Decimal Squares

[Dion Worles]

Thisinteractive activity explores the representation of fractions,decimals and percentages using either a square or circle divided intoequal parts. When the activity is launched, a 100 square grid isshown. Click the random button to create agrid of different colors. The squares change so they are either orangeor white. You can change the number of colors using the color number control, change it to 5 and pressrandom again and there will now be 5 differentcolors in the grid. You can arrange the grid automatically by clickingarrange button, to reset the grid back towhite click the trash buttonTo select your own fraction simply select one of the colors andclick and drag your mouse over the either the grid or the circle.

The initial set up is ideal for explaining percentages since there are100 squares, but this can be changed by using the divisionsselection. You can also change from the square to a circle by clickingthe shape toggle control

On the right side of the screen our colored rectangles with ?labels. Click one of these to turn the rectangle over to display itsdecimal,percentage or fraction value. To change a whole column clickone of the buttons above to toggle hide or show. Notevalues on display automatically change as the grid or circle ischanged.

Students may begin to notice that there are different ways to write decimals that represent the same fraction. It is not essential to discuss this in depth, as students will look at equivalent decimals more closely in upcoming activities.

In this activity, students practice representing and writing decimals given another representation (fraction notation or a diagram). The idea that two decimals can be equivalent, just like two fractions can be equivalent, is made explicit here. When students make connections between quantities in word form, decimal form, and fraction form, they reason abstractly and quantitatively (MP2).

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Owners or masters of Scottish fishing vessels under 12m overall length must declare a latitude and longitude position (DD MM) on each fishing day indicating where the majority of the catch was taken. This data has been recorded since 2016 for vessels submitting Fish 1 forms and from 2018 onwards for vessels submitting paper logbooks.

This dataset aggregates the positions declared between 2017 and 2021, along with the associated catch weight and values, into C-Squares of 0.05 x 0.05 decimal degrees. The data is grouped into sectors of

"Pots and traps" - e.g. creels for crabs, lobsters, or Nephrops; whelk pots; or wrasse traps

"Bottom trawls" - e.g. bottom trawls for Nephrops, squid, or demersal fish

"Dredges" - e.g. dredging for bivalve molluscs such as scallops and surf clams

"Rod and lines"- e.g. handlines or jigging for mackerel; set lines for demersal fish

"Other" - e.g. set nets; diving; hand gathering etc

This data includes catches of razor clams up until 1st February 2018. Since this date, only vessels involved in the scientific trial can land razor clams. Data will be published on these vessels once the trial is complete.

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Tip: Based on their properties, all rectangles, squares, and rhombuses are parallelograms, but not all parallelograms are rectangles/squares/rhombuses! Similar idea occurs with rectangles and squares - all squares are rectangles, but not all rectangles are squares.

In another study by student researchers at a community college, mindset was measured with a Mindset Quiz at the beginning of the semester in a remedial English class, at the end the semester in the remedial English class, then at the beginning of the next semester in the next higher English class, and at the end of that semester in the next higher English class. Thus, the same students were measured four times to see if their mindset improved through journaling activities related to growth mindset. Mindset Quiz scores can range from 20 to 60, with higher scores showing that the student has more Growth Mindset (and less Fixed Mindset). At the end of the second semester, 12 students had completed the Mindset Quiz pre-test and post-test during each class (at the beginning and end of each semester), and had attended most classes throughout the semester to experience the journaling activities related to mindset (N = 48).

Null Hypothesis: Students will have a similar average scores on the Mindset Quiz in all four conditions: Beginning of Remedial English, End of Remedial English, Beginning of Next English Class, and End of Next English Class

If you will never have to calculate the Sums of Squares by hand, skip this part and just fill in the ANOVA Summary Table (Table \(\PageIndex5\)) at the end of this section. If you are practicing the Sums of Squares, each Sum of Square will have its own Example. Heads up, to do all of these can take about an hour!

\[\left[ \left(\overlineX_group-\overlineX_T\right)^2 \times(n_group) \right] \nonumber \]

\[\textN1 =\left[0.96 \right] \nonumber \]

\[\textN2 =\left[99.48 \right] \nonumber \]

Again, if you had saved more than two decimals, you would end up with \(S S_B=244.31 \). And if you used that number in the ANOVA Summary Table, the calculated F-value would be nearly identical to the same calculations but with only the two numbers after the decimal.

Once that process is completed for each participant (so, 12 times in this scenario), we add all of the numbers in the last column (the column that divides by k). That provides the bracketed information in the formula:

Table \(\PageIndex4\) shows the Total mean subtracted from each score in the column to the right of the raw scores, then that is squared in the column to the next right. The squared values are then summed for all of the scores.

We reject the null hypothesis because our critical value is smaller than our calculated value. This means that at least one time period's average Mindset Quiz score was different from at least one other time period's average Mindset Quiz score groups.

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