Type:

Full Course, Lesson Plan, Video

Description:

This module introduces the concept and process of decomposition, the first step in Computational Thinking. Examples of decomposition are shown and resources for teaching decomposition skills in the classroom are introduced.

Subjects:

  • Computer Science > Coding
  • Computer Science > Computational Thinking
  • Computer Science > Computers in Society
  • Computer Science > Human Computer Interaction

Education Levels:

  • Grade 6
  • Grade 7
  • Grade 8
  • Grade 9
  • Grade 10
  • Professional Education & Development
  • Vocational Training

Keywords:

Computational, thinking, decomposition, pattern, recognition, abstraction, generalization, algorithm, design, problem, solving, critical, computer, science, Next Generation Science Standards

Language:

English

Access Privileges:

Public - Available to anyone

License Deed:

Creative Commons Attribution Non-Commercial

Collections:

None
Update Standards?

CCSS.Math.Content.K.OA.A.3: Common Core State Standards for Mathematics

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

CCSS.Math.Content.1.OA.A.1: Common Core State Standards for Mathematics

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

CCSS.Math.Content.2.OA.A.1: Common Core State Standards for Mathematics

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

CCSS.Math.Content.3.OA.A.2: Common Core State Standards for Mathematics

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.

CCSS.Math.Content.4.OA.B.4: Common Core State Standards for Mathematics

Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.

CCSS.Math.Content.K.NBT.A.1: Common Core State Standards for Mathematics

Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS.Math.Content.1.NBT.B.2a: Common Core State Standards for Mathematics

10 can be thought of as a bundle of ten ones — called a "ten."

CCSS.Math.Content.1.NBT.B.2b: Common Core State Standards for Mathematics

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS.Math.Content.1.NBT.B.2c: Common Core State Standards for Mathematics

The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

CCSS.Math.Content.2.NBT.A.1a: Common Core State Standards for Mathematics

100 can be thought of as a bundle of ten tens — called a "hundred."

CCSS.Math.Content.2.NBT.A.1b: Common Core State Standards for Mathematics

The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

CCSS.Math.Content.2.NBT.B.7: Common Core State Standards for Mathematics

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

CCSS.Math.Content.4.NBT.A.1: Common Core State Standards for Mathematics

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

CCSS.Math.Content.5.NBT.A.3a: Common Core State Standards for Mathematics

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

CCSS.Math.Content.1.MD.A.2: Common Core State Standards for Mathematics

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

CCSS.Math.Content.3.MD.C.6: Common Core State Standards for Mathematics

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

CCSS.Math.Content.3.MD.C.7a: Common Core State Standards for Mathematics

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

CCSS.Math.Content.3.MD.C.7c: Common Core State Standards for Mathematics

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

CCSS.Math.Content.3.MD.C.7d: Common Core State Standards for Mathematics

Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

CCSS.Math.Content.4.MD.C.5a: Common Core State Standards for Mathematics

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

CCSS.Math.Content.4.MD.C.7: Common Core State Standards for Mathematics

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

CCSS.Math.Content.5.MD.C.3b: Common Core State Standards for Mathematics

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

CCSS.Math.Content.5.MD.C.5a: Common Core State Standards for Mathematics

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

CCSS.Math.Content.5.MD.C.5c: Common Core State Standards for Mathematics

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

CCSS.Math.Content.K.G.B.6: Common Core State Standards for Mathematics

Compose simple shapes to form larger shapes.

CCSS.Math.Content.1.G.A.2: Common Core State Standards for Mathematics

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

CCSS.Math.Content.1.G.A.3: Common Core State Standards for Mathematics

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

CCSS.Math.Content.2.G.A.2: Common Core State Standards for Mathematics

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

CCSS.Math.Content.2.G.A.3: Common Core State Standards for Mathematics

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

CCSS.Math.Content.3.G.A.2: Common Core State Standards for Mathematics

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

CCSS.Math.Content.5.G.B.3: Common Core State Standards for Mathematics

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

CCSS.Math.Content.6.G.A.1: Common Core State Standards for Mathematics

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

CCSS.Math.Content.6.G.A.2: Common Core State Standards for Mathematics

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

CCSS.Math.Content.6.G.A.4: Common Core State Standards for Mathematics

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

CCSS.Math.Content.7.G.A.3: Common Core State Standards for Mathematics

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

CCSS.Math.Content.4.NF.B.3a: Common Core State Standards for Mathematics

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

CCSS.Math.Content.4.NF.B.3b: Common Core State Standards for Mathematics

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

CCSS.Math.Content.5.NF.B.4b: Common Core State Standards for Mathematics

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

CCSS.Math.Content.6.NS.B.4: Common Core State Standards for Mathematics

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

HS-ETS1-2: Next Generation Science Standards

Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.

S2470557: Next Generation Science Standards

Ask questions based on observations to find more information about the designed world.

S2470518: Next Generation Science Standards

Make observations (firsthand or from media) to collect data that can be used to make comparisons.

S2470551: Next Generation Science Standards

Patterns in the natural world can be observed, used to describe phenomena, and used as evidence.

S2470526: Next Generation Science Standards

Events have causes that generate observable patterns.

S2470552: Next Generation Science Standards

Systems in the natural and designed world have parts that work together.

S2470878: Next Generation Science Standards

A system can be described in terms of its components and their interactions.

S2471389: Next Generation Science Standards

Systems may interact with other systems; they may have sub-systems and be a part of larger complex systems.
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