math-2017:K.G.5math-2017:K.G.6
math-2017:K.G.5 Model shapes in the world by building shapes from components, e.g., sticks and clay balls, and drawing shapes.
math-2017:K.G.6 Combine simple shapes to form larger shapes.
Learning goal: Model shapes using components and drawings, then combine simple shapes to form larger shapes. Use craft sticks with blunt ends, large reusable connectors, paper triangles and squares. An adult should supervise materials. The learner’s own construction is essential; recognizing a finished picture is not enough to demonstrate this target.
Build a triangle using three straight sticks whose ends meet. The three sides must form a closed boundary. A gap leaves an open path rather than the intended triangle. Draw the model and compare the drawing to the construction: both should show three sides and three corners. The drawing does not need decorative detail to communicate the shape.
Build a square using four equal sticks and connectors. Having four equal sides is not the only feature to check: the corners also need to be square corners. Gently push a jointed model sideways and notice that a slanted four-sided shape can retain equal sides without remaining a square. Use the corner of a paper square as an informal comparison tool.
Relate models to the environment. Build a rectangle resembling a window frame or a triangle resembling part of a roof. The model captures selected geometric features, not every detail of the real object. A roof may be a three-dimensional structure while one end or section looks triangular. Name the part being modeled so the representation is not confused with the entire object.
Combine smaller shapes by arranging them edge to edge. The illustrated example has two matching right triangles, each with two equal shorter sides, meeting along their slanted edges to make a square. The outside boundary is the larger square; the diagonal line inside marks the two component triangles. That internal line does not add an extra side to the outside square. Trace the outer boundary separately from the dividing line.
Explore another composition: place two equal squares side by side with complete edges touching. Their outside boundary forms a rectangle. Slide them apart and the gap breaks the single composed region. Rotate or reposition pieces to search for different outcomes, but do not assume that any two triangles automatically make a square. Their sizes, angles and arrangement must fit the desired boundary.
Worked example 1: Repair an open model. Three sticks lie near one another, but two ends do not meet. Name the intended triangle, then move the sticks until they form a closed three-sided boundary. Count the sides and corners to check the result instead of accepting a vaguely triangular arrangement.
Worked example 2: Read a divided square. A square is cut from one corner to the opposite corner, producing two triangles. Rejoin them with no overlap or gap. Trace the outside: four sides. Then trace either piece: three sides. The whole and the parts have different boundaries.
Worked example 3: Combine squares. Two equal squares touch along one complete side. Trace the new outside rectangle. The shared edge is inside the composition; do not count it as a separate outer side. Separate the pieces to verify that the two original squares remain available for another design.
Guided practice: Construct a triangle and a rectangle, then draw each. Give partners two matching paper triangles and ask them to make the pictured square. Let them turn pieces and check gaps themselves before supplying a correction. Ask the child to point separately to a component and to the complete composition.
Independent tasks: Build a shape resembling a classroom object and explain which part it models; draw the construction; combine two or more simple pieces into a larger shape; and trace the larger outside boundary. Photographing the result for private classroom review is optional; an adult observation record is sufficient.
Assessment: Credit the construction for the intended features, the drawing for a recognizable matching model, and the composition for correctly fitting components. Ask the learner to explain the boundary rather than only name the result. If two pieces overlap, separate them and discuss which area has been covered twice. Extend by finding two different arrangements from the same pieces and describing which new outside shapes result.
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.
You want to build a square from sticks and clay balls. How many sticks and how many clay balls do you need, and what must you check?
Four sticks of equal length and four clay balls, one at each corner. Check that the shape is closed and that all four corners are square corners.
Two triangles form the pictured square. How many sides does the outside square have?
Four. The internal diagonal is not an additional outside side.
Does every pair of triangles make a square?
No. Their sizes, angles and arrangement must fit a square without gaps or overlap.
Four equal squares are pushed together, two on top and two below, with whole sides touching. What larger shape do they make?
A larger square. Each side of it is two small sides long, and its corners are square corners.
Draw a shape that models part of a classroom object and name that part.
Example: a rectangle modeling the flat outline of a window. The drawing and explanation should refer to the same part.
Why should the outer boundary be traced separately from the internal dividing line?
The outer boundary defines the composed shape; internal lines identify its component pieces.