Do we take the time to zoom out as well as zoom in? Are we aware of what is essential to learn in the course that precedes ours or the course after?
Zooming out:
From Common Core State Standards: Numbers and Operations__Fractions:
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Apply and extend previous understandings of numbers to the system of rational numbers.
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division
Extend understanding of fraction equivalence and ordering.
Build fractions from unit fractions
Understand decimal notation for fractions and compare decimal fractions
Develop understanding of fractions as numbers
Zooming in:
#LL2LU draft for Develop understanding of fractions as numbers.
Grade 6 – Level 4:
I can understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
Grade 6 – Level 3:
I can interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem.
Grade 6 – Level 2:
I can understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
Grade 6 – Level 1:
I can extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Grade 5 – Level 4:
I can interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem.
Grade 5 – Level 3:
I can add and subtract fractions with unlike denominators, including mixed numbers by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Grade 5 – Level 2:
I can apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Grade 5 – Level 1:
I can interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
Grade 4 – Level 4:
I can add and subtract fractions with unlike denominators, including mixed numbers by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
Grade 4 – Level 3:
I can decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation, and I can justify decompositions by using a visual fraction model.
Grade 4 – Level 2:
I can add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction.
Grade 4 – Level 1:
I can understand a multiple of a/b as a multiple of 1/b, and I can use this understanding to multiply a fraction by a whole number.
Grade 3 – Level 4:
I can decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation, and I can justify decompositions by using a visual fraction model.
Grade 3 – Level 3:
I can explain equivalence of fractions in special cases, and I can compare fractions by reasoning about their size using a visual fraction model.
Grade 3 – Level 2:
I can compare two fractions with the same numerator or the same denominator by reasoning about their size.
Grade 3 – Level 1:
I can express whole numbers as fractions, and I can explain why fractions that are equivalent to whole numbers.
What if we vertically align and share learning progressions based on both the zoomed out view and the zoomed in view?
Experiments in Learning by Doing 