Math Program
Investigations 3
The Newton Public Schools mathematics program is designed to ensure that every child develops a comprehensive mathematical identity, meets grade level benchmarks and is challenged at their appropriate level. We believe that student success in school mathematics depends on a combination of teacher skill, a strong core program, sufficient time for instruction, teacher-guided exploration of mathematical ideas, individual practice, class discussion, reasoning about mathematical concepts and solving non-routine problems. In 2019, NPS fully implemented Investigations 3 in K-5. Students engage in interactive lessons, the Mathematical Practices and instructional routines in order to develop deep understanding of grade level concepts. Unit 1: Coins, Number Strings, and Story Problems
Addition, Subtraction, and the Number System 1
- Understand and extend the counting sequence
- Be fluent with facts to 20
- Understand, represent, and solve problems involving addition and subtraction
- Understand place value
- Does order matter when adding or subtracting numbers?
- What strategies can you use to find the difference between two quantities?
- Play Guess My Number, focusing on place value and comparing quantities
- Explore tools: money, clocks, fact cards and the 100 chart
- Solve addition and subtraction story problems using manipulatives and tools; share strategies
Unit 2: Attributes of Shapes and Parts of a Whole
- Describe, identify, and compare attributes of 2-D and 3-D shapes
- Visualize the structure of arrays
- Be fluent with facts to 20
- Understand equal parts of a whole
- How can you use geometry vocabulary to describe 2-D and 3-D shapes?
- What are the properties of a polygon?
- Can halves look different?
Students will:- Draw, sort and describe 2-D and 3-D shapes
- Compare attributes of polygons
- Investigate how many different rectangles can be made from a given number of tiles
- Fold a square or rectangular piece of paper to make halves, thirds and fourths
Unit 3: How Many Stickers? How Many Cents?
Addition, Subtraction, and the Number System 2
- Understand place value
- Understand, represent, and solve problems involving addition and subtraction
- Be fluent with facts to 20
- Understand and extend the counting sequence
- How many more do you need to get to 100?
- What strategies can you use to solve problems with the unknown in different parts of the equation?
Students will:- Explore Sticker Stations with strips of ten stickers and singles
- Play place value games with number cubes, 200 charts, connecting cubes, and number cards
- Use an open number line to solve addition and subtraction problems
Unit 4: Pockets, Teeth, and Guess My Rule
- Sort and classify
- Collect and represent data
- Describe and interpret data
- How can you use a bar graph, a Venn diagram and a line plot to represent data?
- What can we learn about a topic when we collect data?
Students will:- Play Guess My Rule with images
- Collect and analyze data about the students in our class
- Create bar graphs to represent multiple categories
Unit 5: How Many Tens? How Many Hundreds?
Addition, Subtraction, and the Number System 1
- Be fluent with facts to 20
- Understand, represent and solve problems involving addition and subtraction
- Understand place value
- Use knowledge of place value to add and subtract
- Understand and extend the counting sequence
- How can you make my strategy for solving addition and subtraction problems efficient?
- How can you use what you know about hundreds, tens and ones to solve addition and subtraction problems?
- How can you represent my solution strategy?
Students will:- Play games Capture 5, Make a Dollar and Close to 100
- Consider the composition of three digit numbers as hundreds, tens and ones
- Explore place value concepts in the 1,000 Book
- Represent three digit numbers with visual models
- Use addition or subtraction to compare two numbers and find the difference
Unit 6: How Far Can You Jump?
- Use linear units
- Collect and represent data
- Understand, represent and solve problems involving addition and subtraction
- Measure with standard units
- Why might students get different results when measuring the same object?
- Why does it take more of a smaller unit or fewer of a larger unit to measure the same object?
Students will:- Measure three different types of jumps with nonstandard units and graph the data
- Build a measuring tool with standard units
- Compare measurements of objects in the classroom
- Use a yardstick to measure the classroom
- Go on a scavenger hunt for things that are one meter long and one centimeter long
Unit 7: Partners, Teams, and Other Groups
Foundations of Multiplication
- Investigate odd and even numbers
- Visualize equal groups in the structure of arrays
- Describe and represent equal groups as the foundation of multiplication
- How can you convince someone that every number that makes two equal teams, also makes partners?
- How can you show or explain what each number in a data table represents?
Students will:- Organize cubes and develop a definition for even and odd
- Build cube buildings with equal groups of different sizes
- Represent the total amount of equal groups with addition equations and in a table
- Look for patterns when covering a pattern block shape with a mystery shape
Unit 8: Enough for the Class? Enough for the Grade?
Addition, Subtraction, and the Number System 4
- Understand, represent and solve problems involving addition and subtraction
- Use knowledge of place value to add and subtract
- Be fluent with facts to 20
- Understand time
- What is a strategy you can use to solve this story problem?
- How can you write equations that accurately represent multiple situations?
- What time will it be in …?
- How can you represent the tens and ones when regrouping to find a solution?
Students will:- Play Spend $1.00 by making trades, and Get to 0 by subtracting multiples of 5
- Continue sorting fact cards into Facts I Know and Facts I Am Still Working On
- Answer elapsed time questions by moving the hands of a clock
- Solve story problems about comparing using tools
ST Math is an online visual instructional program that leverages the brain's innate Spatial-Temporal reasoning ability to solve mathematical problems. The program:- Builds a strong conceptual foundation
- Teaches through challenging puzzles, non-routine problem solving, and formative feedback
- Eliminates language barriers, making puzzles accessible to all students
- Follows a learning progression, starting with more concrete problems that gradually become more abstract, shifting from non-symbolic to symbolic
- Integrates with Investigations, our core program, and complements the content of each unit
Students engage with the program during the math block or at other times during the school day.