math-2017:1.G.1math-2017:1.G.2
math-2017:1.G.1 Distinguish between defining attributes, e.g., triangles are closed and three-sided, versus non-defining attributes, e.g., color, orientation, overall size; build and draw shapes that possess defining attributes.
math-2017:1.G.2 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. Students do not need to learn formal names such as "right rectangular prism."
Learning goal: Distinguish defining shape attributes from features such as color, size or orientation, construct matching shapes, and combine shapes to make and remake composite shapes. Use paper pieces and suitable blocks. Identifying a completed illustration is useful preparation, but the target requires the learner’s own building and drawing.
A defining attribute helps determine what kind of shape an example is. A triangle must have a closed boundary of three straight sides. Its color and whether a point faces upward do not define it. Show differently sized and oriented triangles, then an open three-segment path. The open path fails the closed-boundary requirement even if it looks approximately triangular.
Build a triangle with sticks and draw it. Ask the learner to check its defining features and describe one feature that could change without changing its name. For a rectangle, check for a closed shape with four straight sides and four square corners; for a square, include equal side lengths as well. Do not teach that every four-sided figure is a square or that a rotated square stops being one.
Compose smaller shapes by fitting them together without accidental gaps or overlaps when the goal is a single filled region. Two matching right triangles whose two shorter sides are equal can form a square, and two equal squares can form a rectangle. Three matching triangles with equal sides can form a trapezoid, and two such trapezoids can then form a hexagon. Two matching quarter-circles make a half-circle when, without overlapping, their square corners meet at the same point and a whole straight edge of one lies along a whole straight edge of the other. A half-circle and another matching half-circle can form a circle when their whole straight edges touch. Four matching quarter-circles can also form a circle when all four square corners meet at its center. The arrangement matters: with the square corners at opposite ends of the shared edge, two quarter-circles do not make a half-circle, and not every pair of triangles makes a square.
A composite shape can become a building piece for another design. After forming a square from two triangles, combine that square with another square to make a rectangle. The learner can describe the new design as two squares or as the underlying smaller pieces. These are different ways to organize the same shape, not extra pieces that have appeared.
Solids can also be combined. Two matching cubes placed face to face can form a larger rectangular-prism shape (a box shape). A cone set on top of a cylinder with a matching circular face makes a new composite, such as a model tower with a pointed roof, and that tower can then be joined to a box-shaped block to make a larger building. Explain the difference between an actual solid construction and a flat drawing showing it. Children do not need to memorize technical phrases such as right rectangular prism to describe the composite using appropriate informal language.
The illustrated two-triangle square is one starting composition, not the only possible outcome from all materials. Its diagonal marks the component boundary inside the whole square. Trace the outside when naming the whole and trace a smaller boundary when identifying a component.
Worked example 1: Defining versus decorative. A blue triangle and a red, turned triangle both have three straight sides and a closed boundary. Their colors and orientations differ but their shape category remains triangle. A blue open path is not made a triangle by its color.
Worked example 2: Reuse a composite. Join the two matching triangles from the picture into a square. Place that new square beside another equal square, with edges aligned, to make a rectangle. Name the square as a component of the larger rectangle and the triangles as components within the square.
Worked example 3: Solid construction. Put two equal cubes together along whole faces. The result has a longer overall solid form. A line drawn around a picture is not a second actual solid; identify the physical cubes and the combined object separately.
Guided construction: Sort examples by defining features, build and draw one of them, and explain which visual changes preserve the name. Then compose with triangles, squares, rectangles, trapezoids, half-circles or quarter-circles as available. Use safe blocks for an optional solid example.
Independent tasks: Build and draw a shape meeting a stated definition; identify a non-defining feature; create a composite; and use that composite to create another shape. Explain the parts at both stages. Include enough different pieces that the child is constructing rather than merely copying one familiar puzzle.
Assessment and feedback: Credit the defining features, faithful drawing, correctly fitted composition and explanation of reused components. If a learner counts an internal edge as part of the whole’s outside boundary, trace the boundaries separately. If a construction overlaps unintentionally, separate and reassemble the pieces. Extend by finding two different arrangements using the same original components and comparing the resulting boundaries.
An adult may read the prompts aloud. Answer independently with words, objects, drawings or a demonstration before opening the answer guide. Award 1 point for a correct result or claim and 1 point for a matching explanation or demonstration; where a question asks only for a result (a corrected sentence, a spelling, a count), a fully correct result earns both points, and the answer guide shows what a complete response contains. Record prompting separately. The total (two points per question) is local practice feedback, not an Ohio proficiency level.
Which of these are defining attributes of a rectangle: four straight sides, blue color, four square corners, large size, lying on its long side?
Four straight sides that close the shape and four square corners define a rectangle. Color, size and the way it is turned do not.
A shape is made of three straight sticks, but two of the ends do not meet. Is it a triangle? Explain, then draw a shape that is a triangle.
No. A triangle is closed; an open path of three sticks is missing that defining attribute. A correct drawing is closed and has three straight sides; any size, color or turn is acceptable.
Does every pair of triangles make a square?
No. The pieces and their arrangement must fit the square’s defining boundary.
Describe a composite that can be reused in another shape.
Example: two matching right triangles like the pictured ones make a square, then that square joins another square to make a rectangle. Any example with two stages, in which the first new shape is used as one piece of the second, earns credit.
Two matching quarter-circles are placed so that their square corners touch at the same point and a whole straight edge of one lies along a whole straight edge of the other, with no overlap. What shape do they make? Then two of those new shapes are joined with their whole straight edges touching and no overlap. What shape is made now?
First a half-circle, then a circle. The half-circle is a composite that is used again as a piece of the circle.
Two matching cubes are joined so that one whole face of each touches exactly, with no overlap. Describe the new solid. Then describe something larger you could build with that new solid as one piece.
The two cubes make a box shape that is two cubes long. Example of reusing it: place a second two-cube box beside it to make a wider box shape made of four cubes. Any larger solid that uses the two-cube box as one piece earns credit.
With paper shapes: join smaller shapes to make a larger shape and draw it. Then use that whole new shape as one piece of another, larger shape. Explain the parts at both stages.
Performance review: correct defining features, a matching drawing, a valid first composition and a new composition using it; explain the parts at both stages.