Practicing the Four Operations

  • The four operations are addition, subtraction, multiplication, and division

  • Students must solve problems involving numbers up to five digits

  • Students should compute in “long form” - multiplication, addition, and subtraction problems should be written in the form shown below and division should be done in long division form.

 

  • Repetition is key: have kids complete worksheets with you. We recommend rewriting the problems on a virtual whiteboard and doing the problems with your students, correcting their mistakes as they go.

  • We recommend these worksheets

 

Factors, Multipliers, Multiples

  • Choose a whole number between 1 and 100 and find all its factor pairs

    • e.g. 64 → 1&64, 2&32, 4&16, 8&8

 

Angle Measurement

  • If they are not already familiar with them, teach your student the following three rules by demonstrating with drawings on a whiteboard

  1. The sum of angle measurements around a point is 360 degrees. 

  2. The sum of angle measurements on a line is 180 degrees. 

  3. Hence, from 1 and 2, students see that vertical angles are equal. 

  • Armed only with these facts, students are able to generate and solve equations as in the following problem



 

Unknown angle problems help to unlock algebraic concepts for students because they must search for a missing variable for the first time. 

 

These worksheets are good practice


 

  • Students must be familiar with the following terms: points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. 

    • Draw these things out and make sure students can identify them and distinguish between them.

 

Fractions

Rising Fifth Graders are only expected to work with fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

  • We recommend using this tool to demonstrate

  • Students must understand the concept of proportionality

    • Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) with visual models; explain how the number and size of the parts may change, but the two fractions themselves are the same size.

    • Give students fractions and ask them to find equivalent fractions (e.g. ½ and 2/4)

    • Try playing a game where students are given a bunch of fractions and must match up pairs of equivalent fractions

    • We recommend these worksheets on coloring equivalent fractions and writing equivalent fractions

  • Once students grasp this, they should compare fractions with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 

  • Mixed numbers: students must be able to convert fractions to mixed numbers (e.g. 1 ⅙ and 7/6). This can simply be shown on a whiteboard.

  • Operations with fractions: students must be able to add, subtract, and multiply fractions 

    • Adding and subtracting fractions

      • Students must understand a fraction a/b as a sum of fractions 1/b (1/b being the “unit fraction”) (e.g. ¾ is the unit fraction, ¼ , added three times). This will teach students to add fractions.

      • We recommend these worksheets on Adding like fractions and Subtracting like fractions in equation form, and this worksheet on word problems

    • Multiplying fractions *by whole numbers only

      • Students must understand a fraction a/b as a multiple of 1/b (1/b being the “unit fraction”) (e.g. ¾ is the product the unit fraction, ¼ , and 3, or 3 × ¼). This will teach students to multiply fractions.

      • We recommend this worksheet on Multiplying fractions by whole numbers

    • Add and subtract mixed numbers with like denominators

resources

Virtual number line 

Virtual base ten blocks

Virtual number frames 

Multiplication tables

Blank multiplication tables

Multiplication games

Worksheets for Pre-Algebra - Calculus

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