PS 172 is dedicated to a project-based, problem-solving, approach to mathematics that allows student to engage in hands-on, relatable experiences. Our mathematics program is based on the Engage NY curriculum and incorporates projects throughout the year. We are committed to having students take ownership of their learning and construct meaning in math, choosing which strategies work best, for them to solve complex word problems. Students are encouraged to explore different strategies and explain and justify their reasoning when solving. Common models, teaching strategies, and problem solving strategies are used to help students progress through each grade level.
Sequence of Modules Module 1: Sums and Differences to 100 Module 2: Addition and Subtraction of Length Units Module 3: Place Value, Counting, and Comparison of Numbers to 1000 Module 4: Addition and Subtraction Within 200 with Word Problems to 100 Module 5: Addition and Subtraction Within 1000 with Word Problems to 100 Module 6: Foundations of Multiplication and Division Module 7: Problem Solving with Length, Money, and Data Module 8: Time, Shapes, and Fractions as Equal Parts of Shapes
Module 1: Sums and Differences to 20
From Grade 1, students have fluency of addition and subtraction within 10 and extensive experience working with numbers to 100. Module 1 of Grade 2 establishes a motivating, differentiated fluency program in the first few weeks that will provide each student with enough practice to achieve mastery of the new required fluencies (i.e., adding and subtracting within 20 and within 100) by the end of the year. Students learn to represent and solve word problems using addition and subtraction: a practice that will also continue throughout the year.
Module 2: Addition and Subtraction of Length Units
In Module 2, students learn to measure and estimate using standard units for length and solve measurement word problems involving addition and subtraction of length. A major objective is for students to use measurement tools with the understanding that linear measure involves an iteration of units and that the smaller a unit, the more iterations are necessary to cover a given length. Students work exclusively with metric units, i.e. centimeters and meters, in this module to support upcoming work with place value concepts in Module 3. Units also play a central role in the addition and subtraction algorithms of Modules 4 and 5. An underlying goal for this module is for students to learn the meaning of a “unit” in a different context, that of length. This understanding serves as the foundation of arithmetic, measurement, and geometry in elementary school.
Module 3: Place Value, Counting, and Comparison of Numbers Up to 1,000 and the Box Top Project
We will launch this module with our Box Top Project. In this project the students will be helping the PTA count all the box tops that were collected during our Box Top Contest. Students will work in small groups to construct their own learning and strategize to find the best way to count and keep track of the number of box tops collected. Once strategies are developed students will share their strategies with their peers, ultimately leading to the understanding of bundling ten ones to make a ten and ten tens to make a hundred. Unlike the length of 10 centimeters in Module 2, these bundles are discrete sets. One unit can be grabbed and counted just like a banana―1 hundred, 2 hundred, 3 hundred, etc. A number in Grade 1 generally consisted of two different units, tens and ones. Now, in Grade 2, a number generally consists of three units: hundreds, tens, and ones. The bundled units are organized by separating them largest to smallest, ordered from left to right. Over the course of the module, instruction moves from physical bundles that show the proportionality of the units to non-proportional place value disks and to numerals on the place value chart.
Module 4 and Module 5: Addition and Subtraction Within 1,000 with Word Problems to 100 and the Age Project
In Module 4, students developed addition and subtraction fluency within 100 and began developing conceptual understanding of the standard algorithm via place value strategies. In Module 5, students build upon their mastery of renaming place value units and extend their work with conceptual understanding of the addition and subtraction algorithms to numbers within 1,000, always with the option of modeling with materials or drawings. We will bridge these two modules with the Age Project where students will continue to practice the strategies they learned in Module 4 to explore the ages of their family members. Students will look into the past and calculate how hold their family members were when they were born. Then they will take a trip into the future and calculate how old their family member will be when they are their age now. Throughout the module, students continue to focus on strengthening and deepening conceptual understanding and fluency.
Module 6: Foundations of Multiplication and Division
In Module 6, students extend their understanding of a unit to build the foundation for multiplication and division wherein any number, not just powers of ten, can be a unit. Making equal groups of “four apples each” establishes the unit “four apples” (or just four) that can then be counted: 1 four, 2 fours, 3 fours, etc. Relating the new unit to the one used to create it lays the foundation for multiplication: 3 groups of 4 apples equal 12 apples (or 3 fours is 12).
Module 7: Problem Solving with Length, Money, and Data and the Survey Project
Module 7 presents an opportunity for students to practice addition and subtraction strategies within 100 and problem-solving skills as they learn to work with various types of units within the contexts of length, money, and data. Students represent categorical and measurement data using picture graphs, bar graphs, and line plots. They revisit measuring and estimating length from Module 2, though now using both metric and customary units.
How you can help at home:
Review with your student all the ways to make 10; students will need to have these memorized as we work through this module.
Practice “10 plus” problems, such as 10 + 9, 20 + 8, 40 + 6, 70 + 7, and so on, so that your student becomes very adept at doing them mentally and quickly.
Ask questions that encourage your student to estimate lengths of household items
Continue to review adding and subtracting up to 20
Practice measuring lengths longer than a ruler by marking and measuring from a mark
Ask how many ones, tens, and hundreds are in numbers that you and your student come across
Help your student begin to compare numbers by asking questions about “more than”, “less than”, and “equal”
When possible, encourage your student to explain their mathematical thinking by drawing a diagram or picture that links to their addition and subtraction problems
Help your student practice counting both backward and forward by 10’s and 100’s
Using any number of small objects, challenge your students to sort them into equal groups.