What blocks can you use to make a trapezoid

Explain or show your reasoning. How is the pattern in this activity the same as the pattern you saw in the previous activity? How is it different? Build a scaled copy of your assigned shape using a scale factor of 2. Use the same shape blocks as in the original figure. Start building a scaled copy of your assigned figure using a scale factor of 3. How many blocks would it take to build scaled copies of your figure using scale factors 4, 5, and 6? How many blocks do you think it would take to build a scaled copy of one yellow hexagon where each side is twice as long?

Three times as long? Do you see a pattern for the number of blocks used to build these scaled copies? Explain your reasoning. Students may forget to check that the lengths of all sides of their shape have been scaled and end with an inaccurate count of the pattern blocks.

Remind them that all segments must be scaled by the same factor. The goal of this discussion is to ensure that students understand that the pattern for the number of blocks in the scaled copies depends both on the scale factor and on the number of blocks in the pattern. Poll the class on how many blocks it took them to build each scaled copy using the factors of 2 and 3.

Record their answers in the table. Invite selected students to share the pattern that their groups noticed and used to predict the number of blocks needed for copies with scale factors 4, 5, and 6. Record their predictions in the table. In this activity, students transfer what they learned with the pattern blocks to calculate the area of other scaled shapes MP8. In groups of 2, students draw scaled copies of either a parallelogram or a triangle and calculate the areas.

Then, each group compares their results with those of a group that worked on the other shape. They find that the scaled areas of two shapes are the same even though the starting shapes are different and have different measurements and attribute this to the fact that the two shapes had the same original area and were scaled using the same scale factors. One parallelogram base 5, height 2.

One triangle base 4, height 5. While students are not asked to reason about scaled areas by tiling as they had done in the previous activities , each scaled copy can be tiled to illustrate how length measurements have scaled and how the original area has changed.

Some students may choose to draw scaled copies and think about scaled areas this way. Select students using each approach. Invite them to share their reasoning, sequenced in this order, during the discussion. You will need the Area of Scaled Parallelograms and Triangles blackline master for this activity.

Distribute slips showing the parallelogram to half the groups and the triangle to the others. Give students 1 minute of quiet work time for the first question, and then time to complete the rest of the task with their partner. Students may not remember how to calculate the area of parallelograms and triangles. Make sure that they have the correct area of 10 square units for their original shape before they calculate the area of their scaled copies.

When drawing their scaled copies, some students might not focus on making corresponding angles equal. As long as they scale the base and height of their polygon correctly, this will not impact their area calculations. If time permits, however, prompt them to check their angles using tracing paper or a protractor.

Some students might focus unnecessarily on measuring other side lengths of their polygon, instead of attending only to base and height. If time is limited, encourage them to scale the base and height carefully and check or measure the angles instead.

Invite selected students to share their solutions. Ask questions such as:. Highlight the connection between the two ways of finding scaled areas. Point out that when we multiply the base and height each by the scale factor and then multiply the results, we are essentially multiplying the original lengths by the scale factor two times. Scaling affects lengths and areas differently.

When we make a scaled copy, all original lengths are multiplied by the scale factor. The area of the copy, however, changes by a factor of scale factor 2. The first rectangle has the vertical side labeled 2 and the horizontal side labeled 4.

The second rectangle has the vertical side labeled 6 and the horizontal side labeled Two horizontal dashed lines and 2 vertical dashed lines are drawn in the second rectangle dividing it into 9 identical smaller rectangles. We can see that the large rectangle is covered by 9 copies of the small rectangle, without gaps or overlaps.

Lengths are one-dimensional, so in a scaled copy, they change by the scale factor. Area is two-dimensional, so it changes by the square of the scale factor. The fact that the area is multiplied by the square of the scale factor is true for scaled copies of other two-dimensional figures too, not just for rectangles.

In English-speaking countries outside of North America, the equivalent term is trapezium. The parallel sides may be vertical , horizontal , or slanting. In these figures, the other two sides are parallel, too and so they meet not only the requirements for being a trapezoid quadrilateral with at least one pair of parallel sides but also the requirements for being a parallelogram. The definition given above is the one that is accepted within the mathematics community and, increasingly, in the education community.

Many sources related to K education have historically restricted the definition of trapezoid to require exactly one pair of parallel sides. This narrower view excludes parallelograms as a subset of trapezoids, and leaves only the figures like , , and.

Students use Pattern Blocks to develop the concept of equivalence while working informally with halves, thirds, and sixths. This helps them develop an intuitive understanding of probability. Frogs on a Log. Student learn to write number sentences for word problems. Using Pattern Blocks in the intermediate grades gives students spatial problem-solving experience, leading to the use of fractional notation to describe what they build.

Pattern Blocks are also great for aligning geometry to number patterns. Other excellent skills to teach using these manipulatives are sorting, counting, comparing, and graphing. Here are 3 activities for getting to know Pattern Blocks and to begin using them to learn and understand the math that they represent.

A Seat at the Table. Students investigate the perimeter of polygons and composite shapes in order to solve problems. They also determine the perimeter of those shapes.

Students will classify and sort 2-dimensional shapes based on attributes, using formal language. Patterns All Around. Hands-on manipulatives continue to be an effective and powerful tool to build understanding and apply knowledge for students in the middle grades.

Pattern Blocks provide concrete examples to help students visualize problems and keep them interested and engaged in classroom lessons. Pattern Blocks can be used to further a deep understanding of geometry, measurement, algebra, statistics and probability, and more. Here are 3 activities for getting to know Pattern Blocks and beginning to use them to learn and understand the math they represent. Pattern Block Riddles. Students use deductive reasoning while working with fractions and percents as they compare the area of geometric figures.

The store will not work correctly in the case when cookies are disabled. Home Learning About Pattern Blocks. Pattern Blocks. Shop Now. Pattern Blocks Explore fractions and learn how to recognize fractional equivalence. View all. Sets Small group and classroom sets are available. Accessories A wide variety of accessories are available. Learning About Pattern Blocks.

Exploring Pattern Blocks Working With Pattern Blocks Assessing Students' Understanding A set of Pattern Blocks consists of blocks in 6 geometric, color-coded shapes: green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons. The following are just a few of the possibilities: When playing "exchange games" with the various sizes of blocks, students can develop an understanding of relationships between objects with different values such as coins or place-value models.

When trying to identify which blocks can be put together to make another shape, students can begin to build a base for the concept of fractional pieces. When the blocks are used to completely fill in an outline, the concept of area is developed.

If students explore measuring the same area using different blocks they learn about the relationship of the size of the unit and the measure of the area. When investigating the perimeter of shapes made with Pattern Blocks, students can discover that shapes with the same area can have different perimeters and that shapes with the same perimeter can have different areas.

When using Pattern Blocks to cover a flat surface, students can discover that some combinations of corners, or angles, fit together or can be arranged around a point. When finding how many blocks of the same color it takes to make a larger shape similar to the original block which can be done with all but the yellow hexagon , students can discover the square number pattern-1, 4, 9, 16,