Pattern Blocks
Pattern blocks are an excellent introduction to geometry and allow for exploring a wide range of patterning.
Standards
Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.
Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Kindergarten||Mathematical Practices|||K.G.1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.2. Correctly name shapes regardless of their orientations or overall size.||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.3. Identify shapes as two-dimensional (lying in a plane, “”flat””) or three- dimensional (“”solid””).||Common Core Mathematics||Kindergarten||Geometry||Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres)|||K.G.4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/””corners””) and other attributes (e.g., having sides of equal length).||Common Core Mathematics||Kindergarten||Geometry||Analyze, Compare, Create, And Compose Shapes|||K.G.5. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.||Common Core Mathematics||Kindergarten||Geometry||Analyze, Compare, Create, And Compose Shapes|||K.G.6. Compose simple shapes to form larger shapes. For example, “”Can you join these two triangles with full sides touching to make a rectangle?””||Common Core Mathematics||Kindergarten||Geometry||Analyze, Compare, Create, And Compose Shapes|||K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3||Common Core Mathematics||Kindergarten||Measurement And Data||Classify Objects And Count The Number Of Objects In Each Category|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 1||Mathematical Practices|||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 to possess defining attributes.||Common Core Mathematics||Grade 1||Geometry||Reason With Shapes And Their Attributes|||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.4||Common Core Mathematics||Grade 1||Geometry||Reason With Shapes And Their Attributes|||1.G.3. 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.||Common Core Mathematics||Grade 1||Geometry||Reason With Shapes And Their Attributes|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 2||Mathematical Practices|||2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.||Common Core Mathematics||Grade 2||Geometry||Reason With Shapes And Their Attributes|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||3.G.1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.||Common Core Mathematics||Grade 3||Geometry||Reason With Shapes And Their Attributes|||3.MD.8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.||Common Core Mathematics||Grade 3||Measurement And Data||Geometric Measurement: Recognize Perimeter As An Attribute Of Plane Figures And Distinguish Between Linear And Area Measures
1.2 Identify, describe, and extend simple patterns (such as circles or triangles) by referring to their shapes, sizes, or colors.||CA Mathematics||Grade Kindergarten||04. Statistics, Data Analysis, and Probability||1.0 Students collect information about objects and events in their environment.|||2.1 Identify and describe common geometric objects (e.g., circle, triangle, square, rectangle, cube, sphere, cone).||CA Mathematics||Grade Kindergarten||03. Measurement and Geometry||2.0 Students identify common objects in their environment and describe the geometric features.|||2.1 Describe, extend, and explain ways to get to a next element in simple repeating patterns (e.g., rhythmic, numeric, color, and shape).||CA Mathematics||Grade 1||04. Statistics, Data Analysis, and Probability||2.0 Students sort objects and create and describe patterns by numbers, shape, size, rhythm, or color.|||2.1 Identify, describe, and compare triangles, rectangles, squares, and circles, including the faces of three-dimensional objects.||CA Mathematics||Grade 1||03. Measurement and Geometry||2.0 Students identify common geometric figures, classify them by common attributes, and describe their relative position or their location in space.|||2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12 …; the number of ears on 1 horse, 2 horses, 3 horses, 4 horses).||CA Mathematics||Grade 2||04. Statistics, Data Analysis, and Probability||2.0 Students demonstrate an understanding of patterns and how they grow, and describe them in general ways.|||2.1 Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.||CA Mathematics||Grade 2||03. Measurement and Geometry||2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space.|||2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).||CA Mathematics||Grade 3||03. Measurement and Geometry||2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems.|||2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).||CA Mathematics||Grade 3||03. Measurement and Geometry||2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems.
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