 square to the right. Sketch or describe the next 2 shapes in Mai’s pattern.

   

   pattern of square blocks. Step 1, 3 squares total, base of 2 squares, 1 square on top of the left square. Step 2, 5 squares total, base of 3 squares, 2 squares on top of the left square.

2. Will Mai's pattern ever use 20 squares? Explain your reasoning.

Diego types the letters a, s, d, f and then repeats them in that order, over and over.

1. What is the 5th letter Diego will type? What about the 10th? The 20th?

2. Diego numbers each letter he types, starting with 1 for the first a. What are the numbers given to the first 6 f’s in his pattern? 

3. What do you notice about the numbers for the f's?

The rule for a pattern is “start with 25, keep adding 25.”

1. Complete the table with the first 8 numbers of the pattern.
2. What do you notice about the numbers in the pattern? Explain or show why you think it happens.
3. Could 475 be a number in this pattern? Explain or show your reasoning.

1. Make a list of the multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10. Stop when you get a multiple of 10. For example, for 2, the list is 2, 4, 6, 8, 10.
2. What do you notice about your lists? Make some observations.

Tyler draws this picture and writes the equation \(1 + 3 + 5 = 9\).

1. How do you think the equation relates to the picture?
2. Tyler keeps drawing circles to make larger squares. How many new circles does he need to draw to make a 4-by-4 square, and then a 5-by-5 square?
3. What pattern do you notice in the number of circles Tyler adds in each step?
4. Why do you think the number of circles is increasing that way?

Here is a growing pattern of squares that makes rectangles. The pattern follows the rule "keep adding 1 square to the row."

pattern of rectangles. Step 1, rectangle partitioned into 2 squares. Step 2, rectangle partitioned into 3 squares. Step 3, rectangle partitioned into 4 squares.

1. Find the area and perimeter of the rectangles in steps 2 and 3.

   step	number of squares	area of rectangle (square units)	perimeter of rectangle (units)
   1	2	2	6
   2
   3

2. What do you notice when you look at the numbers in the chart? Use what you notice to complete the chart for steps 4 and 5.

3. Draw the next two diagrams (for steps 4 and 5). Were your predictions for the area and perimeter of each rectangle correct?

4. How would you describe what you noticed about this pattern to a classmate?

Mai and Tyler make their own pattern. Mai's pattern repeats @, #, and $. Tyler's pattern repeats ~ and @.

Some of their pattern symbols are the same, some are different. The table shows the first 6 symbols in Mai’s pattern and the first 4 in Tyler’s pattern.

1. Complete the table with the next symbols in each pattern.
2. At what step do you think Mai and Tyler will draw the same symbol at the same time? Explain how you know.