Unit 9: Introducing Measurement Concepts: Perimeter, Time Intervals, Weight, and Liquid Volume Measuring Perimeter - One big idea in this unit is using addition and subtraction to solve problems related to perimeter of polygons. Students learn that perimeter is the combining/joining of linear distances. Students use their knowledge of addition and subtraction relationships when given the perimeter of a polygon but need to find the missing length measure. Students may use a strip diagram to see the relationship between the side lengths and the perimeter (total). This is useful both in finding perimeter and also in finding a missing length measure when thinking of the part-part-whole model. Students need to use the ruler to measure length distances as a part of finding perimeter. The second grade TEKS 2.9D is included to make sure students are continuing to measure to the nearest inch or centimeter and are doing so when finding perimeter. Example of a strip diagram with perimeter of a triangle with a missing side is below:
Measuring Intervals of Time - Another big idea in this unit is using addition and subtraction to solve problems related to measuring time intervals in minutes. Students use pictorial models or clocks to help them find the sum or difference. When solving problems related to time, students use their understanding that there are 60 minutes in 1 hour to help them do simple conversions with hours and minutes as needed in a problem situation. TEA also states in the TEKS Supporting Information booklet that problems may include a start time with an interval or end time with an interval. Intervals may be less than or greater than 1 hour. Problems may not include a start time and an end time as elapsed time is addressed in grade 4 TEKS 4.8C. Number lines are an efficient way to help students understand what is happening in a time situation. Some examples are below:
Measuring Weight - customary system only - Students also work with the big idea of measuring weight. Students will also weigh objects using the customary system (ounces, pounds, tons). Two scales were purchased and are available for checkout through the school library. One scale is an 11 pound scale and the other is a 16 oz scale. Students discover how the scales work and what they are useful in measuring through exploratory lessons and activities provided. Students gain benchmark ideas about the relative sizes of ounces and pounds through these explorations. They experience an intriguing lesson that helps them negotiate between ounces used for weight and ounces used for capacity (liquid ounces). They use understandings about strip diagrams to help them make connections between pounds and ounces. Students have been using length measurement tools as having number lines with halves, fourths, and eighths. When using the scales that are available, students may find that the measure is between pounds such as halfway - using notation such as 2 1/2 pounds or however precise the tool allows will help students in fractional parts.
Measuring Liquid Volume and Capacity - customary and metric systems - Another measurement big idea in this unit is determining liquid volume and capacity - the measurement of an object's ability to hold a liquid and is the amount of space taken up by the liquid. In Kindergarten students made comparison observations about weight and liquid volume, but this is their first experience making actual measurements, including fractional measurements to reinforce TEKS 3.7A. Students will use liquid measurement tools for both the customary (cups, pints, quarts, gallons, liquid ounces) and metric (liter, milliliter) systems. Students have been using length measurement tools as having number lines with halves, fourths, and eighths. Liquid volume is possibly easier to use with 1/2 cup or 1/2 gallon. These measurements don't need to go to the extreme with fractional units, but when a measure isn't on the whole number mark, considerations need to be made. Students experience a 3-Act Math lesson where they are intrigued by a video showing ice melting over time and then have to predict how much liquid is in the gallon jug. This gives reasons for learning about the customary measurements of capacity and gets students excited about learning about these units. They use the metric capacity tools including graduated cylinders to measure and solve problems with liters and milliliters.
Problem solving with capacity and weight are also included in this unit as students use their skills to solve interesting problems with these units and tools. Connecting Big Ideas Operation Meanings & Relationships - The same number sentence (e.g. 12-4=8) can be associated with different concrete or real-world situations, AND different number sentences can be associated with the same concrete or real-world situation. (TEKS 3.4A, 3.5A, 3.7B-C) In grade 2, students worked on addition and subtraction through 1,000 writing number sentences for problem situations and writing situations for given number sentences. This was taken up again in 3rd grade unit 2 and in spiral review for units 3 and 4. In this unit, students use understandings of addition and subtraction to apply to perimeter problems involving adding lengths to get total or subtracting lengths from total. Joining minutes for time intervals involves addition and subtraction depending upon the problem situation with 2-digit and 3-digit numbers. Students should be writing number sentences for all of these types of problems. Students should also have to write a problem situation for a given number sentence involving measuring perimeter or time intervals. They also solve problems connecting addition and subtraction to weight and capacity. In units 9, 10, 12, and 13, addition and subtraction number sentences will be continued during the unit and in spiral review. Elapsed time is not studied until fourth grade TEKS. Basic Facts & Algorithms - Basic facts and algorithms for operations with rational numbers use notions of equivalence to transform calculations into simpler ones. (TEKS 3.4A, 3.7C) In grade 2, students used the idea of "commutative property of addition" to order addition addends in a way that makes the computation easier for basic facts and then applied to larger numbers. (students may not have used "commutative" but the idea of the property) In this unit, students make decisions about how to add using properties such as the commutative property of addition to make the computation easier. In future 3rd grade units, students will have more opportunities to apply properties in order to make the addition work easier for them. Estimation - Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally. Measurements can be approximated using known referents as the unit in the measurement process. (TEKS 3.4B) In second grade, estimation was based on asking questions about the reasonableness of the solution, such as when I add 325 and 458, I know my sum will be greater than 700 (not using rounding but thinking about combining the numbers) but my answer will be less than 1,000 based on the numbers both being less than 500. In 3rd grade unit 2, students learned to round numbers to the nearest 10 or 100 in order to estimate sums and differences. They also may have used compatible numbers to estimate. In this unit, students continue to make estimates based on rounding to the nearest 10 or 100 and on using compatible numbers. These estimates need to be made on perimeter problems. Estimates with time might included statements like, "I know the sum will be more than 1 hour or less than 1 hour." Estimation is also important as students work with liquid capacity and weight - using tools and making estimates based on experiences with the units. In future units and on STAAR, students will use estimation to solve problems and know if their answer is reasonable. Variable - Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations. (TEKS 3.5A) In grade 2, students wrote equations but normally didn't use a variable - they may have used a blank, question mark, or other symbol for the unknown. This idea of variable was also introduced in grade 3 unit 2, and then revisited in spiral review of units 3 and 4. In this unit, students continue to work with number sentences and variables related to perimeter, time interval, weight, and capacity problem solving. These variables should also be included in any strip diagrams made to help understand the part-part-whole situation. In future units, students will continue to write and solve equations with a variable included. Measurement - Some attributes of objects are measurable and can be quantified using unit amounts. (TEKS 2.9D, 3.7B) In grade 2, students measured length to the nearest whole number measurement for inches and centimeters using rulers. They also learned to tell time to the nearest minute. In this unit, students apply addition and subtraction to finding the measure of a polygon's perimeter. They have polygons that they also must measure with a ruler to find the length of each side in order to find perimeter. Students use the knowledge of 1 hour equals 60 minutes to help them find total minutes in problems involving time intervals in minutes. Students use measurement tools to find liquid capacity and weight. In units 10 and 12, these measurement concepts return to give students more practice in mastering measuring with a ruler and finding perimeter, solving time interval problems, and measuring weight and capacity. Essential Questions:
Operation Meanings & Relationships - How do I decide which operation or operations are needed to solve problems?
Basic Facts & Algorithms - How do I decide which strategy to use to add or subtract numbers quickly and accurately? How do I calculate using measurements with unlike units?
Estimation - How can I verify that an answer is reasonable?
Variable - How can I use numbers and symbols to represent real-life situations?
Measurement - How does what I measure influence how I measure?
Unit 8: Environments and Food Chains
The student is expected to observe and describe the physical characteristics of environments, and how they support populations and communities within an ecosystem; AND describe environmental changes, such as floods and droughts where some organisms thrive and others perish or move to new locations. The student is expected to identify and describe the flow of energy in a food chain and predict how changes in a food chain affect the ecosystem, such as removal of frogs from a pond or bees from a field. In second grade, students identified factors in the environment, including temperature and precipitation, that affect growth and behavior, such as migration, hibernation, and dormancy of living things. Students have previously identified the basic needs of plants and animals. In addition, students have previously investigated evidence of interdependence in environments and were introduced to energy flow in food chain. In third grade, students learn to identify and describe the physical characteristics of an environment and determine ways these characteristics support the survival of organisms. Students will make predictions of how changes in ecosystems affect the survival of organisms. Students are introduced to the terms “drought” and “flood” to describe drastic changes in precipitation. Students should identify the effects of these events on changes in a food chain, and thus a change in an organism’s ability to survive/thrive in that environment. Essential Questions: What are the physical characteristics of an environment and how do they support populations and communities within an ecosystem?
How do environmental changes affect organisms within an ecosystem?
What can we observe about the flow of energy within a food chain?
What happens to a food chain in an ecosystem if an organism is removed?
Unit 4: The Free Enterprise System in Our World: Thinking Like an Economist
3.6 Economics. The student understands the purposes of earning, spending, saving, and donating money. The student is expected to: (A) identify ways of earning, spending, saving, and donating money; (B) create a simple budget that allocates money for spending, saving, and donating. 3.7 Economics. The student understands the concept of the free enterprise system. The student is expected to: (A) define and identify examples of scarcity; (B) explain the impact of scarcity on the production, distribution, and consumption of goods and services; (C) explain the concept of a free market as it relates to the U.S. free enterprise system. 3.8 Economics. The student understands how businesses operate in the U.S. free enterprise system. The student is expected to: (A) identify examples of how a simple business operates; (B) explain how supply and demand affect the price of a good or service; (C) explain how the cost of production and selling price affect profits; (D) explain how government regulations and taxes impact consumer costs; (E) identify individuals, past and present, including Henry Ford and other entrepreneurs in the community such as Mary Kay Ash, Wallace Amos, Milton Hershey, and Sam Walton, who have started new businesses. 3.16 Science, technology, and society. The student understands how individuals have created or invented new technology and affected life in various communities, past and present. The student is expected to: (A) identify scientists and inventors, including Jonas Salk, Maria Mitchell, and others who have discovered scientific breakthroughs or created or invented new technology such as Cyrus McCormick, Bill Gates, and Louis Pasteur; (B) identify the impact of scientific breakthroughs and new technology in computers, pasteurization, and medical vaccines on various communities. Essential Questions: How do businesses operate in a free enterprise system?
Why is technology important in the free enterprise system?
Unit 6 Looking Through the Informational Lens
3.1 Reading/Beginning Reading Skills/Phonics. Students use the relationships between letters and sounds, spelling patterns, and morphological analysis to decode written English. Students are expected to:
(A) decode multisyllabic words in context and independent of context by applying common spelling patterns including:
(i) dropping the final "e" and add endings such as -ing, -ed, or -able (e.g., use, using, used, usable);
(B) use common syllabication patterns to decode words including:
(i) closed syllable (CVC) (e.g., mag-net, splendid);
(ii) open syllable (CV) (e.g., ve-to);
(iii) final stable syllable (e.g., puz-zle, con-trac-tion);
(E) monitor accuracy in decoding.
3.2 Reading/Beginning Reading/Strategies. Students comprehend a variety of texts drawing on useful strategies as needed. Students are expected to:
(A) use ideas (e.g., illustrations, titles, topic sentences, key words, and foreshadowing clues) to make and confirm predictions;
(B) ask relevant questions, seek clarification, and locate facts and details about stories and other texts and support answers with evidence from text; and
(C) establish purpose for reading selected texts and monitor comprehension, making corrections and adjustments when that understanding breaks down (e.g., identifying clues, using background knowledge, generating questions, re-reading a portion aloud).
3.4 Reading/Vocabulary Development. Students understand new vocabulary and use it when reading and writing. Students are expected to:
(B) use context to determine the relevant meaning of unfamiliar words or distinguish among multiple meaning words and homographs;
(C) identify and use antonyms, synonyms, homographs, and homophones;
(E) alphabetize a series of words to the third letter and use a dictionary or a glossary to determine the meanings, syllabication, and pronunciation of unknown words.
3.12 Reading/Comprehension of Informational Text/Culture and History. Students analyze, make inferences and draw conclusions about the author's purpose in cultural, historical, and contemporary contexts and provide evidence from the text to support their understanding. Students are expected to:
(A) identify the topic and locate the author's stated purposes in writing the text.
3.13 Reading/Comprehension of Informational Text/Expository Text. Students analyze, make inferences and draw conclusions about expository text and provide evidence from text to support their understanding. Students are expected to:
(A) identify the details or facts that support the main idea;
(B) draw conclusions from the facts presented in text and support those assertions with textual evidence;
(C) identify explicit cause and effect relationships among ideas in texts;
(D) use text features (e.g., bold print, captions, key words, italics) to locate information and make and verify predictions about contents of text.
3.15 Reading/Comprehension of Informational Text/Procedural Texts. Students understand how to glean and use information in procedural texts and documents. Students are expected to:
(A) follow and explain a set of written multi-step directions;
(B) locate and use specific information in graphic features of text.
3.16 Reading/Media Literacy. Students use comprehension skills to analyze how words, images, graphics, and sounds work together in various forms to impact meaning. Students will continue to apply earlier standards with greater depth in increasingly more complex texts. Students are expected to:
(A) understand how communication changes when moving from one genre of media to another;
(B) explain how various design techniques used in media influence the message (e.g., shape, color, sound); and
Figure 19 Reading/Comprehension Skills. Students use a flexible range of metacognitive reading skills in both assigned and independent reading to understand an author’s message. Students will continue to apply earlier standards with greater depth in increasingly more complex texts as they become self-directed, critical readers. The student is expected to:
(B) ask literal, interpretive, and evaluative questions of text;
(D) make inferences about text and use textual evidence to support understanding;
(E) summarize information in text, maintaining meaning and logical order;
(F) make connections (e.g.: thematic links, author analysis) between literary and information texts with similar ideas and provide textual evidence.
3.25 Research/Research Plan. Students ask open-ended research questions and develop a plan for answering them. Students are expected to:
(A) generate research topics from personal interests or by brainstorming with others, narrow to one topic, and formulate open-ended questions about the major research topic;
(B) generate a research plan for gathering relevant information (e.g., surveys, interviews, encyclopedias) about the major research question.
3.26 Research/Gathering Sources. Students determine, locate, and explore the full range of relevant sources addressing a research question and systematically record the information they gather. Students are expected to:
(A) follow the research plan to collect information from multiple sources of information, both oral and written, including:
(i) student-initiated surveys, on-site inspections, and interviews;
(ii) data from experts, reference texts, and online searches;
(iii) visual sources of information (e.g., maps, timelines, graphs) where appropriate;
(B) use skimming and scanning techniques to identify data by looking at text features (e.g., bold print, captions, key words, italics);
(C) take simple notes and sort evidence into provided categories or an organizer;
(D) identify the author, title, publisher, and publication year of sources;
(E) differentiate between paraphrasing and plagiarism and identify the importance of citing valid and reliable sources.
3.27 Research/Synthesizing Information. Students clarify research questions and evaluate and synthesize collected information. Students are expected to:
(A) improve the focus of research as a result of consulting expert sources (e.g., reference librarians and local experts on the topic).
3.28 Research/Organizing and Presenting Ideas. Students organize and present their ideas and information according to the purpose of the research and their audience. Students are expected to:
(A) draw conclusions through a brief written explanation and create a works-cited page from notes, including the author, title, publisher, and publication year for each source used. Essential Questions: What details and facts support the main idea, or central idea?
What conclusions can you draw and support from the facts in the text?
What cause and effect relationships are in the text?
How do strategic readers use text features and graphic features?
What strategies are helpful when researching information?
How can I use the research process to explore, learn, and teach others about my topic?
Unit 6 Looking Through the Informational Lens
3.20 Writing/Expository and Procedural Texts. Students write expository and procedural or work-related texts to communicate ideas and information to specific audiences for specific purposes. Students are expected to:
(A) create brief compositions that:
(i) establish a central idea in a topic sentence;
(ii) include supporting sentences with simple facts, details, and explanations; and
(iii) contain a concluding statement;
3.22 Oral and Written Conventions/Conventions. Students understand the function of and use the conventions of academic language when speaking and writing. Students continue to apply earlier standards with greater complexity. Students are expected to:
(A) use and understand the function of the following parts of speech in the context of reading, writing, and speaking:
(i) verbs (past, present, and future);
(iii) adjectives (e.g., descriptive: wooden, rectangular; limiting: this, that; articles: a, an, the);
(vii) coordinating conjunctions (e.g., and, or, but);
(viii) time-order transition words and transitions that indicate a conclusion;
(B) use the complete subject and the complete predicate in a sentence;
(C) use complete simple and compound sentences with correct subject-verb agreement.
3.23 Oral and Written Conventions/Handwriting, Capitalization, and Punctuation. Students write legibly and use appropriate capitalization and punctuation conventions in their compositions. Students are expected to:
(B) use capitalization for:
(i) geographical names and places;
(ii) historical periods;
(C) recognize and use punctuation marks including:
(i) apostrophes in contractions and possessives;
(D) use correct mechanics including paragraph indentations.
3.24 Oral and Written Conventions/Spelling. Students spell correctly. Students are expected to:
(B) spell words with more advanced orthographic patterns and rules:
(ii) dropping final "e" when endings are added (e.g., -ing, -ed);
(iv) double consonants in the middle of words.