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Pitfalls to avoid when teaching 3.MD.A.2

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3.MD.A.2 is focused on using the four operations to solve word problems involving masses of objects or liquid volumes that are in the same units.

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Students in 3rd grade learn to solve a variety of problems involving measurement. This standard, 3.MD.A.2, is focused on using the four operations to solve word problems involving masses of objects or liquid volumes that are in the same units. Students also measure and estimate using the standard units of grams, kilograms, and liters. It is important for students to estimate and draw visual representations.

This scale shows the mass, in grams, of 100 paper clips.Based on the mass of 100 paper clips, what is the mass of 10 paper clips?

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100 / 100 = 1 1 gram = 1 paperclip 1 gram x 10 paper clips = 10 grams

Students in 3rd grade learn to solve a variety of problems involving measurement. This standard, 3.MD.A.2, is focused on using the four operations to solve word problems involving masses of objects or liquid volumes that are in the same units. Students also measure and estimate using the standard units of grams, kilograms, and liters. It is important for students to estimate and draw visual representations.

This scale shows the mass, in grams, of 100 paper clips.Based on the mass of 100 paper clips, what is the mass of 10 paper clips?

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Many of the problems for 3.MD.A.2 should support the Grade 3 emphasis on multiplication and the mathematical practices of making sense of problems and representing them with equations, drawings, or diagrams.

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Students need an understanding of units so they can solve problems. For example, students need to know that a liter is a unit of measurement for the volume of liquids. But they do not need to convert units yet.

Many of the problems for 3.MD.A.2 should support the Grade 3 emphasis on multiplication and the mathematical practices of making sense of problems and representing them with equations, drawings, or diagrams.

This standard is about the typical units of measurement: grams, kilograms and liters and milliliters.

Jim buys a soccer ball and a basketball at a sports store. The mass of the soccer ball is 843 grams and the mass of the basketball is 972 grams. In grams, how much greater is the mass of the basketball than the mass of the soccer ball?

One step word problems are the boundary for this standard.

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem

It is important to incorporate all four operations in examples of word problem samples (multiplication, division, addition, and subtraction).

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Unpack the standard

2.MD.B.5

2.MD.A.1

2.MD.A.3

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.B.5Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

2.MD.A.3

2.MD.A.1

2.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

Connections to Prior Learning

Click on the yellow index cards below to learn about how these standards connect to 3.MD.A.2.

3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

3.MD.B.3Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

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Avoid moving too quickly through any problem. Instead of solving steps with a quick algorithm, allow students time to explore, discuss, and draw.

Avoid pitfall #1!

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Samuel has 4 large boxes. Each box has the same mass. One box has a mass of 7 kilograms. What is the total mass, in kilograms, of all Samuel’s boxes?

Avoid moving too quickly through any problem. Instead of solving steps with a quick algorithm, allow students time to explore, discuss, and draw.

Avoid pitfall #1!

Samuel has 4 large boxes. Each box has the same mass. One box has a mass of 7 kilograms. What is the total mass, in kilograms, of all Samuel’s boxes?

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Avoid moving too quickly through any problem. Instead of solving steps with a quick algorithm, allow students time to explore, discuss, and draw.There are multiple methods to solve this problem: addition, visual labeling, multiplication. Allow students time to productively struggle with the task.

Avoid pitfall #1!

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Avoid prescribing a specific strategy to solve estimation problems. Students may need to experiment with estimation.

Avoid pitfall #2!

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Molly and Janet have beakers of the same size. The beakers are filled with different amounts of water as shown.

Avoid prescribing a specific strategy to solve estimation problems. Students may need to experiment with estimation.

Avoid pitfall #2!

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Typography and Font Size

Three Columns

One Column

Two Columns

One column layout with header up to two lines of text.

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus.

One column layout without a left aligned header.

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa. Cum sociis natoque penatibus et magnis dis parturient montes, nascetur ridiculus mus.

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa.

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa.

Two column layout with header up to two lines of text.

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa.

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget dolor. Aenean massa.

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion:

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Aenean commodo ligula eget

Lorem ipsum dolor sit amet, consectetuer adipiscing elit.

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As a nonprofit dedicated to educational equity, we need to know our work has an impact. And so do our 800+ partner schools and systems. Harvard University’s Center for Education Policy Research conducted a randomized control study funded by a prestigious i3 (Investing in Innovation) grant from the DOE. They found that when schools have the right basic conditions in place and partner with ANet, they achieve six months of additional learning over a two-year period.

4.NF.B.4.a is about students extending their understanding of multiplication to include fractions. It’s NOT about students performing multiplication with fractions but rather, about developing their conceptual understanding of a fraction as the numerator times the unit fraction with the same denominator.

4.NF.B.4.a is about students extending their understanding of multiplication to include fractions. It’s NOT about students performing multiplication with fractions but rather, about developing their conceptual understanding of a fraction as the numerator times the unit fraction with the same denominator.

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ANet is a nonprofit dedicated to the idea that every child deserves an excellent education and the opportunities it provides. How do we work toward this vision? Through an integrated system of tools and training, ANet helps schools and districts boost student learning with great teaching that’s grounded in learning standards, informed by data, and built on the successful practices of educators around the country.

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ANet is a nonprofit dedicated to the idea that every child deserves an excellent education and the opportunities it provides. How do we work toward this vision? Through an integrated system of tools and training, ANet helps schools and districts boost student learning with great teaching that’s grounded in learning standards, informed by data, and built on the successful practices of educators around the country.

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Then, to the power of all parentheses and numbers in the power, from left to right (from the beginning to the end of the example). Perform the remaining steps in the usual order

If the example contains a numeric or alphabetic expression in parentheses that needs to be raised to a power, first perform all actions inside the parentheses

Order of operations and exponentiation.

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Let's make sure the proportion is correct:

Basic Property of the Proportion

Now write down the proportion and draw a cross over the equal sign with a pencil By drawing a cross, it is much easier to make the right product (to fulfill the basic property of the proportion)

If the proportion is correct, that is, the ratios that make up the proportion are really equal, then the following is true for the proportion: To apply the rule correctly, we suggest that you memorize the (cross) "X" rule. Let's examine it with an example of the proportion:

4x growth

Tier 1

2x growth

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3X ELA 2X MATH

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In New York, ANet schools made proficiency gains that were 3x more in ELA and 2x more in math than non-ANet schools in the state.

in Michigan and Ohio, Atet partners outpaced their peer schools in economically- disadvantaged communities by more than two times in ELA and Math.

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in Colorado, ANet partner schools outpaced statewide gains in ELA and Math for the third year in a row.

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Click on the index cards below to learn how these standards connect to 4.NF.B.4a

Multiply or divide to solve word problems involving multiplicative comparison, e.g. by using drawings and equations with a symbol for the problem, distinguish multiplicative comparison from additive comparison.

4.OA.A.2

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.

3.OA.A.1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.A.1

4.NF.B.4a

Understand a fraction a/b as a multiple of 1/b. For example, us a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

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Connections to Prior Learning

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12. Teachers (characters and environment)

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12. Place

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12. Fragments and parts

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12. Teacher - Neutral Expression

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12. Teacher - Neutral Expression

3. Watch out

2. Oh no

1. Beware Expression

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14. Teacher - Watch out / Oh no / Beware Expression

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14. Teacher - Watch out / Oh no / Beware Expression

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15. Teacher - Aha!

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16. Student - Thinking

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17. Student - Aha!

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18. Group of 3 Students working

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18. Group of 4 Students working

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19. Teacher Standing in Background

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19. Teacher Standing in Background

10×100=1000

10×10=100

100+100+100+100+100+100+100+100+100+100

10+90=100

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20, 21, 22, 23 Popsicle Sticks or other classroom object - 1, 10, 100, 1000 item

10×100=1000

10×10=100

100+100+100+100+100+100+100+100+100+100

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20, 21, 22, 23 Popsicle Sticks or other classroom object - 1, 10, 100, 1000 item

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10+10+10+10+10+10+10+10+10+10=100

1×10=10

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20, 21, 22, 23 Popsicle Sticks or other classroom object - 1, 10, 100 item

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10

10

10

10

10

10

10

10

10

10

100

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20, 21, 22, 23 Popsicle Sticks or other classroom object - 1, 10, 100 item

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24. Circle with "pie slices" - all variations of filled slices (1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 7/7)

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25. Bar Model - all variations of filled bars

4 major lines and smaller half, quarter, and eight marks

4 major lines and smaller half marks

4 major lines and smaller half and quarter marks

4 major lines

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26. Number Line

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26. Number Line

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26. Number Line

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26. Number Line

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26. Number Line

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30. Fractional Grids (Full 100, Broken up into 10s, Broken up into 1s)

100

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30. Fractional Grids (Full 100, Broken up into 10s, Broken up into 1s)

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30. Simple explanation of fractions (toys and parts)

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10

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33. Frame - Anchor Chart or Whiteboard

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33. Frame - Anchor Chart or Whiteboard

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33. Frame - Anchor Chart or Whiteboard

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33. Frame - Anchor Chart or Whiteboard

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33. Frame - Anchor Chart or Whiteboard

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35. Caution Cone

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36. Something for "Don't take shortcuts" or "Don't use this trick"

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37, 38, 39, 40, 41. Symmetry in the natural and in the artificial environment

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37, 38, 39, 40, 41. Symmetry in the natural and in the artificial environment