How to learn Grade 3: Mathematics

Maine academic standards: Mathematics, Grade 3

0 of 13 concepts ready to learn · Markdown, for your AI

1. Statistical Reasoning · Relate area to the operations of multiplication and addition.

1. Area by Tiling: Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
2. Understanding angles (age 8+): Multiply side lengths to find areas of rectangles and represent whole-number products as rectangular areas
3. Area of compound shapes: Recognise area as additive; find areas of rectilinear figures by decomposing into non-overlapping rectangles and summing their areas
4. Area and the distributive property: Use tiling to demonstrate the distributive property: the area of a rectangle with sides a and (b+c) equals a×b + a×c; use area models to represent the distributive property

2. Statistical Reasoning · Recognize area as an attribute of plane figures and understand concepts of area measurement.

1. Understanding Area: Understand that a unit square has one square unit of area and that the area of a plane figure is the number of unit squares that cover it without gaps or overlaps

3. Quantitative Reasoning · Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

1. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
2. Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
3. Reasoning with Equivalences: Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
4. Equivalent fractions on a number line: Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams
5. Equivalent fractions (age 9+): Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths

4. Quantitative Reasoning · Understand a fraction as a number on the number line; represent fractions on a number line diagram.

1. Fractions on a number line: Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
2. Fractions on a number line (age 8+): Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b
3. Fractions on a number line: Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows