Long Descriptions for Appendix C

Figure C.1: Gina’s Bike Ride

Figure shows five shaded circles inside an oval shape, labeled “Gina’s ride.” To show Gina’s mother’s ride, the same image (five shaded circles inside an oval shape) is repeated three times, showing a total of 15 circles. In illustration B, a line segment represents 5 miles (labeled “Gina, 5 miles”). Below that line segment a line segment three times that length is shown. The second line segment is comprised of three equal size parts joined as one length: The first 5-mile length is one color, the second 5-mile length is a different color, and the third 5-mile length is another color. This is labeled “Gina’s mother 5 miles + 5 miles + 5 miles.”

Figure C.3: Documentation of Jax’s Multiplication Method

The figure shows steps in Jax’s thinking. At the top of the figure is the 7 x 24 expression provided by the teacher. Annotation underneath the 24 with a “cherry diagram” illustrates how the 24 is composed of 20 + 4. The next two rows illustrate how Jax calculated with the resulting 20 and 4. First, they multiplied 7 x 20 to get 140. Next, they multiplied 7 x 4 to get 28. The final row shows the addition of the resulting sums from the prior two rows with the equation 140 + 28 = 168.

Figure C.8: Current Maps

The “Current Maps” shows Seal Beach with a pier on the right extending into the Pacific Ocean. Arrows on the water illustrate northeasterly wind, which is blowing in the direction of an oil drilling platform at 3/4 knots per hour. Below image, notes read, “rate = miles per hour of how fast she can swim.” Lynne’s rate is calculated at “2 miles an hour (knots)” and shown on a number line. Lynne’s new rate is calculated at “1 1/4 mile an hour (knots).” It is also shown on number line and includes the expression 2 - 3/4 = 1 1/4.

Figures C.9 and C.10: Student Table and Graph Based on Ocean Current Data

Two sheets of graph paper. Sheet 1 shows the old rule (+ 2) in a table comparing hours (A) to miles (B) and the new rule (+ 1 ¼) in a table comparing hours (A) to miles (B).

Rule: +2

Rule: + 1 1/4

Sheet 2 illustrates the graph of the old rate and the new rate in Miles (Y axis) over Hours (X axis).

Figure C.11: Hours at Minimum Wage Needed to Afford Rent

2015 Hours at minimum wage needed to afford rent for a one-bedroom unit. An asterisk indicates the state’s minimum wage exceeds the federal minimum wage.

A living wage is a wage that is high enough to maintain a normal standard of living. A minimum wage is the lowest an employer can pay an employee for their work. The graphic depicts that in no state can a minimum wage worker afford a one-bedroom rental at Fair Market Rent, working a standard 40-hour week, without paying more than 30 percent of their income.

Figure C.14: Double-Number Line Diagram for Orange Sunglow Paint Problem

Double-number line with Yellow on top and Red below. Both lines start at 0, with a line going through both number lines. Other lines going through both number lines are at

• 3/4 Yellow and 1 Red (blue color line)
• 1 1/2 Yellow and 2 Red (blue color line)
• 3 Yellow and 4 Red (black color line, indicating given information)
• 15 Yellow and 20 Red (blue color line with green oval around it)

Above the Yellow line, there are two arrows:

• From 3 pointing back to 3/4, labeled, “÷ 4”
• From 3 pointing forward to 15, labeled “× 5”

Below the Red line, there are two arrows:

• From 4 pointing back to 1, labeled “÷ 4”
• From 4 pointing forward to 20, labeled “× 5”
  

Figure C.18: Percentage of Diabetes Diagnoses by Race/Ethnicity and Sex

A bar graph includes data for age-adjusted estimated prevalence of diagnosed diabetes by race/ethnicity group and sex. The graph shows:

• American Indian/Alaskan Natives: men 14.9 percent, women 15.3 percent
• Asian: men 9 percent, women 7.3 percent
• Black, non-Hispanic: men 12.2 percent, women 13.2 percent
• Hispanic: men 12.6 percent, women 11.7 percent
• White, non-Hispanic: men 8.1 percent, women 6 percent

Figure C.19: Table of Insulin Levels as a Function of Time

Table of Insulin Levels as a Function of Time. Student work showing values listed underneath and differences are then marked between consecutive y values.

* Labeled, “Doesn’t make sense”

** 0 and 10 are circled, with the label, “Time ‘0’ start at”

There are also handwritten notes indicating the difference between values in the 10(.95)x column, labeled “decreasing” with an arrow pointing down. The differences are:

• 10.526 and 10: –.526
• 10 and 9.5: –.5
• 9.5 and 9.025: –.475
• 9.025 and 8.5735: –.45125
• 8.5735 and 8.14506: –.42869
• 8.14506 and 7.737: –.40806

Figure C.29: Facsimiles of Student-Created Representations of Silkworm Length Data

This figure shows three different student graphs. Graph A is a bar graph; length is on the y-axis (no markings or units); there are numbers on the x-axis as follows: 5, 7, 8, 9, 9, 10, 10, 10, and 10. New page has 10, 10, 11, 12, 12, 12, 12, 12, 12, and 12. New page has 13, 14, 14, 15, 15, 15, 15, 15, 15, and 17…
Graph B is a bar graph. On the y-axis is the label “Count” marked from 0 to 6+ in increments of 2. On the x-axis is “Length (mm)” and ranges from 0 to 29… in increments of 1. There are no bars at 0 to 4; a bar with height 1 at 5; 6 is empty; 7 has 1; 8 has 2; 9 has 2; 10 has 6+; 11 has 3; 12 has 6+; 13 has 1; 14 has 3; 15 has 6+; 16 has 0; 17 has 2; 18 has 5; 19 has 3. New page: 20 has 6+; 21 has 2; 22 has 3; 24 has 0; 25 has 6+; 26 has 2; 27 has 1; 28 has 2; 29 has 2.

Graph C is a kind of bar graph with intervals. On the y-axis is the label “Count” with no markings or units. On the x-axis in Length in mm. The first interval is 0-10 and has 4 in it. The second interval is 10–20 and has 10 in it. The third interval is 20-30 and has 10 in it. Also, because of the size difference in the ovals and the gap in the data, this line appears much taller than the one before it. The fourth interval is 30-40 and has 8 in it. The fifth interval is 40-50 and has 4 in it. The sixth interval is 50-60 and has one in it.