grade 1 mathematics, quarter 4, unit 4.1 using fractions ... · pdf filegrade 1 mathematics,...

Cumberland, Lincoln, and Woonsocket Public Schools C-59 in collaboration with the Charles A. Dana Center at the University of Texas at Austin

Grade 1 Mathematics, Quarter 4, Unit 4.1

Using Fractions as Part of a Whole

Overview Number of instructional days: 10 (1 day = 45–60 minutes)

Content to be learned Mathematical practices to be integrated

• Explore area models to show part to whole relationship of a/2, a/3, a/4.

• Develop understanding of the concept of equal parts of a whole.

• Develop conceptual understanding of 2/2, 3/3, and 4/4 being equal to one whole.

Reason abstractly and quantitatively.

• Make sense of quantities in problem situations.

• Know and flexibly use different properties of operations and objects.

Attend to precision.

• Clear definitions.

• Accurate and efficient calculations.

Essential questions Routines • How can you represent a fraction using an area

model?

• How can you find the number of equal shares of a shape/figure?

• How can you tell if the shares are equal?

• How can you share a brownie with three friends?

• Compare and order numbers up to 100.

• What are different ways to create numbers?

• Extend numeric and non-numeric patterns.

Grade 1 Mathematics, Quarter 4, Unit 4.1 Using Fractions as Part of a Whole (10 days) 2010–2011

C-60 Cumberland, Lincoln, and Woonsocket Public Schools in collaboration with the Charles A. Dana Center at the University of Texas at Austin

Written Curriculum

Grade-Level Expectations

M(N&O)–1–1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 100 using place value, by applying the concepts of equivalency in composing or decomposing numbers; and in expanded notation using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations. (Local)

Routines

M(N&O)–1–2 Demonstrates understanding of the relative magnitude of numbers from 0 to 100 by ordering whole numbers; by comparing whole numbers to each other or to benchmark whole numbers (5, 10, 25, 50, 75, 100); by demonstrating an understanding of the relation of inequality when comparing whole numbers by using “1 more”, “1 less”, “5 more”, “5 less”, “10 more”, “10 less”; and by connecting number words (from 0 to 20) and numerals (from 0 to 100) to the quantities and positions that they represent using investigations, models, representations, or number lines. (Local)

M(F&A)–1–1 Identifies and extends to specific cases a variety of patterns (repeating and growing [numeric and non-numeric]) represented in models, tables, or sequences by extending the pattern to the next one, two, or three elements, by finding a missing element (e.g., 2, 4, 6, ___, 10), or by translating repeating patterns across formats (e.g., an abb pattern can be represented as snap, clap, clap; or red, yellow, yellow; or 1,2,2). (Local)

Clarifying the Standards

Prior Learning

In kindergarten, students learned about the concept of 1/2 as a fair share.

Current Learning

In grade 1, students are broadening their understanding of fractions as it relates to area by being able to demonstrate a/2, a/3, and a/4. According to Bloom’s taxonomy, student responses are at the knowledge (identify, label), analysis (classify, compare), and synthesis (organize, plan) levels.

Future Learning

In grade 2, students will continue to broaden their understanding of fractions as it relates to area and they will be introduced to the concept of set model. Second-graders are able to identify fractions a/2, a/3, and a/4. In grade 3, students’ understanding will expand to a/6 and a/8. In grade 4, students will be expected to use area, set, or linear models to identify fractions up to a/10. Grade 4 students will also learn about multiples and factors of the denominator as well as equivalent fractions. The concept of fractions leads to decimals, and percents needed for instruction in all future grades.

Using Fractions as Part of a Whole (10 days) Grade 1 Mathematics, Quarter 4, Unit 4.1 2010–2011


Additional Research Findings

According to Principles and Standards for School Mathematics:

In addition to work with whole numbers, young students should also have some experience with simple fractions through connections to everyday situations and meaningful problems, starting with common fractions such as “half”. At this level, it is more important for students to recognize when things are divided into equal parts than to focus on fraction notation (p. 82).

Grade 1 Mathematics, Quarter 4, Unit 4.1 Using Fractions as Part of a Whole (10 days) 2010–2011


Notes About Resources and Materials

Resources will vary by district (i.e., Everyday Mathematics, Investigations, and/or Pearson-Scott Foresman).

Suggested Materials • computers and geometric software

• geoboards

• geometric solids

• graph paper

• pattern blocks

• real-life objects

• rulers

• straws and string

• tangrams

Websites • http://harcourtschool.com/menus/math2004/ga/math2004_gr1.html

• Houghton Mifflin Parents Place Home Activity Center: www.eduplace.com/parents/resources/hac/figure

• AAA Math: www.aaamath.com

• Education 4 Kids: http://drill.edu4kids.com

• Primary Games: www.primarygames.co.uk

K–2 Math Skills • www.cobbk12.org/sites/literacy/math/math.htm

• www.teachertube.com/view_video.php?viewkey=7ce40169f16cd1e49a17

• PlayKidsGames.com: math, vocabulary, social studies, and more: www.playkidsgames.com

• Math Glossary: Harcourt School Publishers: www.harcourtschool.com/glossary/math2/index_temp.html

• Change Maker: Test your money skills: www.funbrain.com/cashreg

• http://freemathworksheets.com

• www.math-drill.com

• www.nlvm.usu.edu



Telling Time to the Hour and Half Hour

Overview Number of instructional days: 8 (1 day = 45 minutes)

Content to be learned Mathematical practices to be integrated • Recognize an hour and half hour as units of

measurement for elapsed time.

• Identify activities that can logically take place within an hour, a minute, and a second.

• Read an analog clock to the hour and to the half hour.

• Record digital time to the hour and half hour.

• Identify the hour hand and minute hand on an analog clock.

Use appropriate tools strategically.

• Use tools to visualize concepts to deepen understanding.

• Recognize tools have limitations and strengths.

Look for and make use of structure.

• Identify patterns.

• Build understanding using prior knowledge.

Essential questions Routines • What can you do (i.e., tie your shoe) within an

hour, half hour, minute, or second?

• How will you estimate how long it will take to (i.e., tie your shoe)?

• How do you tell the difference between the hour and minute hand?

• What time is it? How do you know?

• How can you record the time from an analog clock in digital format?

• Use fractions to describe objects and quantities.

Grade 1 Mathematics, Quarter 4, Unit 4.2 Telling Time to the Hour and Half Hour (8 days) 2010–2011


Written Curriculum


M(G&M)–1–8 Determines elapsed and accrued time as it relates to calendar patterns (days of the week, months of the year), the sequence of events in a day; and recognizes an hour and “on the ½ hour.” (Local)

Routines

M(N&O)–1–1 Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 100 using place value, by applying the concepts of equivalency in composing or decomposing numbers; and in expanded notation using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations. (Local)


Prior Learning

In kindergarten, students determined elapsed and accrued time as it relates to calendar patterns and the sequence of events in a day, and they identified a clock as a measurement tool.

Current Learning

Students in first grade determine elapsed time and accrued time and recognize an hour and half hour. Students use both analog and digital clocks to tell and represent time; they also relate the concept of time to their daily lives. At the end of grade 1, this GLE may be assessed at the local level.

Routines established in quarter 1 should continue and extend throughout quarter 2.

According to Bloom’s Taxonomy, students’ responses should reflect knowledge and comprehension levels.

Future Learning

In grade 2, students will begin to tell time in 15-minute intervals. They will develop an understanding of equivalencies such as 60 minutes = 1 hour. Later, in grade 3, students will tell time in five-minute intervals.


According to Principles and Standards for School Mathematics the study of measurement is important “because of the practicality and pervasiveness of measurement in so many aspects of everyday life” (p. 44).

Telling Time to the Hour and Half Hour (5 days) Grade 1 Mathematics, Quarter 4, Unit 4.2 2010–2011





• geoboards


• graph paper

• pattern blocks


• rulers


• tangrams














Grade 1 Mathematics, Quarter 4, Unit 4.2 Telling Time to the Hour and Half Hour (8 days) 2010–2011




Measuring and Comparing Length, Height, Weight, Temperature, and Capacity

Overview Number of instructional days: 10 (1 day = 45–60 minutes)

Content to be learned Mathematical practices to be integrated • Describe and compare attributes of objects such

as length, height, weight, temperature, and capacity using nonstandard units.

• Measure length and height of two-dimensional object(s) using nonstandard units of measurement.

Attend to precision.

• Specific units of measurement

Use appropriate tools strategically.

• Available tools that students are familiar with

• Appropriate to grade level and students’ developmental stages

Essential questions Routines • Which object is taller/shorter? How do you

know?

• Which object is longer/shorter? How do you know?

• Which object is heavier/lighter? How do you know?

• Which is warmer/cooler?

• Which is more/less?

• How many cubes (paper clips, etc.) long is this object?

• Continue to work on telling time to the hour and half hour.

Grade 1 Mathematics, Quarter 4, Unit 4.3 Measuring and Comparing Length, Height, 2010–2011 Weight, Temperature, and Capacity (10 days)


Written Curriculum


M(G&M)–1–7 Demonstrates conceptual understanding of measurable attributes using comparative language to describe and compare attributes of objects (length [longer, shorter], height [taller, shorter], weight [heavier, lighter], temperature [warmer, cooler], and capacity [more, less]); compares objects visually, with direct comparison, and using non-standard units. (Local)

M(G&M)–1–6 Demonstrates conceptual understanding of the length/height of a two-dimensional object using non-standard units (e.g. comparing objects to trains of small cubes, using iterations of a small unit to measure an object). (Local)

Routines

M(G&M)–1–8 Determines elapsed and accrued time as it relates to calendar patterns (days of the week, months of the year), the sequence of events in a day; and recognizes an hour and “on the ½ hour.” (Local)


Prior Learning

In kindergarten, students visually described and directly compared objects’ attributes such as length (longer/shorter) and height (taller/shorter).

Current Learning

In grade 1, students visually compare and describe attributes of objects such as length (longer/shorter), height (taller/shorter), weight (heavier/lighter), temperature (warmer/cooler), and capacity (more/less) using direct comparison and non-standard units.

According to Bloom’s Taxonomy, student responses will be at the knowledge (describe, tell, write), comprehension (conclude, tell, demonstrate), and analysis (compare) levels.

Routines include making and revising estimates of the number of objects in a set up to 30. Students practice numerical fluency by mentally adding and subtracting whole numbers and naming the number that is one or two more or less than the original number. They add and subtract whole number facts to 10, and order whole numbers from 0–100 by comparing whole numbers to each other or to benchmark whole numbers (5, 10, 25, 50, 75, 100). In routines, students compare whole numbers by using one more/less, 5 more/less, and 10 more/less. They also connect number words from 0–20 and numerals to the quantities and positions that they represent from 0–100. Routines should continue and extend throughout the quarter.

Future Learning

In grades 2–5, students will measure using standard units appropriately and consistently. They will make conversions within systems when solving problems across the content strands. Students will also demonstrate conceptual understanding of perimeter and area by using models and manipulatives to surround and cover polygons.

Measuring and Comparing Length, Height, Grade 1 Mathematics, Quarter 4, Unit 4.3 Weight, Temperature, and Capacity (10 days) 2010–2011


In grade 3, students will demonstrate conceptual understanding of perimeter of polygons and the area of rectangles on grids. Students will express all measures using appropriate units.

In grade 4, students will demonstrate conceptual understanding of perimeter of polygons and the area of rectangles, polygons, or irregular shapes on grids or in formulas. Students will express all measures using appropriate units.

In grade 5, students will demonstrate conceptual understanding of perimeter of polygons, area of rectangles or right triangles on grids, and volume of rectangular prisms (cubes). Students will express all measures using appropriate units.


According to Atlas of Science Literacy, Vol. 1, (Proportional Reasoning cluster, Ratios and Proportionality map) the understanding of numerical descriptions and comparisons begins with describing and comparing things in terms of their number, shape, texture, size, weight, color, and motion. Numerical data is used in describing and comparing objects and events (p. 119).

Benchmarks of Science Literacy states students “should be encouraged to make relative physical comparisons directly whenever they can, concluding, say, that B is taller than A, C holds more than D, etc.” … “they should also begin to develop a preference for numerical comparisons—B is 2 inches taller than A, box C holds 14 more marbles than box D” (p. 211).

Grade 1 Mathematics, Quarter 4, Unit 4.3 Measuring and Comparing Length, Height, 2010–2011 Weight, Temperature, and Capacity (10 days)





• geoboards


• graph paper

• pattern blocks


• rulers


• tangrams
















Using Location and Position


Content to be learned Mathematical practices to be integrated • Use positional words to describe location in the

environment, on a map, or in a diagram.

• Use positional words such as close by, on the right, underneath, above, and beyond to describe one location in reference to another.

• Make sense of problems and persevere in solving them.

• Give verbal descriptions of location and position.

Essential questions Routines • How can you describe where to find location X

on a map? On a diagram?

• What words can you use to explain how to get from point A to point B?

• Using positional words, where is (your chair, the table) in the classroom?

• Measure objects around the room.

• Continue to use descriptive words to describe warmer/cooler, taller/shorter, and lighter/heavier.

Grade 1 Mathematics, Quarter 4, Unit 4.4 Using Location and Position (4 days) 2010–2011


Written Curriculum


M(G&M)–1–9 Demonstrates understanding of spatial relationships using location and position by using positional words (e.g., close by, on the right, underneath, above, beyond) to describe one location in reference to another on a map, in a diagram, and in the environment. (Local)

Routines




Prior Learning

In kindergarten, students used positional words to describe the location of objects in the environment.

Current Learning

In grade 1, students continue not only to use positional words to describe the location of objects in the environment, but they also now use these words to locate places on maps and diagrams as well. Students develop the sense of location as it relates to other places and objects.

Routines established in unit 3.1 should continue and extend throughout this unit.

Future Learning

In grade 2, students will use positional language in two- and three-dimensional situations to describe and interpret relative positions (e.g., above the surface of the desk, below the triangle on the paper). Students will also create and interpret simple maps as well as naming locations on simple coordinate grids.

In grade 3, students will interpret and use positional words to give directions from one location to another (i.e., from the classroom to the gym, from school to home). They will also describe locations on a map or coordinate grid (first quadrant) using positional words or compass directions.

In grade 4, students will plot points in the first quadrant in context (gains, mapping). They will also find the horizontal and vertical differences between points on a coordinate grid in the first quadrant.

Using Location and Position (4 days) Grade 1 Mathematics, Quarter 4, Unit 4.4 2010–2011


In grade 5, students will plot points in all four quadrants in context (gains, mapping, identifying the vertices of polygons as they are reflected, rotated, and translated).


Principles and Standards for School Mathematics states that students can use mathematical questions about location to help navigate through their environment. These skills are extended into other areas of the curriculum such as science, art, and social studies.

Grade 1 Mathematics, Quarter 4, Unit 4.4 Using Location and Position (4 days) 2010–2011





• geoboards


• graph paper

• pattern blocks


• rulers


• tangrams
















Determining Likely or Unlikely Events


Content to be learned Mathematical practices to be integrated

• Use experiments to describe the likelihood of an outcome or chance of an event using more likely, less likely, or equally likely.

Reason abstractly and quantitatively.

• Are able to flow between contextual and noncontextual situations

Construct viable arguments and critique the reasoning of others.

Construct arguments using objects, drawings, diagrams, and actions.

Essential questions Routines • Explain how likely it is that _______ will

occur?

• How can you tell if the outcome is more likely/less likely/equally likely?

• Continue to use objects to measure.

• Use words to describe height, weight, temperature, and length.

Grade 1 Mathematics, Quarter 4, Unit 4.5 Determining Likely or Unlikely Events (8 days) 2010–2011


Written Curriculum


M(DSP)–1–5 For a probability event in which the sample space may or may not contain equally likely outcomes, groups use experiments to describes the likelihood or chance of an event (using “more likely,” “less likely”, or “equally likely”). (Local)

Routines




Prior Learning

Students may not have any prior knowledge of probability, as this is a new concept to grade 1. Students may have had experiences relating the concept of likely/not likely to weather predictions.

Current Learning

In grade 1, students are learning to use the terms more likely, less likely, or equally likely for given events. According to Bloom’s taxonomy, student responses are at the knowledge (identify, label), analysis (classify, compare), and synthesis (organize, plan) levels. This standard should be assessed locally.

Future Learning

In grade 2, students will learn the concepts of certain or impossible when talking about the probability of an event. In future grades, the language of probability will include fairness. Students will participate in experiments (theoretical or experimental) to determine probability and express the results as a fraction. In future grades, this concept can be tested at both local and state level.


Principles and Standards for School Mathematics states:

At this level, probability experiences should be informal and often take the form of answering questions about the likelihood of events, using such vocabulary as more likely or less likely. Questions about more and less likely events should come from the students’ experiences, and the answers will often depend on the community and its location (p. 114).

Determining Likely or Unlikely Events (10 days) Grade 1 Mathematics, Quarter 4, Unit 4.5 2010–2011





• geoboards


• graph paper

• pattern blocks


• rulers


• tangrams














Grade 1 Mathematics, Quarter 4, Unit 4.5 Determining Likely or Unlikely Events (8 days) 2010–2011


grade 1 mathematics, quarter 4, unit 4.1 using fractions ... · pdf filegrade 1 mathematics,...

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