In AIS (“Academic Intervention Service”) Math we meet in small groups to work on strategies and skills that will help build proficiency in mathematics. AIS Math aims to targets the foundational math concepts necessary for success in the classroom. We use an array of hands-on methods and manipulatives.

Students are selected based on a combination of factors including teacher recommendation and assessments. Our assessments are ongoing, therefore our math groups may change throughout the school year.

Kindergarten Overview

In Kindergarten, instructional time should focus on two areas: (1) developing a sound sense of numbers by representing and comparing numbers, initially using sets of objects; (2) recognizing and describing shapes and using spatial relations. More learning time in Kindergarten should be devoted to number than to any other topic.

- Count to 100 by ones and by tens
- Count to 100 by ones beginning from any given number (instead of beginning at 1)
- Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects)
- Understand the relationship between numbers and quantities up to 20; connect counting to cardinality.
- Answer counting questions using as many as 20 objects arranged in a line, a rectangular array, and a circle. Answer counting questions using as many as 10 objects in a scattered configuration.
- Given a number from 1–20, count out that many objects.
- Identify whether the number of objects in one group is greater than (more than), less than (fewer than), or equal to (the same as) the number of objects in another group.
- Compare two numbers between 1 and 10 presented as written numerals.
- Represent addition and subtraction using objects, fingers, pennies, drawings, sounds, acting out situations, verbal explanations, expressions, equations, or other strategies.
- Add and subtract within 10.
- Solve addition and subtraction word problems within 10.
- Decompose numbers less than or equal to 10 into pairs in more than one way.
- Find the number that makes 10 when given a number from 1 to 9.
- Fluently add and subtract within 5.
- Duplicate, extend, and create simple patterns using concrete objects.
- Compose and decompose the numbers from 11 to 19 into ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
- Describe measurable attributes of an object(s), such as length or weight, using appropriate vocabulary.
- Directly compare two objects with a common measurable attribute and describe the difference.
- Classify objects into given categories; count the objects in each category and sort the categories by count.
- Explore coins (pennies, nickels, dimes, and quarters) and begin identifying pennies and dimes.
- Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
- Analyze, compare, sort, and compose shapes.

Grade 1 Overview

In Grade 1, instructional time should focus on three areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; and (3) developing understanding of linear measurement and measuring lengths as iterating length units.

- Use addition and subtraction within 20 to solve one step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions.
- Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
- Apply properties of operations as strategies to add and subtract.
- Understand subtraction as an unknown-addend problem within 20
- Relate counting to addition and subtraction.
- Add and subtract within 20 using strategies such as: counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction and creating equivalent but easier or known sums.
- Fluently add and subtract within 10.
- Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
- Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions.
- Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
- . Understand that the two digits of a two-digit number represent amounts of tens and ones.
- a. Understand 10 can be thought of as a bundle of ten ones, called a "ten".
- b. Understand the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- c. Understand the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

- Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Grade 2 Overview

In Grade 2, instructional time should focus on four areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) analyzing and classifying two dimensional shapes as polygons or non-polygons.

- Use addition and subtraction within 100 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
- Use addition and subtraction within 100 to develop an understanding of solving two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
- Fluently add and subtract within 20 using mental strategies. Strategies could include: counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, creating equivalent but easier or known sums.
- Know from memory all sums within 20 of two one-digit numbers.
- Determine whether a group of objects (up to 20) has an odd or even number of members.
- Write an equation to express an even number as a sum of two equal addends.
- Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as a sum of equal addends.
- Understand that the digits of a three-digit number represent amounts of hundreds, tens, and ones.
- Count within 1000; skip-count by 5s, 10s, and 100s.
- Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
- Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Add up to four two-digit numbers using strategies based on place value and properties of operations.
- Add and subtract within 1000, using • concrete models or drawings, and • strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate the strategy to a written representation.
- Understand that in adding or subtracting up to three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to compose or decompose tens or hundreds.
- Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900
- Explain why addition and subtraction strategies work, using place value and the properties of operations.
- Measure and estimate lengths in standard units.
- Relate addition and subtraction to length.
- Tell and write time from analog and digital clocks in five minute increments, using a.m. and p.m. Develop an understanding of common terms, such as, but not limited to, quarter past, half past, and quarter to.
- Count a mixed collection of coins whose sum is less than or equal to one dollar.
- Solve real world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, using the ¢ (cent) symbol appropriately.
- Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Present the measurement data in a line plot, where the horizontal scale is marked off in whole-number units.
- Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a picture graph or a bar graph.
- Classify two-dimensional figures as polygons or non-polygons.
- Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
- Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.