Grade 9 Math Unit 1

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Phoebe Sibilio

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Aug 3, 2024, 10:30:56 AM8/3/24

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Do you want to know what taking the Mathematics portion of the NJSLA is like? A practice test for each grade is available below for you to use to familiarize yourself with the kinds of items and format used for the tests

Information on Accessibility Features

The full list of accessibility features embedded for all students and accessibility features that need to be identified in advance can be found in the NJ Accessibility Features and Accommodations Manual..
Answer masking, color contrast (background/font color) and text-to-speech for mathematics and science, are available for all participating students who need these tools, but need to be identified in advance via the Personal Needs Profile (PNP).

The interaction has been updated to a more common design that aligns to the standard interaction used by screen reader users. Now, when students navigate into a multiple choice field, the radio button given focus by the Screen Reader will automatically be selected. Students can use the space bar to remove the selection.

A screen reader is a software application, separate from text-to-speech embedded in TestNav, which conveys web content through audio. Screen readers are appropriate for students who are trained to use the software and who use it in the classroom, including those who are blind or have a visual impairment.

I am fascinated with your blog in general and especially the first grade math part. I love math now--but didn't when I was in school! Your games and centers could really inspire a love of math right from the start, and isn't that better? I think so!

The full experience and value of eMATHinstruction courses are achieved when units and lessons are followed in order. Students learn skills in earlier units that they will then build upon later in the course. Lessons can be used in isolation but are most effective when used in conjunction with the other lessons in this course. All Lesson/Homework files, Spanish translations of those files, and videos are available for free. Other resources, such as answer keys and more, are accessible with a paid membership.

Each month August through May we release new resources for this course that are accessible with a Teacher Plus membership. We release new resources in unit order throughout the school year. You can see a list of our new releases by visiting our blog and selecting the most recent newsletter.

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This course begins with a unit on reasoning about area and understanding and applying concepts of surface area. Instead of front-loading review and practice from prior grades, these materials incorporate opportunities to practice elementary arithmetic concepts and skills through warm-ups, in the context of instructional tasks, and in practice problems as they are reinforcing the concepts they are learning in the unit. Students will encounter plenty of examples of a mathematical or statistical idea in various contexts before that idea is named and studied as an object in its own right.

3rd Grade Math focuses on four key advancements from previous years: (1) developing understanding of and fluency with multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.

Students estimate quantities using rounding and develop fluency with the standard algorithm of addition and subtraction. Students focus on the precision of their calculations, and use them to solve real-world problems.

Students begin to explore the concepts of multiplication and division, beginning in the context of equal group and array problems, moving to skip-counting and repeated addition, and ending with more complex and/or abstract problems.

Students deepen their understanding of multiplication and division, including their properties and extending their study of factors to include all units from 0 to 10, as well as multiples of 10 within 100.

Students explore attributes of shapes in different categories, then learn to measure at least one of these attributes, their perimeter. They come to differentiate between perimeter and area as different measurements.

Students understand fractions as numbers on the number line and explore fraction equivalence and comparison in simple cases, then apply this fractional understanding to measure fractional lengths and represent them on a number line plot.

In Unit 1, Rounding, Addition, and Subtraction, students rely on their substantial work in 2nd grade on place value to develop an understanding of rounding. They then develop fluency with addition and subtraction within 1,000. Finally, they use both aforementioned skills to solve one-and two-step word problems involving addition and subtraction, using rounding to assess the reasonableness of their answers. While the content taught in this unit is not major work of 3rd grade as determined by the Common Core State Standards, it serves as a foundation for later work, such as assessing the reasonableness of all types of two-step word problems and multiplying one-digit numbers by multiples of ten, making it a useful introduction to 3rd grade math.

In Unit 2, Multiplication and Division Part I and Unit 3, Multiplication and Division Part II, students are introduced to the other two major operations, multiplication and division. They come to understand multiplication as finding the total number of objects in a certain number of equal-sized groups, and division as finding either the size of the group or the number of groups. Students work towards fluency of all multiplication and division facts within 100, relying on the properties and patterns to help in particular with the difficult facts of 6, 7, 8, 9. Students solve one-step multiplication and division word problems involving equal groups and arrays, and solve two-step word problems involving all four operations. They also explore myriad connections to multiplication and division, including exploring patterns, including patterns in the skip-counting sequence, and scaled picture and bar graphs.

In Unit 4, Area, students define area to be the number of square units needed to cover a two-dimensional space. They initially find the area of rectangles by counting unit squares or skip-counting by rows and columns. Then, seeing the connection between skip-counting and multiplication that was built in the prior two units, students apply their recently acquired skills with multiplication and division to calculate the area of a rectangle and solve real-world problems involving area. Finally, they find the area of composite rectilinear shapes, by decomposing them into rectangles, finding the area of those rectangles, and adding those areas together.

In Unit 5, Shapes and their Perimeter, students start by exploring two-dimensional shapes in different categories, seeing that shapes in those categories share attributes. They then explore the attribute of perimeter, and come to differentiate between perimeter and area as different measurements.

In Unit 6, Fractions, students build on their work partitioning circles and rectangles in 2nd grade to study fractions. They build more complex fractions from unit fractions, and start to understand fractions as numbers, rather than portions of shapes. To do so, students do extensive work with placing fractions on a number line, a helpful representation for comparing and finding equivalent fractions. Students also explore line plots with fractional measurements, a key advancement from 2nd grade work with line plots that connects to their work with fractions.

In Unit 7, Measurement, students study time as well as liquid volumes and masses. Students learn to read time to the nearest minute and use their work with number lines in Unit 1 (with rounding) and Unit 5 (with fractions) to solve problems involving elapsed time. They also rely on their work with number lines to read measurement scales, and use those measurements to solve one-step word problems in all four operations with liquid volumes and masses.

Students in third grade math focus on 4 key math skills: Fluently multiplying and dividing within 100, comparing and finding equivalent fractions, defining and computing areas, and analyzing two-dimensional shapes.

3.OA.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.