Primary Standard:
MAFS.4.NF.3.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
MAFS.4.NF.3.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.52 as 52/100; describe a length as 0.52 meters; locate 0.52 on a number line diagram.
MAFS.4.NF.3.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Content Knowledge:
In 4th grade, students are introduced formally to decimals by connecting the concepts to their understanding of fractions. Students will explore fractions with denominators of 10 and 100 using models like 10 x 10 grids, hundredths disks, and base-ten blocks to gain insights about the relationship between tenths and hundredths.
The continued use of models helps students make sense of confusing decimal notation, (e.g. 0.50 and 0.05) as they learn to read and write decimals to the hundredths.
Students will also use their knowledge of equivalent fractions and their experience visualizing tenths and hundredths to add tenths and hundredths. Students will also continue to use models to explore comparison of decimals, building upon their knowledge of comparing fractions earlier in the year. Students may notice that when comparing 0.3 and 0.45 they can change the 0.3 to 0.30 to more easily see the comparison. They may make connections to their understanding of decimals as fractions to realize that 0.3 is greater than 0.07 because 3 tenths is greater than 7 hundredths.
GCG 1 – Learning Goal: As a mathematician, I can use models to combine fractions with denominators of 10 and 100
- Step 1: Use models to recognize fractions with denominator 10 as equivalent fractions with denominator 100
- Step 2: Use models to add fractions with denominator 10 and fractions with denominator 100
- Step 3: Find a missing addend when adding fractions with denominators of 10 and 100
GCG 2 – Learning Goal: As a mathematician, I can model, read, and write decimal values to the hundredths
- Step 1: Use models to represent and relate tenths and hundredths as decimals
- Step 2: Use models to represent mixed numbers as decimals
- Step 3: Locate equivalent decimals and mixed numbers on a number line
GCG 3 – Learning Goal: As a mathematician, I can create and read decimal comparisons using <, >, and = symbols