CLASS 3 MATHS WORKSHEET LESSON 5

Fun with Shapes (Preparatory Stage Math)

Concepts • Computational Skills • Problem-Solving & Modeling • 10 questions each • 40% Easy, 40% Average, 20% Challenging • One toggle shows Answer + Solution

Worksheet A: Concepts

Easy

Q1. In Amma’s rangoli made on dots, name any three shapes that commonly appear (e.g., square, triangle, circle-like arcs) [lesson context].

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Answer

Square, triangle, and curved-line petals/arcs.

Solution

Rangoli on dot grids mixes straight-edged polygons (squares/triangles) and curved motifs, as shown in the chapter prompts on dot patterns and naming shapes.

Easy

Q2. Which shapes can be traced by opening a small cardboard box flat (net)? Name two face shapes seen on such a box [flattening boxes].

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Answer

Rectangles and squares.

Solution

Cuboid faces trace as rectangles; a cube’s faces trace as squares; flattening shows face shapes on the net clearly.

Easy

Q3. State one difference between a square and a rectangle in simple words [same-to-same section].

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Answer

All sides equal in a square; only opposite sides equal in a rectangle.

Solution

Both have four right corners, but equality of all four sides holds only for squares, not for general rectangles.

Easy

Q4. Use paper folding of a circle (paper plate) to find the center: what do the folds show about the longest line through the circle and where folds meet [circle activity]?

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Answer

The longest fold-line is a diameter; fold lines meet at the center.

Solution

Folding in half produces diameters; their intersection marks the center of the circle clearly.

Average

Q5. Classify each as “flat only,” “curved only,” or “both”: square, rectangle, circle, cylinder (think faces/surfaces) [faces/curves focus].

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Answer

Square: flat only; Rectangle: flat only; Circle (disc face): curved edge but flat face; Cylinder (solid): both flat (two circles) and curved (side).

Solution

Polygons have flat edges/faces; a cylinder combines flat circular faces with a curved lateral surface in 3D.

Average

Q6. Trace all faces of an eraser (cuboid). Which shapes do the face tracings make, and can any face be a triangle [tracing faces prompt]?

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Answer

Rectangles; no triangular faces.

Solution

A cuboid’s six faces are rectangles (some may be equal squares); triangles don’t occur as faces on a cuboid.

Average

Q7. State two properties common to both squares and rectangles in classroom terms [sides/corners].

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Answer

Both have 4 sides; both have 4 square corners (right angles).

Solution

They are quadrilaterals with right angles at each corner and straight sides forming closed shapes.

Average

Q8. Using two paper strips, show a corner that is “square,” and describe how to test if a table corner is a square corner [strip test].

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Answer

Make an L with strips; if both edges align with table edges without gaps, it’s a square corner.

Solution

Two perpendicular strips model a right angle; matching to an object corner checks if it is a square corner.

Challenging

Q9. Compare two rangolis: name one similarity and one difference using “straight vs curved” or “square corners vs arcs” language [rangoli comparison].

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Answer

Similarity: both use dot-grid symmetry; Difference: one has more straight-edged squares, the other uses curved petals.

Solution

Visual patterns can share structure yet differ by edge types, demonstrating multiple design choices on dots.

Challenging

Q10. Explain why folding a square and piling square cutouts shows “all square corners are same,” and whether rectangle corners show the same property [corner sameness].

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Answer

Yes for both; square and rectangle corners are all right angles and match on piling.

Solution

Right angles are congruent; superposing corners demonstrates equality for all corners in these shapes.

Worksheet B: Computational Skills

Easy

Q1. Count rectangles: in a 1×3 arrangement of equal small rectangles laid in a row, how many rectangles can be seen (small and large) [counting rectangles idea]?

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Answer

6 (three 1×1, two 1×2, one 1×3).

Solution

Combine adjacent small rectangles to form longer ones; count by lengths 1, 2, and 3.

Easy

Q2. A cube has how many faces and how many corners; a cuboid has how many faces and how many corners [faces/corners recall]?

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Answer

Cube: 6 faces, 8 corners; Cuboid: 6 faces, 8 corners.

Solution

Both are 3D with six flat faces and eight vertices; face shapes differ (squares vs rectangles).

Easy

Q3. A standard rectangle has how many equal sides, and which sides are equal to each other [rectangle properties quick]?

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Answer

Two pairs; opposite sides are equal.

Solution

Left equals right, top equals bottom; adjacent sides can differ in length.

Easy

Q4. In a square, how many sides and corners, and what is special about side lengths [square recap]?

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Answer

4 sides, 4 corners; all sides equal.

Solution

A square is a special rectangle with all sides same and right corners.

Average

Q5. Count triangles: If a rangoli grows by adding one full row of equal small triangles each time, the first three figures have 1, then 3, then 6 triangles. Predict the next two totals [triangle-growth task].

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Answer

10 and 15.

Solution

Triangular numbers add row lengths 1+2+3+…; next sums are 1+2+3+4=10 and +5=15.

Average

Q6. Using matchsticks: make one square corner with two sticks; how many sticks are needed to model four square corners placed apart (not a single square) [corner modeling]?

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Answer

8 sticks.

Solution

Each right angle uses two sticks; four separate corners total eight sticks.

Average

Q7. On a dot grid, draw one small square; then imagine “two bigger squares around it.” How many total concentric squares does that make [square growth prompt]?

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Answer

Three concentric squares.

Solution

Original plus two larger around it creates three total nested squares on the grid.

Average

Q8. “Find my rectangle” on dots: if two opposite vertices are marked, what must be true about the other two points to complete a rectangle [rectangle completion idea]?

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Answer

They must be at equal offsets forming equal opposite sides and parallel pairs.

Solution

Construct from the midpoint and equal horizontal/vertical distances to ensure parallel, equal opposite sides.

Challenging

Q9. Count rectangles in a 2×3 grid of small equal rectangles (two rows, three columns) [counting rectangles challenge].

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Answer

18 total (6 small 1×1, 4 of 1×2 per row ×2 rows = 8, 2 of 1×3 per row ×2 rows = 4, plus 2 of 2×1 per column ×3 columns = 6? Adjust: correct method gives 18 by combinations C(3+1,2)*C(2+1,2)=C(4,2)*C(3,2)=6*3=18).

Solution

Choose two vertical grid lines and two horizontal grid lines: combinations count all possible rectangles systematically.

Challenging

Q10. Using square cutouts, how many different shapes can be formed by joining 2 squares, and by joining 3 squares edge-to-edge (name the idea) [polyomino prompt]?

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Answer

With 2 squares: 1 domino; with 3 squares: 2 trominoes (straight and L).

Solution

Edge-joining squares creates polyominoes; up to rotation/reflection there is one 2-omino and two 3-ominoes.

Worksheet C: Problem-Solving & Modeling

Easy

Q1. Envelope making from a square: after folding corners, which final shape forms the flap, and what original shape ensures all sides align neatly [envelope task]?

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Answer

A triangular flap; starting with a square ensures even folds.

Solution

Square symmetry makes opposite corners meet; folded corner creates a triangle flap that closes neatly.

Easy

Q2. Name three classroom objects with rectangular faces (trace and list) [rectangular faces observation].

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Answer

Book cover, whiteboard, eraser face (examples).

Solution

Many everyday solids expose rectangular faces; tracing confirms the shape property in context.

Easy

Q3. Choose the tile that fits a square corner of a table: a right-angle wedge or a rounded wedge, and explain in one word [square corner fit].

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Answer

Right-angle wedge; square.

Solution

Square corners are right angles; a right-angled tile fits exactly into the corner.

Easy

Q4. Circle center task: after two perpendicular folds on a round paper, what is the special point where folds cross, and which line is longest across the circle [circus with circles]?

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Answer

Center; diameter.

Solution

Intersecting diameters reveal the center; a diameter is the circle’s longest straight chord.

Average

Q5. Odd-one-out: among shapes with only square corners, only curved edges, and mixed corners, pick one odd item in each trio and justify with “corner/edge” language [odd-one-out sets].

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Answer

Examples vary; justification must cite square vs curved corners/edges.

Solution

Differentiate by presence of right angles vs curves; attribute-based sorting supports reasoning.

Average

Q6. Complete a broken rectangle by choosing correct left-side pieces to fill gaps on the right (describe selection rule in one sentence) [rectangle completion].

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Answer

Pick pieces whose straight edges align to make opposite sides equal and parallel.

Solution

Edge matching and equal length ensure the completed outline remains a rectangle with right corners.

Average

Q7. Using four triangles cut from a square, make two different composite shapes and name one difference between them (e.g., symmetry) [triangles from square].

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Answer

Examples vary; one shape may have a line of symmetry, the other may not.

Solution

Joining right triangles yields varied polygons; properties differ by arrangement (symmetry/angles).

Average

Q8. Continue a border pattern that alternates straight and curved lines: if the last three units are straight, curved, straight, what are the next two [line borders task]?

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Answer

Curved, straight.

Solution

Repeat the two-step motif; ABAB… gives the next terms by alternation.

Challenging

Q9. Count squares made by joining 4 equal small squares edge-to-edge in an L-shape; how many total squares of any size are present [make-with-squares challenge]?

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Answer

5 (four 1×1, one 2×2 formed by a 2×2 block if present; for an L of 4 without 2×2 block, total is 4 only—explain based on layout).

Solution

Check if any 2×2 completes; in a pure L tetromino, no full 2×2 appears, so only four 1×1 squares.

Challenging

Q10. Using tangram pieces, can a perfect rectangle be formed with all seven pieces; if yes/no, state a simple condition or note about fitting edges [tangram prompt]?

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Answer

Yes; edges must join without gaps/overlaps using all seven pieces.

Solution

Tangram admits rectangle solutions; alignment requires full use of pieces and straight boundary edges.

Two best activities

Activity 1: Rangoli on Dots — Straight vs Curved Remix

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Answer

Create two versions of the same rangoli on dot grids: one with mostly straight edges, one with curved arcs; then compare.

Solution

Provide dot sheets and shape cutouts/strings. Learners draw Version A with squares/rectangles/triangles; Version B with arcs/petals. Discuss similarities (symmetry, repeats) and differences (edge types, corners), linking to chapter tasks on rangoli, naming shapes, and comparing designs.

Activity 2: Box to Net to Build — Faces and Corners Lab

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Answer

Open real boxes to nets, trace faces, label corners, then rebuild paper models (cube/cuboid), and test corners with the strip right-angle tool.

Solution

Learners flatten small boxes to see rectangles/squares in nets, count faces/corners, rebuild as prisms, and verify right corners using two paper strips. Extend by folding a paper-plate circle to mark center/diameters, and by tracing rectangular faces on objects in class for a display wall.