Patterns and Algebra Patterns
During small group instruction, a kindergarten teacher shows students a necklace with alternating red and blue beads. She asks students to share what they notice about the necklace. In this scenario, the teacher is most likely trying to promote:
an understanding of patterns. Option c is the correct answer.Explanation: The teacher used a necklace with an alternating pattern, therefore she is trying to encourage students to recognize and understand the pattern.
A preschool class works together with teacher guidance to separate various toys into three groups: small toys, medium toys, and large toys. Which of the following skills are students working on during this activity?
classifying objects Option a is the correct answer.Explanation: Students are working on classifying toys based on their size.
Mrs. Janie asked her class to write their own geometric sequence. As she walked around the room, she noticed Brad had 3,6,2,4,43,83,...3,6,2,4,34,38,...written on his paper. When Mrs. Janie asked Brad to explain his sequence, he replied, "My sequence is a geometric sequence because you multiply by 22, then multiply by 1331, then you multiply by 22 again, then multiply by 1331 again and so on." What is the best teacher response to Brad's statement?
"Your reasoning has an error. In order for a sequence to be a geometric sequence, you must multiply by the same common ratio each time. You can not use two different ratios." Option a is the correct answer.Explanation: This is correct, you must multiply by the same common ratio each time to calculate the next term in the sequence. Brad created a complex sequence.
If this pattern continues, the figure that comes next will have:
13 dots Option a is the correct answer.Explanation: The pattern adds 3 dots each time, starting with 4 dots. So, the next figure would have (4, 7, 10,....) 13 dots.
If the pattern below is continued, how many blocks will be in the 7th term?
36 Option d is the correct answer.Explanation: The first model is made with three blocks, 1 in column 1, and 2 in column 2; the second term is made of 1 block in column 1, 2 blocks in column 2, and 3 blocks in column 3. So, term #1 = 1 + 2 blocks; term #2 = 1 + 2 + 3 blocks; term #3 = 1 + 2 + 3 + 4 blocks. Each term, n, is the sum of the numbers from 1 to (n + 1); the sum of the consecutive integers from 1 to (n + 1). So, the 7th term would be: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 or 36 blocks. This is a small enough number that you could actually sketch the model and count the blocks.
What type of sequence is the following number sequence? 4, 12, 20, 28, 36, 44...
It is an arithmetic sequence; you add 8 every time to get the next term. Option b is the correct answer.Explanation: Arithmetic sequences have a common difference. This sequence has a common difference of 8 (12-4=8; 30-12=8; 28-20=8;36-28=8; 44-36=8).
A teacher gives the following scenario to her students and says, "After reading the prompt carefully, do your best to find an answer to the problem and use either symbols or words to describe the pattern." Which of the following math skills is the teacher working to develop? In the springtime, birds lay eggs in their nests, and Rakeem starts to find nests in his trees. The first nest has 5 eggs. Each nest after that has two more eggs than the last nest. How many total bird eggs will be in the 7th nest?
explaining and predicting addition sequences Option b is the correct answer.Explanation: The first nest has 5 eggs. Each subsequent nest has two more than the nest before it: the next one has 7, then 9, 11, 13, 15, etc. This scenario creates an addition sequence where each term is adding 2 to the previous term
Students are learning about adding and subtracting negative numbers. Which of the following exercises would best promote student understanding of this concept?
providing a beginning number on a number line and prompting students with directional arrows to arrive at a mystery number Option b is the correct answer.Explanation: Using a number line to discover how positive and negative numbers are affected during addition and subtraction gives students a concrete way to learn the content.
Use the table below to answer the question that follows. Which of the following equations correctly models the relationship in the table?
y=3x−5 Option d is the correct answer.Explanation: This equation correctly models the relationship in the table. Anytime the x value in the table is substituted for the "x" variable in the equation, the y value in the table is the result of the equation. 10 = 3(5) - 5; 22 = 3(9) -
Kate is starting a new babysitting job in which she will make $7 per hour that she works. Currently, she owes her parents $15, which she will have to pay back from her earnings. Below is a table of the amount of money Kate has saved since starting her job. Which of the following equations could best be used to demonstrate the relationship between x and y?
y=7x−15 Option d is the correct answer.Explanation: This matches the values in the table. If Kate makes $7 per hour, this represents her slope. The $15 she owes her parents represents the y-intercept and is negative.
