# How Many In All DTE

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```					                                           Instructional Unit Plan
School: Desert Trail Elementary

Content Area(s): Investigations Unit:                 Implementation Dates: 25 days
How Many In All?

Unit Focus: Students deepen their understanding of number and number relationships through a variety of
mathematical games and problems. They practice counting quantities ( count, combine and compare
quantities); measure lengths and distances; explore ways to represent quantities (with manipulatives, with
numerals, and with pictures).

New Mexico Content Standards, Benchmarks and Performances Addressed:
Strand 1: Number And Operations
Standard: Students will understand numerical concepts and mathematical operations.
K-4 Benchmark 1: Understand numbers, ways of representing numbers, relationships among numbers, and number
systems.
1. Demonstrate an understanding of the place-value structure of the base-ten number system:
 Count with understanding and recognize “how many” in sets of objects up to 20
 Read and write whole numbers up to 20
 Compare and order whole numbers up to 20
 Connect numerals to the quantities they represent using various physical models
 Use an organized counting method to keep track of quantities while counting (one-to-one correspondence)
(e.g., touch object once and only once as counting a set)
 Order sets of objects and numbers from least to most or most to least.
K-4 Benchmark 2: Understand the meaning of operations and how they relate to one another.
 Represent numbers using pictures, objects, or numerals.
 Use concrete objects to solve simple addition and subtraction story problems (e.g., oral not written).
K-4 Benchmark 3: Compute fluently and make reasonable estimates.
 Estimate quantities of objects up to 20.

Strand 2: ALGEBRA
Standard: Students will understand algebraic concepts and applications.

K-4 Benchmark 2: Represent and analyze mathematical situations and structures using
algebraic symbols.
 Use concrete, pictorial, and verbal representation to develop an understanding of invented
and conventional symbols.
K-4 Benchmark 3: Use mathematical models to represent and understand quantitative relationships.
 Model situations that involve whole numbers using objects or pictures.

Strand 4: Measurement
Standard: Students will understand measurement systems and applications.
K-4 Benchmark 1: Understand measurable attributes of objects and the units, systems, and process of measurement.
 Measure using non-standard units of measurement (e.g., use pencils to measure desk top, use different lengths of
rope to measure distance in classroom).
K-4 Benchmark 2: Apply appropriate techniques, tools, and formulas to determine measurements.
 Explore measuring objects using a repeating non-standard unit of measurement (e.g., paper
clips, cubes, etc.)

1
Paraphrase knowledge and skills required by the Standards:
1. Students count up to 20 objects; represent quantities in pictures, numbers and words; use a
repeating nonstandard unit to quantify length.
2. Students become familiar with combinations of six; record strategies for counting six things
grouped in different ways; determine the larger of two amounts; count up to 20 objects.
3. Students make sense of stories that involve combining and separating; develop strategies for
solving those problems; become familiar with number combinations; record their combinations
with pictures, numbers or words.
4. Students become familiar with combinations of 6 and other numbers; find the total of two or
more single digit numbers; use pictures, numbers, words to record solutions to problems; make
sense of story problems that involve combining and separating situations and develop
strategies for solving those problems.

Description of the Assessments that will be used to provide evidence of student learning that
targets the standards:
1. Can students measure length using sticks or cubes? How do they record their
measurements? Conduct a whole group discussion of their recordings and why they may
2. What strategies do students use to sort and count materials in an Inventory Bag? Have
students explain their inventory recording sheets.
3. Can students create and record a number of different arrangements of six tiles? Have
students share and explain their recordings during whole group discussions.
4. Can students tell which of two groups of objects has more? Which has least? Have students
explain as teacher confers with children while working in pairs.
5. Can students build and record towers of six using two different colors? Have students share
and explain their recording during whole group discussions.
6. Can students role play and articulate how a story problem that needs combining is solved?
Can students role play and articulate how a story problem that needs separating is solved?
Discuss possibilities/strategies during whole class discussion.
7. Can students create and record different combinations of red and blue objects to make sets of
5, and sets of 6 in all? Have students share and explain their recordings during whole group
discussions.
8. Administer Formative Assessment #3 at the end of this unit.

Description of the rubrics or criteria that will be used to assess student performance:

Student responses and teacher observations discussion and individual, pair and group work. See
Observing the Students:
 Measuring Objects and Paths p. 10

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   Measuring with Sticks p. 13
   Measuring with Cubes p. 16
   Collect 15 Together p. 19
   Inventory Bags p. 22
   Six Tiles in All p. 35
   Books of Six in All p. 39
   Grab Two Handfuls p. 41
   Towers of Six p. 44
   Acting Out Story Problems p. 61
   Double Compare p. 64
   Counters in a Cup p. 67
   Racing Bears p. 69
   Five Crayons in All p. 78
   Six Crayons in All p. 83
   Total of Six p. 85

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Learning Activities – Description of the learning activities that will develop the knowledge
and skills required by the performance standard:

INVESTIGATION 1: Counting and Measuring
 Focus Time: Counting and Measuring - Students count up to 10 objects; use a
repeating unit to measure length; record measurements; describe lengths that fall between
two whole numbers.
 Choice Time: Measuring with Sticks – Students measure lengths of objects and paths.
 Choice Time: Measuring with Cubes – Students use interlocking cubes to measure the
longer length of objects.
 Choice Time: Collect 15 Together – Students play Collect 15 Together which focuses
on counting up to 15 objects and keeping track of a growing collection of objects.
 Choice Time: Inventory Bags – Students practice counting up to 20 objects and
represent quantities with pictures, numbers and words.
INVESTIGATION 2: Six Tiles
 Focus Time: Six Tiles in All – Students become familiar with combinations of six; use
numbers to describe arrangements of objects; describe position/spatial relationships
among objects; record strategies for counting objects.
 Choice Time: Books of Six In All – Students make and record arrangements of six tiles.
 Choice Time: Grab Two Handfuls – Students work on counting up to 20 objects and
comparing quantities; represent quantities with pictures, numbers and words.
 Choice Time: Towers of Six – Students work on finding combinations of six; use
objects to model number combinations; record solutions.
 Choice Time: Measuring with Sticks – Students measure lengths of objects and paths.
 Choice Time: Measuring with Cubes – Students use interlocking cubes to measure
longer lengths of objects.
 Choice Time: Collect 15 Together – Students play Collect 15 Together which focuses
on counting up to 15 objects and keeping track of a growing collection of objects.
INVESTIGATION 3: Story Problems
 Focus Time: Story Problems – Students make sense of combining and separating stories
and develop strategies for solving them.
 Choice Time: Double Compare – Students play Double Compare finding the total of
two quantities; find the larger of two quantities.
 Choice Time: Counter in a Cup – Students play Counter in a Cup using objects to
model number combinations and use numbers to record how many.
 Choice Time: Racing Bears – Students play Racing Bears continuing their work on
number combinations up to six.
 Choice Time: Books of Six In All – Students make and record arrangements of six tiles.
 Choice Time: Towers of Six – Students work on finding combinations of six; use
objects to model number combinations; record solutions.
INVESTIGATION 4: Blue and Red Crayons
 Focus Time: Five Crayons in All – Students find combinations of five and recognize
that some problems have more than one solution.
 Choice Time: Six Crayons in All - Students find combinations of six.

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   Choice Time: Total of Six – Students play Total of Six finding the total of two or more
single-digit numbers.
   Choice Time: Towers of Six – Students work on finding combinations of six; use
objects to model number combinations; record solutions.
   Choice Time: Double Compare – Students play Double Compare finding the total of
two quantities; find the larger of two quantities.
   Choice Time: Counter in a Cup – Students play Counter in a Cup using objects to
model number combinations and use numbers to record how many.
   Choice Time: Racing Bears – Students play Racing Bears continuing their work on
number combinations up to six.

Unit Resources/Materials:
Investigations Unit T.E. – How Many In All?
The Line Up Book by M. Russo (optional)

Interlocking cubes
Dot cubes with 1-3 and 1-6 dots
Color tiles                                        Craft sticks
Teddy bear counters                                Classroom objects to measure
Pattern blocks                                     Paper bags
Number cards                                       Various countable items
Counters in two colors                             Shoe boxes or bins
Unlined paper                                      Paper plates
Chart paper                                        Glue sticks
Paper cups
Unit student sheets 1, 2, 3 (pp. 115, 116,         Work folders
119)                                               Blue and red crayons
One-inch grid paper (p. 118)                       Empty crayon box
Construction paper squares –1 in.                  Unlined paper
Racing Bears Gameboard (p. 126)                    Chart paper

5
1
2
Interlocking cubes
Dot cubes with 1-3 and 1-6 dots
Color tiles
Teddy bear counters
Pattern blocks
Number cards
Counters in two colors
Unlined paper
Chart paper

Unit student sheets 1, 2, 3 (pp. 115, 116, 119)
One-inch grid paper (p. 118)
Construction paper squares –1 in.
Racing Bears Gameboard (p. 126)

Craft sticks
Classroom objects to measure
Paper bags
Various countable items
Shoe boxes or bins
Paper plates
Glue sticks
Paper cups
Work folders
Blue and red crayons
Empty crayon box
Unlined paper
Chart paper

3
4
5

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