Math Scope & Sequence

An Easy Stark In Arithmetic by Ruth Beechick

Grade 1

• Numbers - Count Cardinal numbers to 100.  Ordinal numbers up to tenth.
• Groups - Ability to see how many are in a group such as dots on dominoes.  Count by groups of five and ten, using materials (abacus, nickels, dimes).  Ability to count by twos using pairs (eggs in a carton, eyes and ears of people present)
• Measurement -  Gain simple practical experience with clocks (dial & digital), calendars, rulers, measuring cups and other measuring devices.  Use Money - at least pennies, nickles and dimes.
• Vocabulary - Grow in ability to use words having to do with size, quantity, shape and other arithmetic and geometry concepts.
• Addition - Ability to add any two groups with sums of six or less, not including zero as a group.  Some proceed up to ten.
• Subtraction - Ability to "take away" a group from six (or ten) or any lesser number and tell what is left.
• Notation - Ability to read and perhaps to write the digits from 1 to 10.  

Grade 2

• Numbers - Read, write and count up to at least 200.  Ordinal numbers up to tenth, if calendars are understood, ordinal numbers up to thirty first.
• Place Values - Understand tens and ones place in numbers up to at least 39.
• Groups - ability to count by tens and fives at least to 30 and on to 100 if the child can.  Ability to count by twos to 10 or higher using real objects.
• Measurement - Time in hours and half hours, length in inches and feet, coins of pennies, nickels, dimes, and perhaps quarters and half dollars; other simple measurements such as pound, pint, quart and dozen
• Vocabulary and Signs - Learn the word subtract and minus to use instead of take away.  Learn plus, add and equals.  Extend vocabulary of comparison: long, longer longest; high, higher, highest; left and right; top and bottom; and so forth.
• Fractions - One-half, one-fourth and sometimes one-third.  By cutting apples or candy bars.  No writing fractions, no adding or subtraction of fractions and no fractions with numerators other than 1.
• Addition - Ability to add two numbers up to the sum of 12.  Ability to add three numbers.  For children who understand place value and who write problems in their vertical form, you may begin addition of two place numbers without carrying.
• Subtraction - Ability to take away a group from twelve or any lesser number and tell what is left.  With the prerequisites mentioned for addition you may teach subtraction of two-place numbers without borrowing.
• Multiplication and Division - Begin to understand the meaning of combining similar groups two "times" or three "times."  Begin to understand the meaning of diving a large group into smaller groups of two or threes or fives or tens. (Work with real objects rather than with problems written in abstract form.)
• Notation - Learn to write addition and subtraction problems in both their horizontal "sentence" forms and their forms, using and knowing the signs.  Two-place numbers in addition and subtraction and columns of three number in addition may be added to these notation skills for children who are proficient in working the problems.
• Problem Solving - Much experience in solving problems is usually given in second grade.  This will not be new or difficult for children brought up from an early age in real-life arithmetic.  Continue to use the manipulative and mental image modes of thinking.  Occasionally write problems in their abstract forms.