# Three Hidden Rectangles

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The purpose of this task is for students to decompose a figure into rectangles and then find the total area by adding the area of all of its smaller, non-overlapping rectangles.

Material Type: Activity/Lab, Formative Assessment, Lesson, Lesson Plan

Authors: C. Steinert, M. Hinde

# What Do These Shapes Have In Common?

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This task asks students to classify shapes based on their properties. The task itself is straightforward, but there are a number of opportunities to present this task in class and push the level of discussion and reasoning. For example, the rule for the bottom circle is that all shapes must have all sides with the same length. Some students will likely conjecture that the rule is either that all shapes must be regular polygons or that all shapes must be equiangular. Either of these would be true except for the rhombus. Though this would likely extend beyond the scope of 5th grade understanding, it might be interesting to look at the pentagon with the right angle. In the eyes of a 5th grader, it looks as if it might have sides of equal length. They have not yet derived any rules about the sum of interior angles in polygons, but they should be pushed to see that mathematicians cannot make assumptions based on the appearance of shapes. We only know that each of the shapes in the bottom circle is equilateral because the tick marks indicate that the sides are the same length. In that same line of reasoning, we must be careful to specify in part b that the rectangle does not have equal sides. A deep discussion would allow students to construct viable arguments and critique the reasoning of others (MP 3) and attend to precision (MP 6).

Material Type: Activity/Lab, Formative Assessment, Lesson, Lesson Plan

Author: Illustrative Mathematics

# Equivalent Ratios and Unit Rates

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This activity is used in my classroom for intervention when students have a struggle with Fractional Understanding and Equivalence and then struggle with Ratios and Unit Rates in seventh grade RP.

Material Type: Activity/Lab, Lesson, Lesson Plan

Author: Illustrative Mathematics

# Attributes of Plane Figures (engageny)

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Students explore area as an attribute of two-dimensional figures and relate it to their prior understandings of multiplication. Students conceptualize area as the amount of two-dimensional surface that is contained within a plane figure.

Material Type: Activity/Lab, Assessment, Lesson, Lesson Plan

Author: J. Cherf

# Comparing Fractions Game- Illustrative Math

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Students again have a set of fraction cards that they use to compare fractions less than one. There are two sets of cards on set has a visual and the other does not.

Material Type: Activity/Lab, Assessment, Learning Task

Author: J. Cherf

# Addition Fact Strategies - Counting On (+1/+2)

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This lesson is intended to help students begin to transition away from a one-to-one correspondence. Students at this point should be able to use concrete ojects to identify values.Goal: Students will be able to use a number line to "Count On from Greater"

Material Type: Lesson Plan

Author: Samuel Shackleford

# The Catepillar and More

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I used The Hungry Catepillar lesson from this link. https://www.illustrativemathematics.org/content-standards/tasks/1150 However I did an extension off this lesson using this resource to allow teachers to work on the skills of addition, the precise language of tens and some extra ones, and seeing groups of ten. This activity is a great way to include Language Arts along with Mathematics. Using The Very Hungry Catepillar, we used based-ten blocks to place onto a ten frames. Each time the catepillar eats something, we add to the ten frame. At the end of the story, we look at how much the catepillar has eaten. However, I took this activity a step further to continue strengthening the use of addition. Students and I then had a variety of situations at the end of the story where the catepillar ate 4 more leaves. The students then add four more, either in a group of 4 or counting out 4 individual items. We then look again at using our language of, "I have a 3 groups of ten and 4 extra ones." Challenges with this lesson is making sure the students have added a cube onto their ten frame for each item they ate. As well, students would have to also understand how to use a ten frame before the start of the lesson. As well, if you are working to be precise with the language of tens and extra ones, you want to nudge your students to use this language. You will want to model this multiple times.

Material Type: Learning Task

Author: Alicia Korth

# Robot Races

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This task is a great task to use as a wrap up of the Ratios and Proportion skills taught in the seventh grade math standards. I have used this as a small group task in my classroom after I have covered Rates, Unit Rates, Proportional Relationships, Constant of Proportionality, Constant Rate of Change, etc. This task highlights student understanding of what proportional and non-proportional relationships are and the differences. It also does a great job of showing if students understand the connection between Unit Rate, Constant of Proportionality, and Constant Rate of Change. You are also able to identify their deep understanding of the relationship of using the Constant of Proportionality in a linear relationship in the y=kx format, where k is the Constant of Proportionality. I do not give any instruction to this task. I just give them a overview and read the initial introduction of the task and what they need to accomplish. Then as they work, I circulate to the groups questioning rather than answering. After groups have finished the task, (30 minutes) We go through it together and they explain their thinking and why they did what they did and how they arrived at their answer. I then have the other groups ask clarifying questions beginning with "I wonder.." of "I noticed....." This then allows their peers critique the reasoning of others and justify their thinking.

Material Type: Learning Task

Author: Illustrative Mathematics

# Comparing Fractions

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This lesson was used with a tier 3 fourth grade intervention math group to help students understand how to compare fractions with like and unlike denominators. In addition, this promotes conceptual understanding of equal size wholes.

Material Type: Learning Task

Author: Helping With Math

# How to add fractions

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This lesson was used with a tier 3 fourth grade intervention math group to help students understand how to add fractions with like denominators and unlike denominators. It includes worksheets.

Material Type: Lesson Plan

Author: Helping With Math

# Exploring Fact Families

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This is a modification of the Illustrative Math lesson, Fact Families, https://www.illustrativemathematics.org/content-standards/tasks/1214. This lesson was used with a tier 3 fourth grade intervention math group to help students understand inverse relationships with addition and subtraction. I modified it to meet the students' needs by using just page four of the Triangle Worksheet attached resource from the Fact Families Illustrative Math lesson. I used only this page because I wanted students to understand the 8 related equations of fact families. I also modified this lesson by using fact families of 20 instead of 10 and students used a 20 bead Rekenrek to model the equations. A common misconception my students had was with the subtraction equations; they often would subtract the minuend from subtrahend instead of vice versa.

Material Type: Learning Task

Author: MEGAN HINDE

# Grade 1 Mathematics Module 6, Topic B, Lesson 3

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Use the place value chart to record and name tens and ones within a two-digit number up to 100.

Material Type: Learning Task

Author: Engage New York

# Grade 2 Mathematics Module 6, Topic A, Lesson 4

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Objective: Represent equal groups with tape diagrams, and relate to repeated addition.

Material Type: Learning Task

Author: Engage New York

# Crossing the Decade Card Game

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This is a modification of the Illustrative Math lesson, "Crossing the Decade Concentration" https://www.illustrativemathematics.org/content-standards/1/NBT/A/1/tasks/405. This lesson was used with a tier 3 fourth grade intervention math group to help students count forward and backward by ones; specifically focusing on crossing the decades. I modified this lesson by extending the counting sequence to 200 instead of 100 and placed cards in 4 by 4 arrays instead of 3 by 3. My students were quite proficient counting forward across decades, but were not with counting backward across decades, so I also modified the game to practice this. Students picked from the "_0" number cards first and had to verbalize the number one back, the "_9" number. It was very important that they verbalize that number to show that they were truly thinking about crossing the decades versus just "guessing" for the card match. My students also needed additional practice crossing decades with numbers in the 100s so I extended the cards to 200 to practice this.

Material Type: Learning Task

Author: MEGAN HINDE

# Identify Shape Relationships

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I utilized this activity in my seventh grade math intervention group to reinforce Geometric Shapes and the properties they have and the commonality of those shapes. This activity also connects to fractional understanding and spacial relationships as well as symmetry when solving the third activity. Using the Michael Battista's Cognition Based Assessment materials, and used this activity to conceptually work and investigate the common properties of shapes.

Material Type: Learning Task

Author: Lynn Schaal

# Problem Solving with Pattern Blocks

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I used this task with my math intervention group of seventh graders that were shown to have a deficit in Geometric Shapes. Students worked in pairs to solve the tasks and then compared with the other groups when complete. Students critiqued the reasoning of others and looked for similarities and differences in how they solved the tasks. After each group had an opportunity to speak with a different group, we went through the two tasks together.

Material Type: Learning Task

Author: Lynn Schaal

# Fraction of a Number... Huh?

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I used this assessment as formative tasks in my seventh grade math intervention. Students worked in small groups, then pairs, then alone to complete the tasks. This gave me a clear indication of their understanding of the standard. Students used a variety of ways to solve the problems. Some used calculations, others used pictorial representations. This is a modification taken from the Howard County Website. https://hcpss.instructure.com/courses/108/pages/5-dot-nf-dot-4-assessment-tasks

Material Type: Formative Assessment

Author: Lynn Schaal

# Element Cards Number Operations Fractions

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Through the use of folding paper strips into equal size pieces students can apply their understanding that the numerator represents the parts of the whole (i.e., how many of the parts are being considered).Begin with unit fraction which are fractions with a numerator of 1. Students will understand the following concepts, symbols, and vocabulary: numerator, fraction, equal parts. I used this resource as a part of my math intervention of seventh graders to show conceptually that a fraction must be of equal size parts. This activity does a nice job of explaining the showing the process. This was a bit long for my math intervention, but I completed a modified version over several sessions.

Material Type: Activity/Lab

Author: NCSC Wiki