Unit 06 Resources

In Grade 3, students composed and decomposed a fraction with a numerator greater than zero and less than or equal to b as a sum of parts . They compared two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. Grade 3 students explained that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model. Students also represented fractions between zero and one (specifically those with denominators 2, 3, 4, 6, and 8) with strip diagrams and number lines, and determined the corresponding fraction given specified points on a number line. In Grade 4 Unit 01, students represented, compared, and ordered decimals, including tenths and hundredths, using concrete and visual models, and money. Students also determined the corresponding decimal to the tenths or hundredths place of a specified point on a number line.

 

Students relate their understanding of decimal numbers to fractions that name tenths and hundredths, and represent both types of numbers as distances from zero on a number line. Along with representing fractions (including those that represent values greater than one) as sums of unit fractions, students decompose fractions into sums of fractions with the same denominator using concrete and pictorial models and record the results with symbolic representations. These expectations support understanding as students represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations. Students use benchmark fractions of 0, , and 1, referring to the same whole, to evaluate the reasonableness of sums and differences of fractions that may or may not have equal denominators. Using a variety of methods to determine equivalence of two fractions underlies students’ abilities to compare two fractions with different numerators and different denominators and represent those comparisons using symbols.