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Integrating Measurement and Data into Our Daily Practice

By April 19, 2018Uncategorized

You don’t have time to wait, integrate measurement and data standards into your problem solving time today!

Typically, measurement and data (MD) is a unit that comes at the end of the year or the end of the textbook.  It is something that we may or may not get to and usually do not have the luxury of delving into it deeply. However, just because it has always been that way does not mean it has to continue to be that way. When posing problems we can begin to integrate the standards for measurement and data with relative ease. From past experience, teachers usually introduce the measurement and data standard 2-3 weeks before the end of the year or just prior to state testing. This is a “risky” practice for several reasons: 1) that’s not enough time and everyone is rushed, you can’t learn well if you’re stressed, 2) MD is linked to almost all the standards on the SBAC assessment, 3) many data and measurement standards have their beginnings in the primary grades and are built upon in grades 3-5 and 6-8, establishing basic understandings in middle school is extremely difficult.

Graphs

Instead of just asking students in grades K-6 to show their understanding of a problem with an equation, ask them to show it with a graph, line plot, or coordinate grid instead. Consider what the following problem would look like using one quadrant of a coordinate grid: Mary ran 5 kilometers a day to get ready for a marathon. How many kilometers did she run in 9 days? Try it out for yourself. I can also see this same problem being done with an input output table or a ratio table. Get out some grid paper or download coordinate grids from the internet. Ask students to represent their thinking on a table or grid when they are done solving the problem.

In the primary grades, we can introduce students to bar graphs early on. Mary saw 4 butterflies on Monday. She saw 6 butterflies on Tuesday. How many butterflies did Mary see in all? Ask kids to complete the graph when they are done solving on the back of their papers or construct one altogether as a class during a warm-up. Don’t wait until the end of the year, do it tomorrow.

Geometry

I never realized the importance of geometry, until I realized the importance of geometry. It is everywhere!

Students can combine shapes to compose new ones. Two trapezoids make a hexagon, a rectangle is composed of triangles, hence the formula for a rectangle is A= b x h and the formula for the area of a triangle is A = 1/2 b x h this is both a kindergarten and sixth grade standard.

Kindergarten StandardCCSS.MATH.CONTENT.K.G.B.6
Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

Sixth Grade StandardCCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Opposite sides of a rectangle are equivalent. When students KNOW this fact, then determining the missing area or perimeter is a piece of cake. Therefore, when talking about arrays, areas, or rectangles, talk about the relationship between them all. Algebraic thinking is linked to geometry. Get out some paper or better yet get some graph paper and try this out for yourself. Once you see this for yourself, ask your kids to apply this fact to solve an area problem. It makes things much easier for you.

Measurement

Never miss an opportunity to integrate a MD standard.

Mary found 28 cents on the ground. She added it to the 33 cents in her pocket. How much money does she have now? Draw the coins she could have used. You get to work on regrouping and MD at the same time.

Mary jumped 18 inches. John jumped 2 feet. Who jumped further? Get out a ruler and compare.

Mary baked a pie. She cut and ate a slice that was 1/4 of the pie. What type of angle did she cut from the pie. How much of the pie is left in degrees and angles?

Mary the architect drew a ___ angle. She actually needs to make a ___  angle. How much larger must she make her angle?

Mary drew an acute angle, how much does she need to add to make an obtuse angle? If they ask exactly how large the acute angle was, great! Let them debate and figure it out.

The measurement and data standards are not in addition to the math you are already doing, it is integral to the math you are doing. Without an understanding of the multiple representations and relationships within mathematics, students are missing big pieces of the picture, which will make mathematics that much more challenging and expensive (tutors) going forward.

Which measurement and data standard will you connect to tomorrow?