Study Guide

field 305: elementary education left paren grades 1 to 6 right paren 
Sample Multiple-Choice Questions

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Each multiple-choice question has four answer choices. Read each question and its answer choices carefully and choose the ONE best answer.

During the test you should try to answer all questions. Even if you are unsure of an answer, it is better to guess than not to answer a question at all. You will NOT be penalized for choosing an incorrect response.

Objective 0001 
Understand foundations of research-based literacy instruction and assessment and apply knowledge of emergent literacy development.

1. The Illinois Learning Standards for English Language Arts and Literacy include teaching students at the fourth-grade level how to use context, Greek and Latin roots, and reference materials to promote vocabulary acquisition. Which of the following statements best explains how these strategies contribute to students' overall reading development and will help them develop college and career readiness in vocabulary?

  1. Students need to develop a variety of independent word-learning strategies to deal with the volume of new words they will encounter in wide reading.
  2. Students need to develop an awareness of new words they may encounter in their reading so that they will be able to retain them effectively in the future.
  3. Students need to develop an ability to spell and properly pronounce words that they may need to apply in their future speaking and writing endeavors.
  4. Students need to develop knowledge of a range of discipline-specific words so that they are prepared to study a variety of fields or to pursue different careers.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
Contextual analysis, structural analysis, and the use of reference materials are all powerful word-learning strategies. Students will encounter thousands of unfamiliar vocabulary words throughout their school years and beyond. To achieve academically across the curriculum and communicate effectively in their future careers, students need to be able to both comprehend and use these words effectively. Time constraints make it impossible for teachers to explicitly teach students every grade-level academic word they need to know, let alone all the words they will need in the future. Therefore, to ensure that students are college and career ready, teachers must help students develop a repertoire of strategies for determining the meaning of unfamiliar vocabulary they will encounter across the curriculum and beyond the classroom.

Objective 0001 
Understand foundations of research-based literacy instruction and assessment and apply knowledge of emergent literacy development.

2. A first-grade teacher is working with a small group of emergent readers and would like to promote their ability to identify the final consonant sound in spoken words. Which of the following student activities would best promote achievement of this goal?

  1. writing all the words they know that end in the same final sound and reading the words aloud
  2. circling the last letter of each word on a list of grade-level words and saying the letter's name aloud
  3. saying aloud the words depicted on picture cards and sorting the cards by the last sound in each word
  4. reading a simple grade-level poem aloud and segmenting the onsets and rimes of the final word in each line
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
To identify final consonant sounds in spoken words, the students need to be able to isolate, or segment, those sounds. In the picture sorting activity described, the teacher is having students isolate the final consonant sound of each pictured word, thereby providing the students with practice in phonemic segmentation and final sound identification. In order to sort each card accurately, the student must focus on the final sound of the word represented by the picture. The use of picture (word) sorts for developing and practicing phonemic awareness skills is a best practice with emergent readers because it promotes learning through multiple modalities. Students see the picture, say the name of the pictured word, and must listen carefully to its sounds. Then they physically sort the cards by sound categories (e.g., the last sound in the word).

Objective 0002 
Apply knowledge of decoding and fluency development.

3. Which of the following sets of words would be most appropriate to use for assessing third-grade students' ability to use structural analysis skills to decode words?

  1. closed, living, held
  2. contestant, logically, correlation
  3. bunnies, cities, animals
  4. unhappy, daytime, noiseless
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: D.
Structural analysis (sometimes called morphemic analysis) is the analysis of the meaning-bearing elements (i.e., morphemes) in a word to help determine the word's pronunciation and meaning. Unhappy, daytime, and noiseless are all words that can be divided easily into meaningful parts, or morphemes, and are also words that are appropriate to use as example words with third-grade students. The word unhappy can be divided into two component morphemes—the prefix un- (meaning "not") and the root word happy. The word noiseless can also be divided into two component morphemes—the suffix -less (meaning "without") and the root word noise. The word daytime is a compound word, which is a word that consists of (usually two) component morphemes, each of which is a word (i.e., day and time). Students' ability to divide words into morphemes and to analyze the meaning of the morphemes in order to determine a word's overall meaning is helpful in supporting their decoding skills, fluency, vocabulary development, and comprehension. Proficiency in this type of analytic skill is a third-grade expectation according to the Illinois Learning Standards for English Language Arts and Literacy: Foundational Skills .

Objective 0003 
Apply knowledge of development in vocabulary, academic language, and reading comprehension.

4. A fifth-grade teacher periodically has students analyze short science and social studies passages that are written at or slightly above grade level. First, the teacher underlines key words, phrases, and sentences on copies of the text. The teacher then has pairs of students read the passage and ask each other clarifying questions about the underlined elements. Finally, the students paraphrase each of the underlined elements in their own words and use these to construct a written summary of the passage. These activities best demonstrate the teacher's awareness of which of the following factors affecting reading development?

  1. the benefits of guided practice in reinforcing students' word-learning strategies
  2. the role of academic language in supporting students' comprehension of complex texts
  3. the influence of prior language experiences on students' reading comprehension
  4. the importance of selecting texts for students according to multiple dimensions of text complexity
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
In order to be able to comprehend and learn from increasingly complex content-area texts, students must be able to understand academic language (i.e., the vocabulary and language structures used in oral and written academic discourse). Since most students do not encounter academic language often in everyday speech, they need repeated exposure to and opportunities to use academic language in various contexts in class. In the scenario described, the teacher has students use close-reading strategies (e.g., asking clarifying questions, paraphrasing) with challenging passages to provide them with practice constructing meaning from complex text, with the final product being a written summary of the passage. By breaking down the summarization task into different steps, the activity scaffolds students' ability to deconstruct and clarify the meaning of complex words, phrases, and sentences in an academic passage in order to make meaning of the passage.

Objective 0003 
Apply knowledge of development in vocabulary, academic language, and reading comprehension.

5. A sixth-grade English language learner has grade-level literacy skills in Spanish and grade-level fluency skills in English, but the student struggles to comprehend academic texts in English. In an intervention designed to address the student's reading-comprehension difficulties in English, which of the following strategies would be most important for the teacher to focus on first?

  1. developing the student's familiarity with common text structures used in English academic texts
  2. promoting the student's ability to use a cognate strategy to understand academic vocabulary in English
  3. providing the student with systematic, explicit instruction in phonics and other decoding strategies in English
  4. helping the student relate new content encountered in academic texts to the content of texts previously read in English
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
studies show that unless students know 85 to 95 percent of the words in a text they are reading, their comprehension will be compromised. Therefore, it is important to provide explicit vocabulary instruction to English language learners to promote their reading comprehension. Cognates are words in two languages that share common historical roots and that therefore have retained similar spellings and meanings. because of the strong influence of latin and french on the development of english, a little over 80 percent of the words found on academic word lists in english have latin or greek origins. Logically, this means that most of these words have Spanish cognates, as Spanish is descended from Latin and also shares many of the same borrowed words from Greek. Therefore, a sixth-grade English language learner who has grade-level literacy skills in Spanish would significantly improve his/her English academic vocabulary and comprehension of English academic texts by being taught to look for cognates in the texts. In addition, the teacher's assistance with cognate recognition will promote the student's awareness of connections between the two languages (i.e., positive language transfer), thereby supporting the student's application of background knowledge to his/her reading in English.

Objective 0004 
Apply knowledge of skills and approaches for developing comprehension and analysis of literary and informational texts.

6. Read the passage below; then answer the question that follows.

Before students begin reading an informational article about penguins, a teacher conducts a think-aloud while scanning the article. The teacher's think-aloud appears below.

The title of this article tells me that I'm going to read about penguins. I've seen cartoons about penguins, and we read the book Mr. Popper's Penguins in class. Those were funny stories, but they weren't about real penguins. I think this article is going to be about real penguins because I see photographs of real penguins. There are captions under the photographs. If I read the captions, I can probably find out the names of the penguins in the photographs. That way when I read about different kinds of penguins in the article, I'll be able to see what they look like. I also see a chart. It has drawings of 17 species of penguins. Wow! I didn't know there were so many kinds of penguins! The chart tells where each type of penguin lives. I can look at the chart while I'm reading the article.

The teacher's approach will promote students' learning primarily by:

  1. motivating students to conduct research on a topic related to penguins.
  2. promoting students' ability to analyze how graphic features relate to the article.
  3. activating students' background knowledge about types of penguins.
  4. familiarizing students with general academic and domain-specific vocabulary.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
The teacher's purpose for using a think-aloud strategy is to reveal to students the thought process behind completing a comprehension task. By verbalizing this thought process, the teacher demonstrates how students can use graphic features to support and supplement information provided in the text of the article. The think-aloud will promote students' ability to understand how each text feature relates to the article, as well as their ability to use the text features to support comprehension.

Objective 0005 
Apply knowledge of writing development and the writing process.

7. Read the draft paragraph below from a student's informative essay; then answer the question that follows.

1Kites were probably invented in China during the fifth century. 2The first known kites were made of a bamboo frame covered with silk or paper. 3They were usually flat rectangles, and unlike modern kites, they did not have tails. 4  blank  5People used kites to measure distances, to test the wind, and to communicate. 6There is an ancient Chinese story about a Chinese emperor who used a kite to send a message for help when he was trapped by rebel soldiers. 7Some kites could actually carry warriors into the air and over enemy territory.

Which of the following sentences, if inserted as Sentence 4, would most effectively support a logical development of ideas in the paragraph?

  1. In some countries, making and flying kites is an art.
  2. Early South Sea Islanders attached fishing nets to kites.
  3. Early kites were made to fulfill practical purposes.
  4. Kites have been used to learn about aerodynamics.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
The paragraph focuses on the history of kites. To effectively support a logical development of ideas in the paragraph, Sentence 4 should provide a logical transition between the physical description of the first kites in Sentences 2 and 3 and the examples of how early kites were used that follow in Sentences 5, 6, and 7. The sentence "Early kites were made to fulfill practical purposes" provides such a transition by showing the connection between how kites were made and how they were used.

Objective 0005 
Apply knowledge of writing development and the writing process.

8. With the goal of guiding students' revision of their writing, a teacher wants to provide meaningful feedback on students' first drafts during one-on-one conferences. Which of the following approaches would be most effective for the teacher to use to achieve this goal?

  1. highlighting text that needs extensive revision and asking students to describe how they plan to rewrite the highlighted text
  2. identifying errors in grammar and mechanics and showing students examples of correct usage of standard writing conventions
  3. using academic language and domain-specific terms when discussing students' drafts and evaluating students' writing performance
  4. commenting on a draft's strengths before making explicit suggestions for improving the draft to meet specific criteria
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: D.
Feedback is most constructive when it is explicit and timely. Explicit feedback should be based on clear criteria, such as those in a writing rubric, and should indicate how close students have come to meeting that criteria. Explicit feedback should include specific details about what students need to do to meet the next level of performance (e.g., use transitional words or expressions to clarify relationships between ideas, add sensory details to make descriptions more vivid, vary sentence structure to increase readers' interest). By offering explicit feedback between the draft and revision stages and by basing that feedback on a rubric, the teacher can successfully provide students with the opportunity and guidance they need to revise their writing.

Objective 0006 
Apply knowledge of the development of speaking and listening skills.

9. A first-grade teacher has invited a naturalist from a local wildlife center to give a presentation on migratory birds to the class. The teacher is concerned that students may have difficulty sustaining attention during the presentation due to their unfamiliarity with the topic. In advance of the presentation, the teacher leads a class discussion to determine what students already know about migratory birds and then reads aloud from a recent newspaper article on the topic. Which of the following additional steps by the teacher would be most effective for promoting students' active listening during the presentation?

  1. preteaching challenging vocabulary that is relevant to the topic
  2. reminding students of established guidelines for polite listening
  3. displaying colorful photographs of migratory birds in the classroom
  4. showing students the presentation outline provided by the speaker
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
The teacher prepares students for the presentation by helping them relate new knowledge to previous knowledge. By pre-teaching challenging vocabulary that is relevant to the presentation topic, the teacher provides students with additional relevant background knowledge. Students can then apply their newly acquired knowledge of domain-specific vocabulary to enhance comprehension during the presentation.

Objective 0006 
Apply knowledge of the development of speaking and listening skills.

10. Read the transcript of a student's oral book report below; then answer the question that follows.

What is your favorite food? If it's pizza, you should read this book. You probably know that pizza is from Italy. But did you know that kings and queens used to eat it? This book is full of interesting facts. They used to eat it with mozzarella cheese and red tomatoes just like we do now. When people from Italy came to live in the United States they missed pizza. That's why we have pizza in the United States. This book will make you hungry. It even has recipes. You can learn how to toss pizza dough in the air and spin it around.

Given the evidence presented, the student needs instructional support in which of the following oral presentation skills?

  1. engaging the audience
  2. sequencing ideas logically
  3. expressing opinions clearly
  4. using precise language
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
The student's oral book report engages the audience by asking questions ("What is your favorite food?" "But did you know that kings and queens used to eat it?"). The student's opinions are clearly expressed ("If it's pizza, you should read this book," "This book is full of interesting facts," "This book will make you hungry"), and the student uses precise language ("mozzarella cheese," "red tomatoes," "toss," "spin"). However, the student needs instructional support with sequencing ideas logically. By re-sequencing and adding sentences, as well as by adding appropriate transitional words and phrases, the student can better organize ideas and clarify the relationships between them.

Objective 0007 
Apply knowledge of college algebra and statistics.

11. Which of the following graphs could represent the polynomial equation  y equals the quantity x plus y times the quantity x plus 5 times the quantity x minus 2? 

Each response is a Cartesian graph with a single data line. The x axis is labeled from negative 10 to 10 in increments of 1, and the y axis is labeled from negative 60 to 50 in increments of 10.

  1. the data line begins in the lower left quadrant and curves almost vertically up to 30 on the y axis, where it reverses and curves down through 3 on the x axis. at the level of about negative 5 on the y axis, it reverses direction to curve up through 5 on the x axis and continue almost vertically up through the upper right quadrant.

  2. the data line begins in the lower left quadrant and curves almost vertically up through negative 5 on the x axis. at the level of about 5 on the y axis, it reverses direction to curve down through negative 3 on the x axis. at negative 30 on the y axis, it reverses direction to curve up through 2 on the x axis and continue almost vertically up through the upper right quadrant.

  3. the data line begins in the upper left quadrant and curves almost vertically down through negative 5 on the x axis. at the level of about negative 5 on the y axis, it reverses direction to curve up through negative 3 on the x axis. at 30 on the y axis, it reverses direction to curve down through 2 on the x axis and continue almost vertically down through the lower right quadrant.

  4. the data line begins in the upper left quadrant and curves almost vertically down through negative 2 on the x axis to negative 30 on the y axis, where it reverses and curves up through 3 on the x axis. at the level of about 5 on the y axis, it reverses direction to curve down through 5 on the x axis and continue almost vertically down through the lower right quadrant.

Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
The equation y equals left paren x plus 3 right paren left paren x plus 5 right paren left paren x minus 2 right paren is the factored form of a third-degree polynomial function. The roots of a polynomial equation are the values of x that will make the value of y equal zero and show up on the graph as the x-intercepts. One method of solving for the roots of a polynomial equation is to factor the equation and then set each factor equal to zero. In the given question, the equation is already factored, and setting the individual factors equal to zero results in x plus 3 equals 0, so  x equals negative 3;   x plus 5 equals 0  so  x equals negative 5 semi  and  x minus 2 equals 0  so  x equals 2  The three roots are  x equals negative 3,   negative 5,  or 2, so the graph will cross the x-axis at the points  left paren negative 3 comma 0 right paren   left paren negative 5 comma 0 right paren  and  left paren 2 comma 0 right paren  While each graph represents a third-degree polynomial function, the only graph that has the correct x-intercepts is the one shown in response B.

Objective 0007 
Apply knowledge of college algebra and statistics.

12. A community health center conducted a survey to determine how long clerical staff had been in their current positions. The results reported a mean of 28 months, a median of 23 months, and an interquartile range of 14 months. Which of the following box plots could represent these data?

Each response is a box plot with tick marks in increments of 2, labeled from 0 to 50 in increments of 10.

  1. The minimum line is at 3, the left edge of the box is at 9, the line inside the box is at 23, the right edge of the box is at 37, and the maximum line is at 44.

  2. The minimum line is at 8, the left edge of the box is at 16, the line inside the box is at 28, the right edge of the box is at 42, and the maximum line is at 48.

  3. The minimum line is at 8, the left edge of the box is at 16, the line inside the box is at 23, the right edge of the box is at 30, and the maximum line is at 46.

  4. The minimum line is at 14, the left edge of the box is at 21, the line inside the box is at 28, the right edge of the box is at 35, and the maximum line is at 42.

Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
A box plot displays the median, upper quartile, lower quartile, minimum, and maximum as parts of the graph. The median, given to be 23 months, is true for either of the box plots shown in response A or C, as indicated by the vertical line displayed inside the box of each plot corresponding to the value of 23. To find the interquartile range, find the difference between the upper quartile and the lower quartile. The plot in response C has an upper quartile of 30, as indicated by the vertical line displayed on the right side of the box corresponding to the value of 30, and a lower quartile of 16, displayed as a vertical line on the left side of the box corresponding to the value of 16. The difference between these two values is  30 minus 16,  or 14. The box plot that could represent this data set is shown in response C.

Objective 0008 
Apply knowledge of the mathematics curriculum and strategies for teaching counting and cardinality, numbers, and operations in base ten.

13. Use the problem and student work below to answer the question that follows.

Problem: 
A school is planning an assembly for the last day of the school year. There are 100 fourth graders in the school. The principal has arranged the chairs in the auditorium into rows of eight. How many rows does the principal need to save to seat all the fourth graders?

Student work:

100 divided by 8 equals blank 12 times 8 equals 96 100 minus 96 equals 4 The principal has to save 12 rows.

Which of the following statements is the best evaluation of the student's work?

  1. The student's answer is incorrect and the work shows a misunderstanding of how to interpret the remainder in a real-world problem.
  2. The student's answer is incorrect and the work shows a misunderstanding of how to perform the common division algorithm.
  3. The student's answer is correct and the work shows an understanding of the relationship between division and multiplication.
  4. The student's answer is correct and the work shows an understanding of how to model division problems using repeated subtraction.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
This problem requires the candidate to divide the total number of fourth graders by the number of chairs per row. All the fourth graders need to be seated so any remainder will require a new row of chairs. The student chose the correct operation to solve the problem by dividing 100 by 8, and correctly checked that 12 times 8, or 96, is the closest multiple of 8 to 100. However, the student's answer of 12 rows is incorrect because the remainder of 4 represents 4 fourth graders who will need chairs. The principal needs to have 12 rows of 8, plus 4 more chairs, or 13 rows in all. The student's response indicates that he or she has a misunderstanding of the meaning of the remainder in the context of this problem.

Objective 0008 
Apply knowledge of the mathematics curriculum and strategies for teaching counting and cardinality, numbers, and operations in base ten.

14. Use the problem and student work below to answer the question that follows.

Problem: 
A third grader wants to read 95 pages by the end of the week. The student has already read 37 pages. How many pages does the student have left to read?

Student work:
37 plus 3 equals 40
40 plus 50 equals 90
90 plus 5 equals 95
So the student has 58 pages left to read.

A third-grade teacher asks students to solve story problems and explain the solutions. One student's solution method is displayed. The teacher wants to ensure that all students, including English language learners, understand the language of the problem, and plans to present and explain a visual model that best represents the strategy employed by this student. Which of the following visual models would be most appropriate for the teacher to use?

  1. the model uses a number line. an arched arrow labeled 3 points from 37 to 40. the next arched arrow, labeled 50, points from 40 to 90. the last arched arrow, labeled 5, points from 90 to 95.

  2. the model uses three equations: 37 plus blank equals 95, 37 plus 3 plus 50 plus 5 equals 95, and 37 plus 58 equals 95.

  3. the model uses columns of squares. there are 9 columns with 10 squares each and one column of 5 squares. the first 3 columns plus 7 squares of the next column are white, while the remaining squares are shaded. a large x has been drawn over the shaded squares.

  4. the model uses a number grid. the first row is labeled 1 through 10, the second 11 through 20, and so forth to the bottom row, which is labeled 91 through 100. exes have been drawn through all the numbers from 59 to 95.

Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
The student is using a counting on method to find the difference between 95 and 37. First the student counts up to the nearest multiple of ten from 37 to get to 40, then counts up a group of tens to get to 90. Lastly, the student counts up from 90 to 95. The number line model shows the same procedure, starting at 37 and jumping up to 40, then jumping forward by tens to 90, and last jumping up to 95. The arrows above the number line indicate how much each jump is worth and summing the arrow values gives the difference between 95 and 37, which is the number of pages the student has left to read. The number line shown in response A best models this strategy.

Objective 0009 
Apply knowledge of properties of numbers and operations involving fractions and strategies for teaching these concepts to students.

15. Use the diagram below to answer the question that follows.

The diagram shows a row of 6 squares. The first 4 squares are collectively labeled 1 whole.

A teacher uses a tape diagram during a lesson on fractions. If the labeled section on the diagram represents 1 whole, which of the following number bonds (addition facts) best matches the tape diagram?

Each response is a bond diagram showing a central number and a set of smaller numbers that add together to equal the central number.

  1. the central number is 6 sixths. the smaller numbers are 4 sixths and 2 sixths.

  2. the central number is 4 sixths. the smaller numbers are 1 sixth, 1 sixth, 1 sixth, and 1 sixth.

  3. the central number is 6 fourths. the smaller numbers are 4 fourths and 2 fourths.

  4. the central number is 1. the smaller numbers are 1 fourth, 1 fourth, 1 fourth, 1 fourth, 1 fourth, and 1 fourth.

Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
In the tape diagram shown, the whole is labeled as four sections of the tape, so each section is one-fourth. The entire tape diagram is made up of 6 of those sections,  four fourths  and  two fourths  resulting in the improper fraction  six fourths.  A bond diagram is a representation of the part-part-whole relationship of a number showing how smaller numbers make up a larger number. The bond diagram in response C models the fraction  six fourths  as the sum of  four fourths  and ,  two fourths  which matches the tape diagram.

Objective 0009 
Apply knowledge of properties of numbers and operations involving fractions and strategies for teaching these concepts to students.

16. Use the student work below to answer the question that follows.

student work: 2.5 times .3 equals 7.5

A student multiplies two decimals as shown. Which of the following approaches would most likely help the student gain understanding of where to correctly position the decimal point when finding the product of two decimals?

  1. writing out step-by-step instructions for multiplying decimals
  2. converting the decimals to their fraction equivalents and then multiplying the fractions
  3. creating a word problem to model decimal multiplication
  4. using a calculator to multiply pairs of decimals and recording all the results in a table
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
The student incorrectly placed the decimal point so that it lined up with the decimal points in the numbers used in the multiplication. Converting the decimals to their fraction equivalents would allow the student to get the correct result using prior knowledge of how to multiply fractions. The fraction product of 25 tenths times 3 tenths equals 75 hundredths allows the student to understand why the result should be the decimal value of 75 hundredths, or 0.75.

Objective 0010 
Apply knowledge of operations and algebraic thinking and strategies for teaching these concepts to students.

17. A student needs to find the greatest common factor of 12 and 18 to solve a word problem. Which of the following models of student work shows a valid method for finding this greatest common factor?

  1. the model is a venn diagram. the left circle is labeled 12, and the right circle is labeled 18. the left circle contains the number 2. the right circle contains the number 3. the intersection contains the numbers 2 and 3. beneath the diagram is written gcf equals 2 times 2 times 3 times 3.

  2. the model shows the equation 18 minus 12 equals 6. beneath the equation is written gcf equals 2 times 3.

  3. the model shows the factors of the 2 numbers. the first line is 12 equals 2 times 2 times 3. the second line is 18 equals 2 times 3 times 3. the 2 and the first 3 on the second line are vertically aligned with the second 2 and the 3 on the first line. vertical arrows are drawn through the aligned numbers, pointing down to the 2 and the 3 on the next line of text, which is gcf equals 2 times 3.

  4. the model shows sets of multiples of the 2 numbers. the first line is 12, 24, 36, 48, dot, dot, dot. the second line is 18, 36, 54, 72, dot, dot, dot. the 36 in each line is circled, and a line connects the 2 circles. the final line is gcf equals 36.

Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
The greatest common factor of a pair of numbers is the largest whole number value that is a factor of both numbers. One method of finding the greatest common factor is to do the prime factorization of both numbers and find the product of the prime factors that the two numbers have in common. The prime factorization of 12 is 2 times 2 times 3 and of 18 is 2 times 3 times 3. The prime factors that 12 and 18 have in common are 2 and 3 so the greatest common factor is 6.

Objective 0011 
Apply knowledge of measurement and data and strategies for teaching these concepts to students.

18. Use the stem-and-leaf plot below to answer the question that follows.

Test Scores
Stem Leaf
2 2 5
3 cell intentionally left blank
4 3
5 1 8
6 5
7 3 5
8 2 6
9 4
10 0 0
Test Scores Key
Key
2/5 means 25

What is the median for the set of test scores shown?

  1. 65
  2. 68
  3. 73
  4. 78
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
To find the median of a data set, locate the value in the middle of the data set when all the values are arranged in numerical order. This stem and leaf plot has tens digits as the stems in the left hand column and ones digits as the leaves in the right hand column, as indicated by the key at the bottom. In a stem and leaf plot the values are already ordered. There are 13 test scores shown in this stem and leaf plot, so the middle value will be in the seventh position. The seventh value in the list is 73.

Objective 0011 
Apply knowledge of measurement and data and strategies for teaching these concepts to students.

19. Use the diagram below to answer the question that follows.

The diagram is a spinner divided into three equal parts, labeled red, green, and blue.

A spinner is divided into thirds and each third is shaded a different color, as shown in the diagram. If the radius of the spinner is 6 inches, what is the perimeter of the green section of the spinner?

  1. 16 pi
  2. 22 pi
  3. 4 pi plus 12
  4. 12 pi plus 12
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
The green section of the spinner has three edges, the curved edge that is one third the circumference of the circle and two straight edges that are each equal to the radius of the circle. To find the circumference of a circle, multiply the diameter of the circle by pi. This spinner has diameter of 12 inches so the circumference of this spinner is 12 pi. One third of that is 12 pi over 3 equals 4 pi. The radius of the spinner is 6 inches so the perimeter of the green section is 4 pi plus 6 plus 6 equals 4 pi plus 12

Objective 0012 
Apply knowledge of geometry and strategies for teaching geometry concepts to students.

20. Use the diagram below to answer the question that follows.

The diagram shows 4 lines that intersect to form a 4 sided interior shape. From top to bottom, one line has points A, B, C, and D. From top to bottom, the opposite line has points E, F, G, and H. A third line passes through points B and F. The fourth line passes through points C and G.

The diagram shows a sketch of the relative positions of four lines on a plane. If angle FBC is congruent to angle DCG, then which of the following statements must be true?

  1. Line B C is parallel to line F G.
  2. Line B F is perpendicular to line C B.
  3. Line C G is parallel to line B F.
  4. Line F G is perpendicular to line C G.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
Corresponding angles are formed when a transversal passes through two lines. The angles that are in the same position in terms of the transversal are called corresponding angles. Two lines are parallel if the corresponding angles formed by the transversal passing through them are congruent. Angles F B C and D C G are corresponding angles for the two lines C G and B F with transversal A D. Line C G is parallel to line B F.

Objective 0013 
Understand the interrelationships among science, technology, and society.

21. Which of the following activities is most likely to promote students' understanding of the concept of cause and effect in science?

  1. using leaves and a taxonomic key to identify the types of trees present near the school
  2. recording the time it takes for bean seeds to germinate when given different amounts of water
  3. creating cross-sectional models of the Earth with clay to illustrate the thicknesses of different layers
  4. tracking the daily high and low temperatures of two nearby cities during a three month period
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
A cause and effect relationship is a relationship in which one event results in the occurrence of another event. The only response option that addresses this type of relationship is the activity in which bean seeds are given different amounts of water (event 1) and students record the amount of time it takes for the seeds to germinate (event 2).

Objective 0013 
Understand the interrelationships among science, technology, and society.

22. A second grade teacher is planning to read a book to the class as a way of introducing students to the variety of geographic features on Earth's surface. Which of the following types of books is likely to be most effective in stimulating students' interest in the subject matter?

  1. a book that explains the role of plate tectonics in the formation of mountains
  2. a biography of one of the first people to reach the summit of Mount Everest
  3. a book about a migrating bird that describes how the land below changes during its journey
  4. a field guide that describes the characteristics of mountains, canyons, deserts, and waterways
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
The book about the migrating bird would be most effective in stimulating the interest of second graders in the different geographic features of Earth's surface. The story would build students' background knowledge of the subject and their vocabulary in an engaging way. It also would help students make connections between geographic features they are familiar with and those found in other parts of the world.

Objective 0014 
Understand the use of scientific investigations and inquiry skills and apply principles and procedures, including safety practices, related to the design and implementation of scientific investigations.

23. Fourth-grade students have planted a garden at their school and find signs that an animal has eaten some of their vegetables. The students offer several ideas about what happened to their growing crops. Which of the following student statements represents a reasoned argument rather than a speculation?

  1. "Deer tracks are in the garden; deer likely ate our crops."
  2. "I saw a raccoon on the street earlier this week; a raccoon likely ate our crops."
  3. "A dog from a nearby house is allowed to run off leash; the dog likely ate our crops."
  4. "I read that rabbits like to eat vegetables; a rabbit likely ate our crops."
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
Unlike speculation, reasoned arguments are supported by evidence. The response implicating the deer as the cause of the disappearance of the garden vegetables is the only argument that is supported by observable evidence: the presence of deer tracks in the garden.

Objective 0015 
Understand the fundamental concepts, principles, and interconnections of the life sciences, the physical sciences, and Earth and space sciences.

24. Which of the following processes illustrates a conversion of potential energy to kinetic energy?

  1. the wind spins a turbine that is used to produce electricity
  2. the heat from an oven burner is transferred to the handle of a saucepan
  3. a green plant uses light from the sun to synthesize glucose
  4. a rock sitting at the top of a hill is dislodged and begins to roll downward
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: D.
Potential energy may be thought of as stored energy or energy that is associated with the position of an object. Kinetic energy is energy that is associated with motion. The stored energy in the rock (potential energy) is converted to energy of motion (kinetic energy) as the rock begins to roll downward from the top of the hill.

Objective 0015 
Understand the fundamental concepts, principles, and interconnections of the life sciences, the physical sciences, and Earth and space sciences.

25. Students in a third grade class are using weather journals to collect and record temperature data for a variety of locations within Illinois, including Chicago. Students notice that in the fall and early winter average temperatures in Chicago are not as cold as those in the outlying cities. This geographic difference in temperature is best explained by:

  1. the seasonal effect of the polar jet stream in Illinois.
  2. the high specific heat capacity of the water of Lake Michigan.
  3. the increased exposure to solar energy associated with Chicago's latitudinal location.
  4. the decrease in elevation associated with land along the shores of Lake Michigan.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
Large bodies of water, like Lake Michigan, absorb heat and release heat at a slower rate than the surrounding land and air. This is due to the high specific heat capacity of water. As a result, locations near the lake are typically cooler in the summer and warmer in the fall and early winter before the lake freezes.

Objective 0016 
Understand the structures and functions of government; the rights and responsibilities of citizenship in the United States; and the skills, knowledge, and attitudes necessary for successful participation in civic life.

26. Which of the following excerpts from the Illinois Constitution would be most useful for an upper elementary teacher to use in examining with students the concept of due process?

  1. "The House of Representatives has the sole power to conduct legislative investigations to determine the existence of cause for impeachment and, by the vote of a majority of the members elected, to impeach Executive and Judicial officers."1
  2. "The recall of the Governor may be proposed by a petition signed by a number of electors equal in number to at least 15 percent of the total votes cast for governor in the preceding gubernatorial election, with at least 100 signatures from each of at least 25 separate counties.… not more than 150 days after an affidavit has been filed with the State Board of Elections…"1
  3. "No person shall be denied the right to register to vote or to cast a ballot in an election based on race, color, ethnicity, status as a member of a language minority, national origin, religion, sex, sexual orientation, or income."1
  4. "In criminal prosecutions, the accused shall have the right to appear and defend in person and by counsel; to demand the nature and cause of the accusation and have a copy thereof; to be confronted with the witnesses against him or her and... to compel the attendance of witnesses in his or her behalf; and to have a speedy public trial..."1
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: D.
Due process is defined as the constitutional guarantee that no person may be deprived of life, liberty, or property without fair legal proceedings. According to due process requirements, individuals must be given notice of legal proceedings and the opportunity to defend themselves and confront their accusers.

Objective 0017 
Understand the interrelationships of economic and political principles, concepts, and systems and their relationship to historical and contemporary developments in Illinois, the United States, and the world.

27. Proponents of  U S  trade agreements such as the North American Free Trade Agreement left paren N A F T A right paren are most likely to cite which of the following benefits as a reason for their support?

  1. lower consumer prices
  2. reduced competition for businesses
  3. lower cost of production resources
  4. reduced regulatory burdens
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
Trade agreements between the United States and other countries are designed to encourage free trade by reducing or eliminating tariffs, quotas, and other governmental limitations on trade. Free trade allows each country to specialize in goods it can produce more efficiently and cheaply and without added costs from tariffs, all of which are likely to result in lower prices for consumers.

Objective 0017 
Understand the interrelationships of economic and political principles, concepts, and systems and their relationship to historical and contemporary developments in Illinois, the United States, and the world.

28. An upper elementary teacher is preparing a series of lessons on the Voting Rights Act of 1965 and the legal barriers to voting confronting African Americans before this legislation was enacted. Which of the following student activities would likely be most useful for deepening students' understanding of the meaning and significance of the Voting Rights Act?

  1. researching social, economic, and other differences between northern and southern states at the time the legislation passed
  2. reading and discussing excerpts from speeches and writing by individuals who fought for the legislation
  3. using age-appropriate resources to write an account of the steps and procedures that were used to draft and pass the legislation
  4. reviewing and analyzing those sections of the  U S  Constitution that are most relevant to the legislation
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: B.
Primary sources and eye-witness accounts are valuable sources of information about the perspectives, goals, and experiences of individuals involved in a historical event or era. The speeches and writings of people engaged in the debate over the Voting Rights Act of 1965 can provide a unique perspective on the issues that led to the creation of the act, the struggles involved in its passage, and the personal and social circumstances that influenced the individuals who supported it.

Objective 0018 
Understand major principles, concepts, and phenomena of geography, sociology, and culture and the interrelationships between people and their environment.

29. Which of the following geographic questions focuses on a formal region rather than a functional or perceptual region?

  1. What patterns are evident in the distribution of ethnic groups within the city of Chicago, Illinois?
  2. How is the movement of a train station from one suburban town in Illinois to another expected to affect the two towns?
  3. In what areas of the Sunbelt have populations increased most rapidly over the past three decades?
  4. How did the natural resources found in various areas of the Midwestern United States influence the development of local economies?
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: A.
Formal regions are defined by the presence of shared traits that are found throughout the area and that distinguish them from surrounding areas. Examples include countries, states, and cities. The city of Chicago is a precisely bounded formal region defined by its uniformity of law and administration. The question in response A addresses information relevant to the area defined by that precise political boundary.

Objective 0018 
Understand major principles, concepts, and phenomena of geography, sociology, and culture and the interrelationships between people and their environment.

30. In the early history of the United States, conflicts between Native American populations and European settlers most often focused on differences in cultural views and values related to:

  1. wealth and social status.
  2. the role of religion in society.
  3. land ownership and use.
  4. the concept of community.
Answer and Rationale. Enter to expand or collapse. Answer expanded
Correct Response: C.
Many factors contributed to the development of conflict between Native Americans and European settlers in the colonial period, including demands for food, livestock damage to Native American crops, and dishonest traders. But as European settlements grew, the European view of private land ownership increasingly deprived Native Americans of their access to crop lands and hunting grounds and eventually excluded many from their ancestral homelands. Europeans who failed to recognize Native Americans' communal perspectives on hunting grounds and unoccupied areas of land often perceived these ideas as a threat to their communities. The resulting tensions led to many conflicts.

Objective 0019 
Understand historical, cultural, and societal contexts for the arts (visual arts, music, drama, dance) and the interrelationships among the arts.

31. Which of the following activities would best foster students’ ability to appreciate a piece of classical music?

  1. providing students with English translations of Italian terms noted in the score of the composition
  2. helping students recognize the expressive qualities of the composition
  3. instructing students to draw the contour of the main melody of the composition with a pencil
  4. asking students to invent rhymed lyrics that fit the meter of the composition
Answer and Rationale
Correct Response: B.
Composers use musical elements to express mood in the music they create. For example, composers of classical music often evoke a sad mood through the encoded use of minor key and slow tempo. Students may not be able to readily identify such expressive sound qualities in a piece of classical music. Helping them to listen for such expressive qualities will most likely enhance their appreciation of what they are listening to.

Objective 0019 
Understand historical, cultural, and societal contexts for the arts (visual arts, music, drama, dance) and the interrelationships among the arts.

32. The duties of a choreographer for a dance performance are most closely aligned to which of the following duties of a theatre director?

  1. adjusting the pace of dialogue
  2. helping actors discover their characters
  3. blocking each scene
  4. analyzing the script for meaning
Answer and Rationale
Correct Response: C.
A choreographer serves a similar role to a theatre director in that both are the artistic leaders of their respective productions. Choreographers design the form and movements of dancers in a dance performance. The focus on visual composition and the arrangement of bodies on stage is closely aligned with a theatre director's task of blocking—positioning actors on stage for dramatic effect and to ensure that the audience has unobstructed sight lines of the actors.

Objective 0020 
Understand concepts, techniques, and materials related to the visual arts, music, drama, and dance and how to provide students with learning opportunities that encourage them to express themselves through the arts.

33. One area of a painting is an abstract shape painted orange. Which of the following colors painted alongside the orange shape would most enhance or intensify the color of the orange shape?

  1. blue
  2. red
  3. green
  4. yellow
Answer and Rationale
Correct Response: A.
Orange and blue are complementary colors that are opposite each other on the color wheel. When complementary colors are mixed, they cancel each other out and produce a neutral color. When they appear side by side, they contrast sharply with each other, which has the effect of enhancing or intensifying each color.

Objective 0020 
Understand concepts, techniques, and materials related to the visual arts, music, drama, and dance and how to provide students with learning opportunities that encourage them to express themselves through the arts.

34. Which of the following steps would most likely come first in developing a Dance assessment instrument?

  1. asking the physical education teacher to describe the physical fitness of the students
  2. choosing a time during the academic year to administer the assessment
  3. creating a scoring rubric that represents performance expectations
  4. designing learning objectives for measureable learning experiences
Answer and Rationale
Correct Response: D.
The first task in developing an assessment tool is to clearly articulate the learning objectives that will be assessed. Learning objectives describe student outcomes for learning experiences that are observable and measurable.

Objective 0021 
Understand fundamental concepts, principles, and practices related to movement, sports, and team-building skills and the role of physical activity in promoting students’ personal, social, and cognitive development.

35. For a first-grade physical activity, the teacher scatters carpet squares around the gymnasium. Each student finds a carpet square and listens to the teacher's challenge below.

"Imagine that you are inside a giant bubble that has landed on your carpet square. How can you move inside your bubble? How many different ways can you bend and stretch without moving off your carpet square?

"Next, imagine that you and your bubble float off your carpet square and begin moving on a gentle breeze. Float around the room without bumping into anyone so your bubbles do not burst. Move forward, backward, and sideways. Float back to your carpet square on my signal."

Which of the following types of movement concepts are students primarily exploring in this activity?

  1. spatial awareness concepts such as self- and general space, direction, pathways, and levels
  2. balance and weight bearing concepts such as center of gravity, base of support, and sequential transfer of body weight
  3. relationship concepts such as over or under, in front of or behind, or next to or far from objects
  4. effort awareness concepts such as strong and light force, fast and slow time, and interrupted and sustained flow
Answer and Rationale
Correct Response: A.
In this activity, students are exploring spatial awareness concepts. While on their carpet squares, students remain in personal or self-space. When the students leave their carpet squares to move around the gymnasium, they are traveling in general space. This type of activity encourages students to distinguish between self-space and general space, respect the self-space of others, and move within general space safely and with control. As students bend and stretch in self-space, they are likely to move their bodies at low, middle, or high levels and in different directions—up or down, forward or backward, and to the right or left. Moving in general space while avoiding others prompts students to travel in different directions; in straight, curved, or zigzag pathways; and, if they are required to duck or dodge, at different levels.

Objective 0021 
Understand fundamental concepts, principles, and practices related to movement, sports, and team-building skills and the role of physical activity in promoting students’ personal, social, and cognitive development.

36. Research on physical activity and its effects on cognitive development suggests that there is a strong link between regular participation in purposeful vigorous aerobic activity and enhancement of which type of skills?

  1. deductive reasoning skills such as general-to-specific thinking and narrowing a theory to a hypothesis that could be tested
  2. rhythmic and musical composition skills such as distinguishing among musical elements and genres and interpreting musical notations
  3. executive functioning skills such as planning and organizing, controlling emotions and impulsivity, and remembering instructions for a task
  4. linguistic skills such as facility in learning multiple languages; transfer of language skills; and bilingualism in reading, writing, and speaking
Answer and Rationale
Correct Response: C.
Research studies show a positive relationship between aerobic activity and increases in volume in the hippocampus, a brain structure that plays a key role in executive functioning and management, learning, and working memory. In 2013, the Illinois Public Health Institute (I P H I) prepared for the Illinois Enhanced Physical Education Task Force a review of the research on the relationship between physical activity, fitness, and improved academic achievement and cognitive functioning. This review confirmed the link between regular participation in moderate-to-vigorous aerobic activity and the development and enhancement of executive functioning and management, which is associated with the cognitive processes necessary for goal-directed cognition and behavior. These cognitive processes include self-regulatory tasks such as focusing attention and maintaining self-control, as well as information processing and management tasks such as remembering instructions, storing and retrieving information from working memory, reasoning and problem solving, and planning and scheduling.

Objective 0022 
Understand the systems of the human body; health-related and skill-related fitness components, concepts, and practices; and interrelationships between fitness and body systems.

37. In a health and wellness lesson, a fifth-grade class creates the list below of potential adverse health effects on the body's circulatory system. Which of the following lifestyle behaviors is most closely associated with these negative effects on personal health?

  1. binge drinking alcohol
  2. smoking tobacco products
  3. consuming refined sugars
  4. using anabolic steroids
Answer and Rationale
Correct Response: B.
Smoking tobacco products has damaging effects on multiple body systems, including the circulatory system. The carbon monoxide in tobacco smoke attaches to hemoglobin (the oxygen-carrying component in red blood cells) more easily than oxygen does, resulting in a decrease in oxygen transported to the body's tissues and organs. The oxygen content of blood to the heart is reduced, which can cause high blood pressure and increased heart rate. Chemicals in tobacco smoke also damage cells that form the lining of blood vessels. Thus, smokers are at an increased risk of developing atherosclerotic disease, in which coronary arteries become narrowed by a gradual buildup of fatty material within their walls. Smoking also raises the levels of the protein that causes blood to clot, thereby increasing platelet aggregation and the stickiness of blood. This increases the risk of stroke and heart attack due to blockages of the blood supply.

Objective 0022 
Understand the systems of the human body; health-related and skill-related fitness components, concepts, and practices; and interrelationships between fitness and body systems.

38. Which of the following statements best explains why animal walks and dance poses that require students to lower their hips near or below knee level (e.g., frog stand, duck walk, grand plié) are now considered unsafe?

  1. They hyperextend the neck, placing excess weight on cervical vertebrae.
  2. They cause the back to overarch, stressing the muscles and discs in the lower back.
  3. They overstretch the hip flexor muscles, causing muscle fibers and tendons to tear.
  4. They place excessive pressure on knee ligaments and cartilage, leading to strains.
Answer and Rationale
Correct Response: D.
During physical activities, the use of appropriate fitness principles and practices helps safeguard students against injuries. Some movement activities and fitness exercises that may have been traditionally used in elementary education are no longer considered safe. Animal walks and poses such as the duck walk and the frog stance require students to perform deep knee bends, which are contraindicated because of their potential to strain the ligaments and cartilage of the knees. The grand plié ballet position is performed by turning the feet outward and fully bending both knees until the thighs are nearly horizontal. For a novice dancer, this amounts to performing a deep squat with feet turned out, heels raised, and pelvis tucked, which places excessive stress on the knees.

Objective 0023 
Understand principles and practices related to personal, family, and community health and safety and ways to provide students with knowledge and skills that will help them make sound health-related decisions.

39. Which of the following foods are good sources of the carbohydrates used to make the glucose and glycogen that students need to fuel daily physical activities?

  1. nuts, cheese, and eggs
  2. poultry, pork, and lean beef
  3. whole grains, fruits, and vegetables
  4. seeds, oils, and canned and wild-caught fish
Answer and Rationale
Correct Response: C.
Nutrient choices influence overall health, body composition, and availability of energy. Carbohydrates provide energy to the cells of the body. Simple carbohydrates include naturally occurring sugars such as fruits, which are easily digested and provide quick energy. Complex carbohydrates such as whole grains and vegetables take longer to digest, creating a slow, steady increase in blood glucose and longer-lasting energy. Once consumed, carbohydrates break down into sugars and travel to the liver, where they are converted into glucose. Via the bloodstream, glucose travels to the body's tissues and organs, including the muscles and the brain, where it is used as energy. Unused glucose is stored in the liver and skeletal muscles in the form of glycogen, which can be used later for energy as needed.

Objective 0023 
Understand principles and practices related to personal, family, and community health and safety and ways to provide students with knowledge and skills that will help them make sound health-related decisions.

40. Small groups of fifth-grade students will apply the steps in the decision-making model below to hypothetical health-related situations. Each group chooses a health-related issue and documents the process used to make a decision that will help resolve the issue.

Decision-Making Steps

  1. Define the problem/decision to be made.
  2. Identify important criteria for the decision and the result.
  3. Consider all possible options.
  4. Weigh the consequences of solutions against the likelihood of satisfying the criteria.
  5. Choose the best option.
  6. Evaluate and monitor the solution.

Which of the following tasks should be carried out by the students during Step 4?

  1. developing a plan for carrying out the decision and monitoring its effectiveness
  2. reviewing group member roles and responsibilities in a collaborative decision-making process
  3. determining exactly what resources will be needed to implement a decision or course of action
  4. analyzing factors that affect each option and identifying probable outcomes of decisions
Answer and Rationale
Correct Response: D.
In this decision-making process, Step 4 involves tasks such as checking alternative options and decision choices against sound, relevant health knowledge and the goals and desired results of the decision-making task. During this step, it is appropriate for students to examine factors that are likely to affect decisions or courses of action, consider the pros and cons of different options, and compare the advantages and disadvantages of various options. In addition, students should attempt to predict potential outcomes and evaluate potential consequences of alternative decisions. Using a systematic decision-making process helps students determine an appropriate course of action and provides them with valuable practice in using decision-making skills to enhance personal health and safety.

References

1Source for sample multiple-choice question #26: Constitution of the State of Illinois, adopted  December  15, 1970.